Linked Questions

12
votes
3answers
1k views

Can we do path integrals in gauge theories without fixing a gauge?

I am aware that when quantizing gauge theories with a path integral, one needs to add a gauge fixing term to avoid over-counting gauge related field configurations. From an aesthetic perspective, I ...
8
votes
2answers
2k views

Gauge fixing and equations of motion

Consider an action that is gauge invariant. Do we obtain the same information from the following: Find the equations of motion, and then fix the gauge? Fix the gauge in the action, and then find the ...
9
votes
2answers
2k views

Faddeev-Popov Ghosts

When quantizing Yang-Mills theory, we introduce the ghosts as a way to gauge-fix the path integral and make sure that we "count" only one contribution from each gauge-orbit of the gauge field $A_\mu\,^...
9
votes
2answers
563 views

Why the extra term $\frac{1}{2}(\partial_{\rho}A^{\rho})^2$ in the photon Lagrangian?

In my quantum field theory class we have been told to use this Lagrangian for the photon field $$\mathcal{L}=-\frac{1}{4}F_{\alpha\beta}F^{\alpha\beta} -\frac{1}{2}(\partial_{\rho}A^{\rho})^2.$$ but ...
6
votes
1answer
577 views

Why do we have to choose a gauge to quantize a gauge theory?

Why do we have to choose a gauge to quantize a gauge theory? This was an exam question but I couldn't answer it.
4
votes
2answers
724 views

Question about the Faddeev-Popov method for gauge-fixing

The correct way to gauge-fix in a path integral is to insert the Faddeev-Popov determinant, and add a delta-functional constraint. The final action contains three contributions: a Yang-Mills (I'm ...
7
votes
1answer
1k views

QED lagrangian: gauge fixing term

I have a question about the structure of the QED lagrangian, in particular the free photon lagrangian which is contained in it. My premise is: I only know how to exploit canonical quantization in ...
4
votes
1answer
171 views

$R_\xi$ gauges and the EM-field

$R_\xi$-gauges are said to be a generalization of the Lorenz gauge. I dont quite get why we add the term $$ \mathcal L_{GF} = - \frac{(\partial_\mu A ^\mu)^2}{2\xi}\tag{1} $$ to the Lagrangian. If i ...
4
votes
1answer
274 views

How to make this short explanation to path integral approach to QED correct?

Edit: as suggested by @Slereah the following explanation of the path integral approach to QED misses gauge fixing and ghost terms to be correct. So, how can this explanation be made correct? What ...
1
vote
1answer
111 views

Eliminating residual gauge in BRST quantization of Yang-Mills theory

I would like to know if there is a procedure to completely fix a gauge, which I believe we must do in order to make sense of the path integral? In chapter 74 Sredniki introduces the Lagrangian $$ \...