All Questions
Tagged with quantum-field-theory gauge-theory
725
questions
3
votes
2
answers
168
views
Why the massive spin-1 photon gets more degrees of freedom than massless case; while the massive spin-1/2 electron stays the same as massless case?
Spin 1 field without mass term like photon has 2 real degrees of freedom. The polarization with two states. I think I can denote it as quantum state $|s,s_z> = |1,1>$ and $|1,-1>$.
Spin 1 ...
- 149
1
vote
0
answers
125
views
Gauge invariance of simplified weak interaction
I am having difficulties with a homework set. We are given the following lagrangian for a simplified weak interaction between an electron $\psi$, neutrino $\chi$, and a massive (complex) vector-boson $...
1
vote
1
answer
123
views
How to calculate the component term in BFSS matrix model?
I'm reading articles about BFSS, and confused by the calculation.
The Hamiltonian is
$$
H=\frac{g^2}{2}TrP_{I}^{2}-\frac{1}{4g^2}Tr[X_{I},X_{J}]^2
-\frac{1}{2}Tr\psi_{\alpha}\gamma_{\alpha \beta}^{I}[...
- 368
1
vote
0
answers
43
views
Calculating gauge propagator in minimally coupled, non-relativistic fermion system
For context, I am trying to derive Eq. 4.1 of $T_c$ superconductors">this paper. Consider the action
$$S[\psi^\dagger, \psi, a] = -\int d\tau \int d^2r \sum_\sigma \psi^\dagger (D_0-\mu_F-\frac{1}{...
- 59
6
votes
1
answer
180
views
Representation of nonabelian Wilson line in terms of fermionic fields
Context:
The coupling action of a particle of charge $q$ to a $U(1)$ gauge field is given by
\begin{equation}
S = q \int d \tau A_\mu \left( X \right) \frac{dX^\mu(\tau)}{d \tau} = -i \ln W_q,
\tag{...
- 897
3
votes
1
answer
126
views
Dressing an operator by Wilson line in Quantum Electrodynamic
I am reading a paper arXiv:1507.07921 which introduce gravitational dressing. The paper compare it to dressing in QED.
Consider the scalar QED lagrangian
$$\mathcal{L}=-\frac{1}{4}(F^{\mu\nu})^2-|D_\...
- 133
3
votes
0
answers
94
views
Characteristic classes and index theorems for physicists
Since characteristic classes and index theorems are occasionally used in quantum field theory (for example, when discussing instantons or quantum anomalies), I want to learn more about them. Is there ...
3
votes
0
answers
192
views
Stueckelberg mechanism for interacting QFTs
The Stueckelberg mechanism or "trick" (see e.g. Section 4 of https://arxiv.org/abs/1105.3735) is basically a method to take the massless limit of massive gauge theories in a smooth way, ...
- 165
2
votes
0
answers
39
views
Partial gauge fixing a point to infinity in conformal field theory [duplicate]
While deriving the structure of a 4 pt. function in CFT, we write the conformal block with respect to the cross ratios
$$ u = \frac{x_{12}^2x_{34}^2}{x_{13}^2x_{24}^2}, \; v = \frac{x_{14}^2x_{23}^2}{...
- 41
1
vote
0
answers
69
views
Faddeev-Popov Method for Gauge Fixing in CFT (Light-ray Operators)
I was attempting to go through the paper by Petr Kravchuk and David Simmons-Duffin: https://arxiv.org/abs/1805.00098 where I encountered the following
Just below E.4, it is mentioned that for the ...
- 41
0
votes
1
answer
113
views
Lattice $SU(2)$ Higgs model in unitary gauge
I'm currently reading the book Quantum Fields on a Lattice by I. Montvay and G.Münster, and in section 6.1 they describe lattice actions for various higgs models. And I got confused at the moment ...
- 343
1
vote
2
answers
165
views
Comparing "gauge theory" and "(global) spontaneous symmetry breaking"
To construct an effective field theory with spontaneously broken global symmetries, we need building blocks for the Lagrangian (such as covariant derivatives) that seem similar to gauge theory ...
- 213
2
votes
1
answer
158
views
Is there a general argument for why non-dynamical degrees of freedom show up in the propagation of massless gauge bosons?
In both spin-1 and spin-2 gauge theories, the gauge bosons (e.g. the photon & gluon and the graviton respectively) have two physical degrees of freedom, which can be observed quantum mechanically ...
- 858
4
votes
1
answer
130
views
Why is $Z_3= Z_\xi$ in a non-abelian gauge theory?
In my lecture notes for a course on QFT it is said that, also in non-abelian gauge theories, the identity $Z_3 = Z_\xi$ holds, where those renormalization parameters belong respectively to the ...
- 307
1
vote
0
answers
85
views
Global form of flavour symmetry groups in gauge theories
How do we work out the global nature of a flavour symmetry group? To be concrete, consider the simplest example of QED, preferably in D dimensions, with $N$ flavours of fermions with Lagrangian
$$\...
- 51