A solution to cosmological constant problem?

[Mordred]

I don't particularly have a problem with any chosen particle. I mentioned that numerous times.

If you look back though my issue is regardless of any chosen particle or particle field you should still apply Maxwell Boltzmann and not simply use volumes.

Secondly all quantum fields has an inherent quantum uncertainty regardless of temperature. I also showed that the calculations for a QCD vacuum is distinctive to a QED vacuum.

I also includes peer reviewed links describing dual Meissner for QCD. Not just a single Meissner for QED.

This is the details the author didn't include or didn't examine. Let me ask you how many formulas has the author posted showing the numerous amplitudes contained within a proton ?

Each field within that proton has inherent uncertainty.

So how precisely does that match up to a single vector field calculation for the vacuum catastrophe when not even the electric charges match between quarks and electrons ?

The amplitudes mediating the electric charges between protons and electrons don't match each other either. That was part of that examination I did earlier.

If the author had applied those missing details I wouldn't have any real problem however he didn't looked deep enough ie into the mathematical proofs of the theories he tries to put together. He doesn't show the first second third and fourth NLO (next leading order integrals involved)

In essence he's ignoring a huge set of amplitudes with regards to protons/neutrons etc. Every time you use a Greens Function with regards to any Hamilton has uncertainty and that's every single wavefunction in QFT or QM. You have additional uncertainty adding to a total sum .

 

 

Edited 20 hours ago by Mordred

[MJ kihara]

3 hours ago, Mordred said:

I don't particularly have a problem with any chosen particle. I mentioned that numerous times.

If you look back though my issue is regardless of any chosen particle or particle field you should still apply Maxwell Boltzmann and not simply use volumes.

Secondly all quantum fields has an inherent quantum uncertainty regardless of temperature. I also showed that the calculations for a QCD vacuum is distinctive to a QED vacuum.

I also includes peer reviewed links describing dual Meissner for QCD. Not just a single Meissner for QED.

This is the details the author didn't include or didn't examine. Let me ask you how many formulas has the author posted showing the numerous amplitudes contained within a proton ?

Each field within that proton has inherent uncertainty.

So how precisely does that match up to a single vector field calculation for the vacuum catastrophe when not even the electric charges match between quarks and electrons ?

The amplitudes mediating the electric charges between protons and electrons don't match each other either. That was part of that examination I did earlier.

If the author had applied those missing details I wouldn't have any real problem however he didn't looked deep enough ie into the mathematical proofs of the theories he tries to put together. He doesn't show the first second third and fourth NLO (next leading order integrals involved)

In essence he's ignoring a huge set of amplitudes with regards to protons/neutrons etc. Every time you use a Greens Function with regards to any Hamilton has uncertainty and that's every single wavefunction in QFT or QM. You have additional uncertainty adding to a total sum .

 

 

What would make you conclude that cosmological constant problem has been solved in a precise way?

[MJ kihara]

5 hours ago, Mordred said:

The amplitudes mediating the electric charges between protons and electrons don't match each other either. That was part of that examination I did earlier.

How is this related to the vacuum inside a proton?

5 hours ago, Mordred said:

Secondly all quantum fields has an inherent quantum uncertainty regardless of temperature. I also showed that the calculations for a QCD vacuum is distinctive to a QED vacuum.

Putting cut off at planck scale doesn't it  help?

[Mordred]

The amplitudes are directly related to the anplitudes inside a proton. Recall All particles are field excitations.

Not little balls of matter.

1 hour ago, MJ kihara said:

 

Putting cut off at planck scale doesn't it  help?

Great idea take 936 MeV and multiply it by 10^{123} atoms how much energy does that give ?

One doesn't need to be a mathematician to see it will exceed 10^19 GeV which is the total energy density at BB.

Exceeding total energy/mass of the universe.

(Ps 10^19 GeV is the Planck temp cutoff when you convert to Kelvin)

Lol you could for example assume each SU(3) atom has exactly 1 quanta of energy and do the same calculation above just looking at the powers indicate it will exceed also.

 

Edited 13 hours ago by Mordred

[joigus]

4 hours ago, MJ kihara said:

What would make you conclude that cosmological constant problem has been solved in a precise way?

1st: Find the reason for the monumental overcount in QFT

Example: The exactly supersymmetric Hamiltonian gives zero for the expectation value of energy of the vacuum.

2nd: Find the reason why the actual energy is not exactly zero, but a little positive correction to that

Example: Postulate a mechanism to break SUSY ever so slightly that the expectation value of vacuum energy is slightly above zero. Then solve for the values of symmetry-breaking parameters for different models. Then go to the lab.

Something like that.

Edited 12 hours ago by joigus
minor correction

[MJ kihara]

2 hours ago, Mordred said:

The amplitudes are directly related to the anplitudes inside a proton. Recall All particles are field excitations.

Not little balls of matter.

I think there is a lot of misunderstanding going around here...a proton is a proton because the fields inside it( quark fields) behave in a certain way( the way those quark combine)...by restricting those fields you get a proton otherwise we could have one proton filling the whole universe.when we measure a proton,I assume sum of this 'restricted'fields within that 'volume' give a result consistent with a proton.

Do you mean a proton is just a mathematical object?

2 hours ago, Mordred said:

Great idea take 936 MeV and multiply it by 10^{123} atoms how much energy does that give ?

You are getting me wrong,am talking about the formula used by the author to derive zero point energy..what's wrong with that formula? and yet it's clear they are talking of summing up all available quantum including for gravitons.

[JosephDavid]

1 hour ago, joigus said:

1st: Find the reason for the monumental overcount in QFT

Example: The exactly supersymmetric Hamiltonian gives zero for the expectation value of energy of the vacuum.

2nd: Find the reason why the actual energy is not exactly zero, but a little positive correction to that

Example: Postulate a mechanism to break SUSY ever so slightly that the expectation value of vacuum energy is slightly above zero. Then solve for the values of symmetry-breaking parameters for different models. Then go to the lab.

Something like that.

 

First off, let's chat about supersymmetry, or SUSY for short. Think of SUSY as this grand idea where every particle we know, the electrons, quarks, has a partner called a superpartner. But here's the catch: despite decades of searching with our most powerful technology, particle accelerators, we haven't found a single one of these superpartners. It's like planning a surprise party for someone who doesn't exist. 

Now, theorists suggest that in a perfectly supersymmetric universe, the vacuum energy, the energy of empty space, would be exactly zero. That's because the positive energy from particles called bosons would perfectly cancel out the negative energy from particles called fermions. It's like having a perfectly balanced seesaw. But since we haven't observed any superpartners, leaning on SUSY is like building a house on quicksand.

On the flip side, the author comes in with an idea rooted in solid, well-tested physics. Instead of banking on speculative theories, he turn to the trusty third law of thermodynamics and the experimental Meissner effect from superconductivity.

The third law of thermodynamics tells us that as a system gets colder and colder, approaching absolute zero, its entropy, or disorder, drops to a minimum. The Meissner effect shows that when certain materials become superconductors at low temperatures, they kick out magnetic fields entirely. It's like a crowded room suddenly clearing out when someone starts playing bagpipes, everything unwanted gets expelled to achieve a more orderly state.

So, the author suggests that the universe isn't this smooth, continuous fabric we often think of. Instead, it's made up of a finite number of tiny building blocks, like cosmic Lego bricks. These are called SU(3) units, based on the symmetry group that describes the strong force holding quarks together in protons. Think of them as the fundamental "atoms" of space itself. That is whynyhe author mentioned Snyder quantum spacetime in his paper. 

Now, Quantum Field Theory (QFT) predicts an enormous vacuum energy because it assumes space is continuous and counts every possible fluctuation, no matter how tiny or improbable. It's like trying to calculate the weight of a library by counting not just the books but every single letter on every page, even the spaces! You end up with a number so huge it's meaningless, a vacuum energy density that's \(10^{123}\) times larger than what we actually observe. That's a one followed by 123 zeros! It's as if you ordered a cup of coffee and they delivered an ocean.

By recognizing that the universe is made up of these finite SU(3) units, the author avoids this overcounting. The vacuum energy is calculated based on actual, physical units. This approach lines up beautifully with what we observe in the cosmos, giving us a precise value for the cosmological constant without resorting to speculative ideas like SUSY.

Now, let's tackle your two specific questions:

**1. Why does QFT predict such a monumental overcount in vacuum energy?**

In QFT, we're essentially adding up the energy of every possible vibration of every field at every point in space, up to incredibly high energies. It's like trying to count every grain of sand in the universe, including ones we haven't discovered yet! This method doesn't consider that space might be made up of discrete chunks—the SU(3) units—limiting the number of vibrations that can actually occur. So, the overcount happens because we're including energy contributions from fluctuations that don't physically exist.

**2. Why isn't the actual vacuum energy exactly zero but a small positive value?**

Some theorists argue that if SUSY were real and unbroken, the vacuum energy would be zero due to perfect cancellations between bosons and fermions. But since we haven't found any evidence for SUSY, and any supersymmetry that might exist must be broken, this perfect balancing act doesn't happen. A broken SUSY would leave a small residual vacuum energy, a little leftover that doesn't get canceled out. But again, this is speculative without experimental confirmation at all for the SUSY theory. 

In contrast, the author's model doesn't rely on unproven theories. By considering the universe as made up of these discrete, stable SU(3) units, using the volume of the proton as the fundamental unit, the vacuum energy naturally comes out as a small positive value that matches what we observe precisely. This isn't some wild guess; it's grounded in the third law of thermodynamics, reminding us that systems prefer to be in low-entropy, stable states, and the Meissner effect, showing how systems expel energy to reach those states.

dismissing the author's idea, which is based on solid, experimentally supported physics, in favor of speculative theories like SUSY seems a bit like choosing a mirage over a glass of water when  thirsty. Sometimes, the best solutions come from re-examining what we already know, using the tools and principles that have stood the test of time. After all, physics isn't just about chasing after exotic, unverified ideas; it's about understanding the universe using concepts we can test and observe. And who knows? Maybe by looking at the universe as a giant Lego set made of protons, we're onto something big. It's like realizing you've been sitting on a treasure chest all along, you just needed to look under your chair!

Edited 11 hours ago by JosephDavid

[joigus]

42 minutes ago, JosephDavid said:

First off, let's chat about supersymmetry, or SUSY for short. Think of SUSY as this grand idea where every particle we know, the electrons, quarks, has a partner called a superpartner. But here's the catch: despite decades of searching with our most powerful technology, particle accelerators, we haven't found a single one of these superpartners. It's like planning a surprise party for someone who doesn't exist. [...]

Blah.

Ahem:

6 hours ago, MJ kihara said:

What would make you conclude that cosmological constant problem has been solved in a precise way?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

As in 'I would be happy if you answered any of my concerns' (2^nd conditional).

From Oxford Dictionary:

Quote

 

would (modal verb)

2. used for talking about the result of an event that you imagine.

She'd look better with shorter hair.

If you went to see him, he would be delighted.

Hurry up! It would be a shame to miss the beginning of the play. 

She'd be a fool to accept it (= if she accepted).

 

(my emphasis)

If 1) an idea like SUSY were confirmed, and 2) the symmetry were broken slightly enough that it allowed for a small value of vacuum energy, that would make us conclude that the problem has been solved.

Has it?

No.

Edited 10 hours ago by joigus
minor correction

[Mordred]

1 hour ago, JosephDavid said:

 

First off, let's chat about supersymmetry, or SUSY for short. Think of SUSY as this grand idea where every particle we know, the electrons, quarks, has a partner called a superpartner. But here's the catch: despite decades of searching with our most powerful technology, particle accelerators, we haven't found a single one of these superpartners. It's like planning a surprise party for someone who doesn't exist. 

Now, theorists suggest that in a perfectly supersymmetric universe, the vacuum energy, the energy of empty space, would be exactly zero. That's because the positive energy from particles called bosons would perfectly cancel out the negative energy from particles called fermions. It's like having a perfectly balanced seesaw. But since we haven't observed any superpartners, leaning on SUSY is like building a house on quicksand.

On the flip side, the author comes in with an idea rooted in solid, well-tested physics. Instead of banking on speculative theories, he turn to the trusty third law of thermodynamics and the experimental Meissner effect from superconductivity.

The third law of thermodynamics tells us that as a system gets colder and colder, approaching absolute zero, its entropy, or disorder, drops to a minimum. The Meissner effect shows that when certain materials become superconductors at low temperatures, they kick out magnetic fields entirely. It's like a crowded room suddenly clearing out when someone starts playing bagpipes, everything unwanted gets expelled to achieve a more orderly state.

So, the author suggests that the universe isn't this smooth, continuous fabric we often think of. Instead, it's made up of a finite number of tiny building blocks, like cosmic Lego bricks. These are called SU(3) units, based on the symmetry group that describes the strong force holding quarks together in protons. Think of them as the fundamental "atoms" of space itself. That is whynyhe author mentioned Snyder quantum spacetime in his paper. 

Now, Quantum Field Theory (QFT) predicts an enormous vacuum energy because it assumes space is continuous and counts every possible fluctuation, no matter how tiny or improbable. It's like trying to calculate the weight of a library by counting not just the books but every single letter on every page, even the spaces! You end up with a number so huge it's meaningless, a vacuum energy density that's 10123 times larger than what we actually observe. That's a one followed by 123 zeros! It's as if you ordered a cup of coffee and they delivered an ocean.

By recognizing that the universe is made up of these finite SU(3) units, the author avoids this overcounting. The vacuum energy is calculated based on actual, physical units. This approach lines up beautifully with what we observe in the cosmos, giving us a precise value for the cosmological constant without resorting to speculative ideas like SUSY.

Now, let's tackle your two specific questions:

**1. Why does QFT predict such a monumental overcount in vacuum energy?**

In QFT, we're essentially adding up the energy of every possible vibration of every field at every point in space, up to incredibly high energies. It's like trying to count every grain of sand in the universe, including ones we haven't discovered yet! This method doesn't consider that space might be made up of discrete chunks—the SU(3) units—limiting the number of vibrations that can actually occur. So, the overcount happens because we're including energy contributions from fluctuations that don't physically exist.

**2. Why isn't the actual vacuum energy exactly zero but a small positive value?**

Some theorists argue that if SUSY were real and unbroken, the vacuum energy would be zero due to perfect cancellations between bosons and fermions. But since we haven't found any evidence for SUSY, and any supersymmetry that might exist must be broken, this perfect balancing act doesn't happen. A broken SUSY would leave a small residual vacuum energy, a little leftover that doesn't get canceled out. But again, this is speculative without experimental confirmation at all for the SUSY theory. 

In contrast, the author's model doesn't rely on unproven theories. By considering the universe as made up of these discrete, stable SU(3) units, using the volume of the proton as the fundamental unit, the vacuum energy naturally comes out as a small positive value that matches what we observe precisely. This isn't some wild guess; it's grounded in the third law of thermodynamics, reminding us that systems prefer to be in low-entropy, stable states, and the Meissner effect, showing how systems expel energy to reach those states.

dismissing the author's idea, which is based on solid, experimentally supported physics, in favor of speculative theories like SUSY seems a bit like choosing a mirage over a glass of water when  thirsty. Sometimes, the best solutions come from re-examining what we already know, using the tools and principles that have stood the test of time. After all, physics isn't just about chasing after exotic, unverified ideas; it's about understanding the universe using concepts we can test and observe. And who knows? Maybe by looking at the universe as a giant Lego set made of protons, we're onto something big. It's like realizing you've been sitting on a treasure chest all along, you just needed to look under your chair!

It's still amazing that we choose to ignore conservation of mass energy in all the above in favor of a model with no calculations.

Sigh I give up if you wish to believe in some paper that on a couple of occasions flat out lies (example mass of photon in OP paper)

Feel free I have better things to do.

I don't feel like arguing that throwing away decades of active research for mainstream physics that you want to throw away in favor of some paper that doesn't show  any qualitative calculations is the wrong approach.

Edited 10 hours ago by Mordred

[MJ kihara]

32 minutes ago, joigus said:

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

What would make you conclude that the cosmological constant problem has been solved?

As in 'I would be happy if you answered any

Ur a great liguist....but on cosmological constant you need to work hard to convince someone otherwise...if you could arrange the ideas like on that video that MigL posted or like the author of the article(OP) i think I could have shut up long time ago.

21 minutes ago, Mordred said:

It's still amazing that we choose to ignore conservation of mass energy in all the above in favor of a model with no calculations.

Even without breaking U(1) symmetry, the SU(3) symmetry of strong force would remain  stable when considering a stable volume...since talking of photon volume is not conceivable.

[TheVat]

delete 

 

 

Edited 9 hours ago by TheVat

[JosephDavid]

1 hour ago, Mordred said:

I don't feel like arguing that throwing away decades of active research for mainstream physics that you want to throw away in favor of some paper that doesn't show  any qualitative calculations is the wrong approach.

You know, physics is a bit like trying to understand a grand symphony while sitting in the orchestra pit. Sometimes, we're so caught up playing our own instruments that we forget to listen to the music as a whole. The third law of thermodynamics and experimental phenomena like the Meissner effect aren't just notes on a page, they're the melodies we've heard and verified time and time again.
 

Now, I understand that after decades of sailing the seas of mainstream physics, charting courses towards supersymmetry, the multiverse, and **extra dimensions, it might feel like we're being asked to abandon ship in favor of some new vessel that seems untested. But here's the thing: if the ship hasn't reached the shore after all this time, maybe it's worth checking if there's a leak. Supersymmetry and its friends are fascinating, they're like the mysterious islands marked on ancient maps with dragons and sirens. Exciting, but we've yet to actually land on them. Meanwhile, the solid ground of experimentally verified physics is right beneath our feet.

The low-energy vacuum near absolute zero isn't some abstract concept; it's a realm we've explored in laboratories. It's like finding a hidden room in a house we thought we knew inside out. Just because it's been overlooked doesn't mean it's not real or significant. I get that it's hard to entertain the idea that years of research might not lead us to the promised land. But science isn't about clinging to familiar shores; it's about daring to set sail for new horizons when the old maps don't quite line up with the stars. So, rather than seeing this as throwing away valuable work, think of it as tuning our instruments to a different key, one that's in harmony with what we've actually observed. Let's not ignore a potentially beautiful melody just because it's not the one we've been rehearsing.

 

[Mordred]

 You can believe what you want about physics here is a little trivia for you it doesn't make any difference whether your describing a system using SUSY or QFT or even classical physics.

Every theory must comply with observational evidence.

Having \(10^{123}\) protons in our universe exceeds All observational evidence for the mass/energy of the observable universe. Thst detail trumps any theory that states otherwise.

Plain and simple. If you ran that mass term  through the FLRW matter dominant equations the very universe would collapse.

No theory becomes mainstream without rigorous testing via experimental evidence.

Edited 8 hours ago by Mordred

[TheVat]

1 hour ago, JosephDavid said:

1 hour ago, JosephDavid said:

You know, physics is a bit like trying to understand a grand symphony while sitting in the orchestra pit. Sometimes, we're so caught up playing our own instruments that we forget to listen to the music as a whole. The third law of thermodynamics and experimental phenomena like the Meissner effect aren't just notes on a page, they're the melodies we've heard and verified time and time again.
 

Now, I understand that after decades of sailing the seas of mainstream physics, charting courses towards supersymmetry, the multiverse, and **extra dimensions, it might feel like we're being asked to abandon ship in favor of some new vessel that seems untested. But here's the thing: if the ship hasn't reached the shore after all this time, maybe it's worth checking if there's a leak. Supersymmetry and its friends are fascinating, they're like the mysterious islands marked on ancient maps with dragons and sirens. Exciting, but we've yet to actually land on them. Meanwhile, the solid ground of experimentally verified physics is right beneath our feet.

 

Could you come down from your pulpit and address the points being made here about experimental evidence?  These pompous and condescending sermonettes are worse than outright trolling.  

[Mordred]

1 hour ago, TheVat said:

Could you come down from your pulpit and address the points being made here about experimental evidence?  These pompous and condescending sermonettes are worse than outright trolling.  

The worse part is I know the mathematics behind every theory that's been mentioned. 35 to 40 years of continous study teaches a lot. So one can only imagine what these condensending tones sound like to me lmao 🤣 😂 😆 😅 

Take Maxwell Boltzmann for example SUSY QFT and All apply it.

It existed prior to all the above. It's been integrated into all the above. That's the understanding one gains when they sit down and study the mathematics of a given theory.

 

 

 

Edited 5 hours ago by Mordred

[joigus]

4 hours ago, JosephDavid said:

You know, physics is a bit like [...]

Yeah, we got it. To boldly think what no one has ever thought.

[Mordred]

2 hours ago, joigus said:

Yeah, we got it. To boldly think what no one has ever thought.

I decided to do a bit of calculations 

The observable Universe mass using Critical density is estimated to be \[10^{53} kg.\]

So using \(10^{123}\) protons at 936 MeV

The corresponding mass is \[1.669 ×10^{96}\] kg

Talk about a HUGE mismatch lol thought I would share that. 

I seriously hope the author isn't using protons or neutrons the theory would automatically be invalid simply on that calculation.

There simply put absolutely no way possible to solve the cosmological constant problem with such a large mismatch none whatsoever superconductivity or not.

It's literally impossible with 10^123 protons or neutrons

Anyone want to try simply multiply 936 MeV times 10^{123} then convert to Kg with e=mc^2

Edited 1 hour ago by Mordred

[joigus]

18 minutes ago, Mordred said:

I decided to do a bit of calculations 

The observable Universe mass using Critical density is estimated to be

1053kg.

 

So using 10123 protons at 936 MeV

The corresponding mass is

1.669×1096

kg

 

Talk about a HUGE mismatch lol thought I would share that. 

I seriously hope the author isn't using protons or neutrons the theory would automatically be invalid simply on that calculation.

There simply put absolutely no way possible to solve the cosmological constant problem with such a large mismatch none whatsoever superconductivity or not.

It's literally impossible with 10^123 protons or neutrons

Anyone want to try simply multiply 936 MeV times 10^{123} then convert to Kg with e=mc^2

Exactly. And it would share cosmological equation of state with ordinary matter. It would be another garden-variety type of matter to be detected in scattering experiments. Why bother with superconductivity if the idea doesn't even leave the ground?

[Mordred]

33 minutes ago, joigus said:

Exactly. And it would share cosmological equation of state with ordinary matter. It would be another garden-variety type of matter to be detected in scattering experiments. Why bother with superconductivity if the idea doesn't even leave the ground?

The universe wouldn't even be able to expand to begin with the potential energy (mass) exceeds the kinetic energy terms of radiation by far to great a factor.

That can be shown through the scalar field equations of state or alternately a matter only universe with no radiation via critical density formula which prior to discovery of the cosmological constant gives the density to of an expanding universe to switch to collapsing.

(It was derived as a matter only solution to begin with ) using GR and Jean's instability.

I don't know about anyone else but this paper is nonsense the primary mistake was not performing any calculations plain and simple.

Including introductory level cosmology or intro level physics.

 

Edited 1 hour ago by Mordred

[MJ kihara]

1 hour ago, Mordred said:

 

The observable Universe mass using Critical density is estimated to be

1053kg.

 

So using 10123 protons at 936 MeV

The corresponding mass is

1.669×1096

kg

 

Talk about a HUGE mismatch lol thought I would share that. 

I think you are adding wrong facts on author's concept....a photon exist but it's massless ....your using proton mass which is not in the arguments....it's a volume derived from SU(3) symmetry that is directly related to proton mass.....people here talk about mass...and  all they can tell you about it is, Higgs field, dark matter has mass but not through Higgs field...it's just sad 😢 that people can't tolerate challenging ideas that don't conform to their thinking...the only option is to apply mud on others concepts. 

[Mordred]

There is no wrongs facts involved one can also use the full energy momentum relationship to include the possibility of massless particles.

However the author specifies a state where there are no massless particles in his first 3 pages.

In particular the portion he entered the particle data group constraint  as a calculated mass term due to U(1)  specifically stating verbally as well. I already pointed out that earlier numerous times. It's specifically the QED langrangian in simplified form.

I also pointed out he defined a Hermitean system which that is fine However as I mentioned he never extracted the relevant terms related specifically isolating the longitudinal waveform components which would be needed to apply to Meissner effect.

 Simply including the generalized QED langrangian isn't useful in any manner.

In QFT anytime you have a specific interaction of any form it will have its own Langrangian.

It is after all the probabilistic path of least action which is the multiple field momentum terms. Those equations motion or vector component equivelence  are literally used for all quantum interactions. One could Alternatively use derivatives the results would be the same.

As they are equivalent methodologies integrals However works extremely well for wavefunctions. The huge advantage is all particles always follow the path of least action regardless of scattering event or not.

You may recall Swansont and others have mentioned the lack of calculations as well.

 

 

 

Edited 7 minutes ago by Mordred