Gauge Symmetry and Conservation?

[SamBridge]

Hi I was wondering exactly how the transfer of force between particles works in current gauge theories. It doesn't really make sense to me, shouldn't particles emit their energy away? But, when scientists come up with a solution to that problem, they say the boson "snaps back", but that doesn't make sense because when a boson interacts its effects then become real and it goes into an Eigenstate so it shouldn't be able to hold its superposition upon interaction with a fermion as to go back to it's parent particle, that would seem to violate the conservation of energy simultaneously as well.

Edited January 10, 2013 by SamBridge

[ajb]

Hi I was wondering exactly how the transfer of force between particles works in current gauge theories.

To really get at this you need to examine perturbation theory in the context of gauge theories. This is probably more than you want to "chew". I imagine that you are only interested in tree level interactions, so you won't need to worry about remormalisation.

 

The place to start is to understand the methods used in scalar field theory and then electromagnetism. I recommend the book by Ryder.

[SamBridge]

I'll go to any depths to figure something out that I want to know, the only problem is I can't always swim. My guess is that if you leave out complex math above basic calculus out I'll be just fine.

[beefpatty]

In terms of math what immediately comes to mind are bra-ket notation, integrals, contour integrals, and dirac delta functions. You can get pretty far with integrals, since when it comes down to it cross sections are just integrals of a square amplitude over all spacetime.

 

The more pertinent question, though, is what sort of background do you have in physics? Do you feel comfortable with Lagrangian mechanics? Special Relativity? QM?

I'm just a lowly master's student so I don't have experience with Ryder yet, although I am currently working through the book by Peskin and Schroeder and don't have major complaints. Although with just a sample size of 1 it's hard to truly recommend!

[ajb]

I'm just a lowly master's student so I don't have experience with Ryder yet, although I am currently working through the book by Peskin and Schroeder and don't have major complaints. Although with just a sample size of 1 it's hard to truly recommend!

Peskin and Schroeder is generally recommended, though I have not used it myself.

[SamBridge]

In terms of math what immediately comes to mind are bra-ket notation, integrals, contour integrals, and dirac delta functions. You can get pretty far with integrals, since when it comes down to it cross sections are just integrals of a square amplitude over all spacetime.

Yeah I'm somewhat familiar with summing different phases to get the probability amplitude when I then square to get the probability density, which I assume is what you're saying to take the integral of, there was something about that integral that had equal some specific number, because if you compare the different energy states, the absolute maximum probability of the function becomes less and less as the energy state increases (ignoring the nodal surfaces) but increases in range, it would seem like the indefinite integral would have to be a limit that approaches some finite value with every energy state, at least for representing particles that can be localized, I want to say it's the number "1" because probability is suppose to total "1", but I don't know for sure. It's something similar to this

or something like this

But that's not totally accurate I couldn't find the specific graph I was looking for.

 

IThe more pertinent question, though, is what sort of background do you have in physics? Do you feel comfortable with Lagrangian mechanics? Special Relativity? QM?

I have a relatively scattered understanding of it that I've been working with in my free time from reading books.

Edited January 24, 2013 by SamBridge

[Arnaud Antoine ANDRIEU]

Yeah I'm somewhat familiar with summing different phases to get the probability amplitude when I then square to get the probability density ...

But that's not totally accurate I couldn't find the specific graph I was looking for.

 

I have a relatively scattered understanding of it that I've been working with in my free time from reading books.

 

You Know you Can Do-it

 

[SamBridge]

You Know you Can Do-it

 

I don't know the exact math though, I can only find generalized or parent equations and not specific ones.

[Arnaud Antoine ANDRIEU]

I don't know the exact math though, I can only find generalized or parent equations and not specific ones.

 

What's the difference between your model, and mine ? Simple question ...

 

[SamBridge]

What's the difference between your model, and mine ? Simple question ...

 

For a start you didn't present a model in this topic so there's no way I can answer that.

[beefpatty]

You could give a shot at David Tong's lectures online. They closely follow the book by Peskin and Schroeder, although I don't believe he goes into gauge symmetries in depth. You can also try an online text by Robert Klauber, in which he does go into gauge symmetries.

[SamBridge]

You could give a shot at David Tong's lectures online. They closely follow the book by Peskin and Schroeder, although I don't believe he goes into gauge symmetries in depth. You can also try an online text by Robert Klauber, in which he does go into gauge symmetries.

Thanks for the link, by the way what about the integral thing? Was I right that it always equals 1?

[beefpatty]

Thanks for the link, by the way what about the integral thing? Was I right that it always equals 1?

 

It depends on the situation. If the wavefunction goes to zero as you go to infinity on either side, or as [math]|x|\to\infty[/math], then the integral will be finite and you can normalize it so it's equal to 1.

[SamBridge]

Yessssss