All Questions
Tagged with gauge-theory commutator
23
questions
0
votes
3
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32
views
Field strength tensor written as commutator of covariant derivatives in QED
I am currently trying to understand the derivation of the relation
$$
\begin{equation}
F_{\mu\nu} = \frac{1}{iq}[D_{\mu}, D_{\nu}]\tag{1}\label{eq1}
\end{equation}
$$
in QED and I have trouble with ...
- 3
2
votes
1
answer
56
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
1
answer
45
views
Commutation in the Local Gauge Transformations
Let's say that I have a Unitary Local Gauge Transformation $U$, in which the Lie Generators are $T$:
$$ \partial_{\mu} U = \partial_{\mu} e^{-i T^{a} \alpha_{a}(x)} = U \partial_{\mu} \left( -i T^{a} \...
user401884
0
votes
0
answers
81
views
Quantizing the electric field without quantizing vector potential
I am trying to quantize the electromagnetic field, without using the vector potential. I start with a Fourier expansion:
$$\begin{equation}
\vec{E}(\vec{r},t) = \sum_{\epsilon} \vec{\epsilon} \int \...
- 1,258
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
$$\mathcal{L}=-\frac{1}{4}(F^{\mu\nu})^2-|D_\...
- 133
0
votes
0
answers
33
views
Field Strength Tensor as Commutator [duplicate]
I'm studying QFT and am confused on the field strength tensor for some quantum field. I've seen the tensor written as the commutator of the covariant derivative $$-igF_{\mu\nu}=[D_\mu, D_\nu].$$ Is ...
- 500
0
votes
1
answer
56
views
Matrix representation for Gupta-Bleuler creation/annihilation operators
I am wondering what would be the closest analogue of the matrix representation for the creation and annihilation operators arising in Gupta-Bleuler formalism, which are defined by
$$
[a,a^\dagger] = -...
- 2,921
1
vote
0
answers
86
views
Commutator of gauge field and the scalar field in the Stueckelberg Lagrangian with gauge-fixing terms
I was trying to add a gauge fixing term to Stueckelberg Lagrangian and cancel the mixing term between scalar $\chi$ field and vector $A_\mu$ field.
$${\cal L}_{Stueckelberg} = -\frac{1}{4}V_{\mu\nu}V^{...
- 139
0
votes
1
answer
219
views
Commutator between covariant derivative and a field
I have field as an element of a Lie algebra as $\Phi = \phi^at^a$ and I want to calculate the commutator $$[D_{\mu}, \Phi],$$
with $$D_{\mu} = \partial_{\mu} + igA^a_{\mu}t^a,$$ the covariant ...
- 43
5
votes
2
answers
319
views
How are these Covariant Derivative Identities found?
In David Tong's Gauge Theory notes on page 137 near eq. (3.30) he makes use of the following expressions for the covariant derivative $D_{\mu}$
$$\frac{1}{2}[\gamma^{\mu},\gamma^{\nu}]D_{\mu}D_{\nu}=\...
- 123
2
votes
0
answers
162
views
Commutation relations in quantised Yang-Mills
Consider Yang-Mills theory with gauge group $G$. Let $\{T^a\}$ be a basis for the Lie algebra $\mathfrak{g}$, so that the connection coefficients can be written as $A_\mu = A_\mu^aT^a$.
In the ...
- 1,455
0
votes
1
answer
103
views
Trace of commutators with flavor indices
I want to explicitly write out the Lagrangian term
$$\operatorname{Tr}\bigg( \sum_{I\neq J}[\phi^I,\phi^J]^2\bigg) ,$$
where $I,J$ are flavor indices and $\phi$ is a scalar field. Why doesn't this ...
user214621
1
vote
0
answers
113
views
Commutators of covariant derivative and Yang-Mills Field Strength in curved spacetime
I am stuck with YM Field Strength and commutator. For example, in flat spacetime we have the commutator
$$F_{\mu \nu}=[\partial_{\mu}+A_{\mu},\partial_{\nu}+A_{\nu}] .$$ But what is the thing in ...
- 995
1
vote
1
answer
55
views
Integral eigenvalues in compact rank-2 symmetric $U(1)$ gauge theory
I am reading a paper related to rank-2 symmetric $U(1)$ gauge theory:
Fracton topological order from the Higgs and partial-confinement mechanisms of rank-two gauge theory (or arXiv:1802.10108).
My ...
- 508
2
votes
1
answer
287
views
Commutation relations in Gupta-Bleuler quantization
Quantization of the free electro-magnetic field has essential differences in comparison to quantization of say scalar or massive vector fields. In fact there are different approches to it.
One of ...
- 2,226