All Questions
Tagged with quantum-field-theory gauge-theory
725
questions
2
votes
1
answer
55
views
Causality for gauge dependent operators in quantum field theories
Suppose that $\mathcal{A}_{ij...}(x)$ and $\mathcal{B}_{ij...}( x')$ are two gauge dependent (so non-observable) operator in some theory. If they are spacelike, should I impose the causality ...
- 43
0
votes
3
answers
214
views
2+1-dimensional $SU(N)$ Yang-Mills Theory
In recent years, there has been significant progress and growing interest in conducting quantum simulations of field theories using quantum devices. This typically involves formulating a Hamiltonian ...
- 857
1
vote
1
answer
50
views
Reference request: scalar $O(N)$ gauge theory
I am interested in scalar $O(N)$ gauge theory and what you can do with it. Is there a standard reference section in a textbook/monograph/paper/whatever that has a decent overview?
Wikipedia has a ...
2
votes
1
answer
90
views
Understanding the Gaussian weight and the parameter $\xi$ when quantizing gauge theories
In section 9.4 of Peskin & Schroeder's textbook on quantum field theory, when applying the Faddeev Popov procedure to quantize an Abelian gauge theory, they obtain the following functional ...
- 3,350
3
votes
0
answers
73
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
$$
\begin{aligned}
A^\mu_B &= \sqrt{Z_A} A^\mu\,, \quad \...
- 51
3
votes
1
answer
96
views
Are Higgs mechanism and SSB different phenomena?
In the Standard Model, the Higgs mechanism is associated with the Spontaneous Symmetry Breaking (SSB).
My understanding is that it is the Higgs field which breaks the $SU(2) \times U(1)$ symmetry at a ...
- 1,665
2
votes
0
answers
64
views
Masses of $SU(2)$ gauge bosons
I'm currently learning quantum field theory and I'm wondering one thing.The way I understood it is that in the $SU(2)$ Yang-Mills theory, all gauge bosons have the same mass due to the spontaneous ...
- 41
2
votes
1
answer
72
views
Topological behavior (or asymptotics at infinity) of gauge fields assumed in Fujikawa method
Chiral anomaly is computed very elegantly by Fujikawa method, which is also presented in Section 22.2 of Weinberg QFT textbook volume 2 or wikipedia.
Here, the underlying spacetime is assumed to be $\...
- 1,665
1
vote
0
answers
38
views
Loop Calculations of A Spontaneous Broken gauge theory with fermions
Let me first rephrase the background. Consider adding a massless fermion to the spontaneously broken $U(1)$ gauge theory through a chiral interaction:
$$
\mathcal{L}=\bar{\psi}_{L}i \gamma_{\mu}D^{\mu}...
- 81
0
votes
1
answer
58
views
Visualization of a gauge field with non-null winding number
In QCD you may add the term $\mathcal{L}_{\theta} = \theta\dfrac{g^2}{16\pi^2} \text{Tr}F\tilde{F}$, which turns out to be a total derivative. Now, it can be proven that the action of this lagrangian ...
- 1,452
1
vote
0
answers
58
views
Unitarity and renormalizability in $R_\xi$ and 't Hooft gauge
Consider the massive propagator with gauge fixing $\frac{1}{2a} (\partial A)^2$
$$
\Delta_{\mu\nu}=-i\left[\frac{g_{\mu\nu}}{k^2-m^2}-\frac{k_\mu k_\nu}{m^2}\left(\frac{1}{k^2-m^2}-\frac{1}{k^2-am^2}\...
- 534
1
vote
0
answers
38
views
What is a gauge transformation? How does it relate to Cauchy intial value problem and second functional derivative of the action?
I am having conceptual problems about 'gauge transformation'. I have well heard that gauge trnasformation is a 'local symmetry' and 'fake symmetry', but I want to understand it more precisely.
I am ...
- 99
3
votes
1
answer
58
views
Why semi-simple and compact Gauge Group in YM Theory? [duplicate]
I'm studying the Yang-Mills theory, with the Action:
$$
S=-\frac{1}{2}\int\mathrm{tr}_{\rho}(\mathcal{F}\wedge\star\mathcal{F})
$$
where $\mathcal{F}:=\mathrm{d} \mathcal{A}+\frac{1}{2}[\mathcal{A},\...
- 77
2
votes
1
answer
74
views
Why the expectation value of three currents is important in the anomaly?
I am studying the anomalies chapter (Chapter 30) of Schwartz's [Quantum Field Theory and the Standard Model]. I want to ask why the expectation of three currents, $\langle J^\mu J^\nu J^\rho \rangle$, ...
- 79
4
votes
1
answer
103
views
How are the gauge transformations of $\epsilon(\mu)$ and $A^\mu$ related?
To find a local field description of massless spin-1 particles that is Lorentz invariant, we can identify $\epsilon^\mu_{\pm}(k)$ with $\epsilon^\mu_{\pm}(k)+\alpha(k)k^\mu$. As $A^\mu$ and $\epsilon^\...
- 1,783