All Questions
55
questions
3
votes
0
answers
74
views
Charge Renormalization in Abelian Gauge Theory under General Gauge Fixing Conditions
In scalar QED or fermionic QED, the relationship between bare quantities (subscript "B") and renormalized quantities is given by
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
- 51
2
votes
1
answer
143
views
Spontaneous Symmetry Breaking, Vacuum Degeneracy, and Goldstone Bosons applied to large gauge transformations
I am reading Strominger's lecture notes on the infrared structure of gravity and gauge theory. I am trying to understand subchapter 2.11, where the author focuses on the notions of "Spontaneous ...
- 3,992
0
votes
0
answers
98
views
Why is the source of the EM Field in QED the probability current and not the electric current?
I have some problems understanding the interaction term in the QED Lagrangian. If we take
$$
\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \bar \psi (\gamma^\mu\partial_\mu-m)\psi+\bar \psi \gamma^\...
- 29
3
votes
1
answer
106
views
Can we eliminate gauge degrees of freedom in QFT by quantizing the field strength directly?
In Matthew Schwartz's Quantum Field Theory and the Standard Model, he says (section 8.6, page 132) that it is possible to avoid introducing the redundant gauge degrees of freedom in QED by quantizing $...
- 3,949
2
votes
1
answer
156
views
Path integral of vector bosons
My question is about the path integral formulation of QFT. Specifically about vector/gauge bosons
I understand that I have measures $\mathcal D \phi$, $\mathcal D\psi$, $\mathcal D \overline\psi$ for ...
- 21
0
votes
0
answers
94
views
Calculating a rectangular Wilson loop for the free photon
I'm studying Creutz's Quarks, gluons and lattices, in chapter 6 on page 33, we have the following exercise
Calculate a rectangular Wilson loop for the field theory of free photons. Using any ...
- 789
1
vote
1
answer
93
views
What is the Ehrensmann connection of QED
I've heard that QED can be described (at least classically) as a $U(1)$ principle bundle.
Given a principle $G$ bundle $\pi:M\rightarrow B$, an Ehresmann connection is defined to be a collection of ...
- 789
1
vote
1
answer
109
views
QED in 1+1 dimensions | Transport equation with an imaginary (reaction) source term
I would like to know what is the contribution of the right source term to this fermion component equation of motion:
\begin{equation}
i(\partial_0+\partial_1)\psi_R= a \psi_R
\end{equation} where $a$ ...
4
votes
1
answer
349
views
On the Ward Identity in QED
I am reading P&S, particularly Chapter 5.5. The authors are trying to derive an expression for the Ward identity (not formally, but still). They claim that the amplitude describing a photon ...
- 3,992
5
votes
1
answer
414
views
The Faddeev-Popov generating functional and its independence on the gauge-fixing function
A technical question on the Faddeev-Popov procedure (P&S Chapter 9). P&S introduce the functional integral, which is equal to one and then they choose the gauge-fixing function $G(A)$ to be ...
- 3,992
7
votes
1
answer
533
views
Why is quantizing the free electromagnetic field in the Lorenz gauge more subtle than in the Coulomb gauge?
Quantizing the free electromagnetic field in the Lorenz gauge, $\partial_\mu A^\mu=0$, is subtle. We must add a gauge-fixing term to the action so that $\pi^0$ does not vanish identically. Also, we ...
- 11.8k
0
votes
0
answers
64
views
Steps in Quantizing Electromagnetic Field for the Gauge Condition $A_0=0$
While reading section 9.3 of QFT An Integrated Approach by Fradkin, it is shown (see equations $(9.49)$ and $(9.54)$ of the book)
$$B_{j}(\boldsymbol{x})^{2}=\boldsymbol{p}^{2} A_{j}^{T}(\boldsymbol{p}...
- 381
4
votes
1
answer
310
views
Equivalence of Maxwell and electric field operator in the Coulomb gauge (minimal and polar coupling)
In the field theory literature, we find the interaction Hamiltonian coupling a point particle with charge $e$ and mass $m$ to the electromagnetic field to be
$$
\hat{H}_\text{int}(t)
=
-
\frac{e}{m}
\...
- 543
3
votes
1
answer
203
views
Gauge invariance at the quantum level post SSB in the case of Abelian Gauge theory
On page 690 in Peskin & Schroeder's book, the Higgs mechanism is discussed in the context of an Abelian Gauge theory. After the SSB, among the many terms that appear, there is a mass term for the ...
- 823
6
votes
2
answers
896
views
Ward Identity and Proca Fields
I'm following the book Quantum Field Theory and the Standard Model by Schwartz and I came to the rigorous non-perturbative proof of the Ward identity with path integrals via the Schwinger-Dyson ...
- 127