Quantum Field Theory. Field quanta

[arnold3000]

what is the size of an electron in quantum field theory? Art Hobson said that the field quanta spread infinitely

[Markus Hanke]

The concept of “size” does not really make much sense in the context of quantum field theory, because you are dealing with excitations of a field that extends throughout all space and time. The only thing you can do is set up a scenario where you let quantum fields interact - for example, you can shoot another particle at your original electron. In this case there will be a well defined probability to “hit” your electron in a specified region, and by the manner of the resultant inelastic scattering, you can draw conclusions as to the internal structure of the electron. 

Such experiments have been done, and the result is that there is no indication of them having any kind of internal structure. At the point of scattering (!) they behave like point particles; however, this is only the point where the quantum fields interact, but the fields themselves extend throughout all space and time, so “size” isn’t really a very meaningful concept in this picture. It’s both a point particle, and an extended field, and the two are equivalent descriptions of the same thing.

[arnold3000]

2 hours ago, Markus Hanke said:

The concept of “size” does not really make much sense in the context of quantum field theory, because you are dealing with excitations of a field that extends throughout all space and time. The only thing you can do is set up a scenario where you let quantum fields interact - for example, you can shoot another particle at your original electron. In this case there will be a well defined probability to “hit” your electron in a specified region, and by the manner of the resultant inelastic scattering, you can draw conclusions as to the internal structure of the electron. 

Such experiments have been done, and the result is that there is no indication of them having any kind of internal structure. At the point of scattering (!) they behave like point particles; however, this is only the point where the quantum fields interact, but the fields themselves extend throughout all space and time, so “size” isn’t really a very meaningful concept in this picture. It’s both a point particle, and an extended field, and the two are equivalent descriptions of the same thing.

And how then does the quantum field theory explain the triboelectricity when the electrons pass from one material to another?

[geordief]

Is the (hypothesized) graviton  expected to be an excitation of a gravity field? 

Were there any gravitons involved in the gravitational waves that have  been detected over the past few years?

 

 

[Mordred]

2 hours ago, arnold3000 said:

And how then does the quantum field theory explain the triboelectricity when the electrons pass from one material to another?

Why would the triboelectric effect have any meaning concerning the size of an electron ? The scattering Markus referred to is the Compton scattering this is the probability of a particles locations which is scattered by the photon whose mass must be also be sufficient to cause an electron to be scattered. No matter how much energy we have experimentally used, we have not been able to determine the size or radius of an electron. It is from all experimental evidence literally pointlike, which is such an infinitesimal length that size becomes meaningless.

Care must be taken in the term quanta however. A quanta of action for example requires displacement from one coordinate to another a quanta of action under QFT is a measureable event ie specifically Observable. The field in QFT is upgraded to an operator but under QM is a propagator as the two operators in QM are position and momentum.

Edited July 2, 2018 by Mordred

[arnold3000]

1 hour ago, Mordred said:

Why would the triboelectric effect have any meaning concerning the size of an electron ? The scattering Markus referred to is the Compton scattering this is the probability of a particles locations which is scattered by the photon whose mass must be also be sufficient to cause an electron to be scattered. No matter how much energy we have experimentally used, we have not been able to determine the size or radius of an electron. It is from all experimental evidence literally pointlike, which is such an infinitesimal length that size becomes meaningless.

Care must be taken in the term quanta however. A quanta of action for example requires displacement from one coordinate to another a quanta of action under QFT is a measureable event ie specifically Observable. The field in QFT is upgraded to an operator but under QM is a propagator as the two operators in QM are position and momentum.

Sorry. I want to clarify in the quantum field theory materials are exchanged by electrons which are wave packets?

[Mordred]

All particles are treated as an excited state of an underlying field in QFT treatments hence they are field quanta. This includes the electron. In point of detail you can literally read entire QFT textbooks and not once come across the term particle. Wave packet is suitable. QFT has a rather different view of a particle, one of the better definitions I've run across is a single-quantum asymptotic free Fock state of a quantum field.

The trick is the probability of locating an electron or rather the quantized fock state that we identify as an electron is smeared over all of the field, the highest probability of finding that state is the field excitation. This is what Hobson is referring to in his "There are no particles there is only fields" article.

This will help out a bit on Fock spaces and the single and multiparticle states

https://www.tcm.phy.cam.ac.uk/~bds10/tp3/secqu.pdf

Edited July 3, 2018 by Mordred

[arnold3000]

15 hours ago, Mordred said:

All particles are treated as an excited state of an underlying field in QFT treatments hence they are field quanta. This includes the electron. In point of detail you can literally read entire QFT textbooks and not once come across the term particle. Wave packet is suitable. QFT has a rather different view of a particle, one of the better definitions I've run across is a single-quantum asymptotic free Fock state of a quantum field.

The trick is the probability of locating an electron or rather the quantized fock state that we identify as an electron is smeared over all of the field, the highest probability of finding that state is the field excitation. This is what Hobson is referring to in his "There are no particles there is only fields" article.

This will help out a bit on Fock spaces and the single and multiparticle states

https://www.tcm.phy.cam.ac.uk/~bds10/tp3/secqu.pdf

You are a good teacher.
I would like to clarify if I understood correctly: electrons are wave packets in quantum field theory. The processes in which electrons are exchanged occur in the same way as in classical theory. The difference lies in the fact that in the classical theory materials are exchanged by the points of particles, and in the quantum field theory materials are exchanged wave packets

 

Edited July 3, 2018 by arnold3000

[Mordred]

More accurately in QFT interactions can involve both pointlike and wavelike characteristics and under QFT treatment in essence the particle and the field is one and the same ie the particle is an excited localized state of the field itself. However the above is accurate but its better to recognize the distinction between QM and QFT in QM the particle is the priori but in QFT the field is of greater significance whereas the particle is a state caused by the field

[geordief]

23 minutes ago, Mordred said:

More accurately in QFT interactions can involve both pointlike and wavelike characteristics and under QFT treatment in essence the particle and the field is one and the same ie the particle is an excited localized state of the field itself. However the above is accurate but its better to recognize the distinction between QM and QFT in QM the particle is the priori but in QFT the field is of greater significance whereas the particle is a state caused by the field

I have been wondering what does "an excitation of a field" mean?

 

Is the field not  simply a set of readings taken at points on a co-ordinate map (not a "thing"as such)

 

Is something causing the "excitation" or is the excitation just an unusual reading on the mathematical object which is the field?

 

Is an "excitation " perhaps a state rather than something that has been "excited"?

 

[Mordred]

An excitation can be described as a discrete finite state. One example would be a signal such as a sine wave with begin and end points that renormalizes to the baseline field value. Once it loses and reconnects to the baseline value you now have a definable signal begin and end points. Another example would be a spike in a signal which re-establishes to the baseline. In all cases you must have a finite portion with definable beginning and end points.

Now think of that in terms of a quanta, this is finite frequencies they are finite in the allowable frequency values and not continuous over all frequencies in a given range.

A signal that is never stable ie always changing values between samplings is a fluctuation signal ie constantly changing. Example continuous wavefunction. The harmonic oscillator of QM is an example of a probabilistic fluctuation ie the uncertainty principle.

Edited July 3, 2018 by Mordred

[geordief]

11 hours ago, Mordred said:

An excitation can be described as a discrete finite state. One example would be a signal such as a sine wave with begin and end points that renormalizes to the baseline field value. Once it loses and reconnects to the baseline value you now have a definable signal begin and end points. Another example would be a spike in a signal which re-establishes to the baseline. In all cases you must have a finite portion with definable beginning and end points.

Now think of that in terms of a quanta, this is finite frequencies they are finite in the allowable frequency values and not continuous over all frequencies in a given range.

A signal that is never stable ie always changing values between samplings is a fluctuation signal ie constantly changing. Example continuous wavefunction. The harmonic oscillator of QM is an example of a probabilistic fluctuation ie the uncertainty principle.

When the field is mapped and there is a particle embedded(?**)Is there any (mathematical) discontinuity between  areas of the map (that of the particle and that of the underlying field)?

 

Is there a smooth join? Is  the particle wave overlayed onto the field  or does it "rise from" the field

 

(you might have to run my post through a gobbledegook checker  )

 

**if that is correct or applicable terminology

Edited July 4, 2018 by geordief

[Mordred]

Well please recall all fields are abstract mathematical tools under a geometry treatment. In QFT the fields are probabilistic oriented. It represents the likely hood of a particle being created at one coordinate and annihilated at another coordinate. The likelihood is a Feymann path integral treatment of all possible spacetime paths. This would normally be an infinite quantity as there is always an infinite number of possible paths between two coordinates, however one applies a weighted boundary of the most likely paths described by the paths of least resistance under the Action principle. However the field will be continuous with the highest probability being the higher amplitudes in the set of real numbers ie positive integers, more precisely the square of the amplitude which under maths would ensure the probability is a positive integer. Each particle would involve its own field which is infinite in extent however that involves the infinite possible paths with which we compactify into a probabilistic finite probabilitiy weighted potential region. Terms such as UV and IR cutoffs and Dirichlet and Neumann boundaries are part of this compactification. The particle will be contained within a probabilistic potential well defined by the effective cutoffs. Until a measurement is taken the field is a superposition state defined by the Klein Gordon equation or rather the Dirac equations which takes into consideration anti particles which when you square the amplitude gives a positive probability as opposed to the Schrodinger equation which isn't Lorentz invariant.

Hope this helps rather than confuse however your question isn't easily answered and maintain accuracy when describing how QFT defines a field

Edited July 4, 2018 by Mordred

[arnold3000]

16 hours ago, Mordred said:

More accurately in QFT interactions can involve both pointlike and wavelike characteristics and under QFT treatment in essence the particle and the field is one and the same ie the particle is an excited localized state of the field itself. However the above is accurate but its better to recognize the distinction between QM and QFT in QM the particle is the priori but in QFT the field is of greater significance whereas the particle is a state caused by the field

If the particles in quantum field theory are stable excitations in a field, they can exist for an unlimited time? And once again I will ask, when in the quantum field theory there is an electrical discharge, do the electrons really go from one material to another?

Edited July 4, 2018 by arnold3000

[geordief]

1 hour ago, Mordred said:

Well please recall all fields are abstract mathematical tools under a geometry treatment. In QFT the fields are probabilistic oriented. It represents the likely hood of a particle being created at one coordinate and annihilated at another coordinate. The likelihood is a Feymann path integral treatment of all possible spacetime paths. This would normally be an infinite quantity as there is always an infinite number of possible paths between two coordinates, however one applies a weighted boundary of the most likely paths described by the paths of least resistance under the Action principle. However the field will be continuous with the highest probability being the higher amplitudes in the set of real numbers ie positive integers, more precisely the square of the amplitude which under maths would ensure the probability is a positive integer. Each particle would involve its own field which is infinite in extent however that involves the infinite possible paths with which we compactify into a probabilistic finite probabilitiy weighted potential region. Terms such as UV and IR cutoffs and Dirichlet and Neumann boundaries are part of this compactification. The particle will be contained within a probabilistic potential well defined by the effective cutoffs. Until a measurement is taken the field is a superposition state defined by the Klein Gordon equation or rather the Dirac equations which takes into consideration anti particles which when you square the amplitude gives a positive probability as opposed to the Schrodinger equation which isn't Lorentz invariant.

Hope this helps rather than confuse however your question isn't easily answered and maintain accuracy when describing how QFT defines a field

Yes ,thanks. It is a great help ,though (as is often  the case with me) it feels like a guide  rather than an answer(for the reason you gave ,no doubt).

 

I think I may have understood your  ". In QFT the fields are probabilistic oriented. It represents the likely hood of a particle being created at one coordinate and annihilated at another coordinate"  and it feels like an important element.

 

 

s.

 

 

[Mordred]

43 minutes ago, arnold3000 said:

If the particles in quantum field theory are stable excitations in a field, they can exist for an unlimited time? And once again I will ask, when in the quantum field theory there is an electrical discharge, do the electrons really go from one material to another?

It might help if you think of the Triboelectric effect as a exchange of charge not an exchange of electrons, There is a distinction, for example in a wire the flow of electrons is slow but the flow of charge is at c. The flow of charge is described by polarizations here is a basic classical article on how electrostatics work when the electric field is treated as a VECTOR Field. Noted in article.

http://www.phys.ufl.edu/~korytov/phy2049/old_notes/all_chapters.pdf

I also hope the Hobson paper taught you to not think of particles as a material ie corpuscular little bullets.... Solid is an illusion this is a needed shift in thinking to understand modern treatments of particles. The term particle is maintained for historical reasons but often leads to the incorrect images of what is described as a particle. This is one of the issues the Hobson paper addresses.

Edited July 4, 2018 by Mordred

[arnold3000]

32 minutes ago, Mordred said:

It might help if you think of the Triboelectric effect as a exchange of charge not an exchange of electrons, There is a distinction, for example in a wire the flow of electrons is slow but the flow of charge is at c. The flow of charge is described by polarizations here is a basic classical article on how electrostatics work when the electric field is treated as a VECTOR Field. Noted in article.

http://www.phys.ufl.edu/~korytov/phy2049/old_notes/all_chapters.pdf

I also hope the Hobson paper taught you to not think of particles as a material ie corpuscular little bullets.... Solid is an illusion this is a needed shift in thinking to understand modern treatments of particles. The term particle is maintained for historical reasons but often leads to the incorrect images of what is described as a particle. This is one of the issues the Hobson paper addresses.

In the classical theory of tribo, electricity is described by the exchange of electrons, for example when rubbing the balloon to the hair. How does it work in quantum field theory? This is also the exchange of electrons. And according to the quantum field theory, electrons are the essence?

[Mordred]

 Your really not getting it, the term particle is a misnomer under QFT. This is specifically what the Hobson paper talks about. Hence its very title in the paper. There are no Particles, there is only fields.. Under QFT the coulomb force is described as the flow of polarization vectors

[arnold3000]

6 minutes ago, Mordred said:

 Your really not getting it, the term particle is a misnomer under QFT. This is specifically what the Hobson paper talks about. Hence its very title in the paper. There are no Particles, there is only fields.. Under QFT the coulomb force is described as the flow of polarization vectors

I do not say electrons are particles. Electrons - entities (field quanta). I want to understand that all objects consist of atoms. Atoms consist of quarks and electrons, when the two materials are in contact, electrons (field quanta) move from one material to another?

[Mordred]

Yes that is a simplified way of describing it.

[arnold3000]

1 minute ago, Mordred said:

Yes that is a simplified way of describing it.

that is, the field quanta can behave like the classical ones ?

[Strange]

1 minute ago, arnold3000 said:

that is, the field quanta can behave like the classical ones ?

Well, they “behave” identically; it is just the mathematical description is different. 

[Mordred]

All advanced theories must be reducible and correspond to classical laws. This is the Principle of correspondence. X posted with Strange.

Edited July 4, 2018 by Mordred

[arnold3000]

1 minute ago, Strange said:

Well, they “behave” identically; it is just the mathematical description is different. 

In quantum field theory, electrons can physically move from one material to another?

[Mordred]

What the QFT defines as the electron in terms of the Operators involved under spinor and vector quantities will transfer. The values of the field will change locality