All Questions
Tagged with gauge-theory special-relativity
32
questions
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
2
answers
75
views
Gauge transformation with harmonic one-form
The electromagnetic four-potential $A^{\mu}$ is not uniquely determined by the physical situation. We have the equation $$\partial^{\mu}A^{\nu}-\partial^{\nu}A^{\mu}=F^{\mu\nu}.$$
Here $F^{\nu\mu}$ is ...
- 1,440
0
votes
1
answer
95
views
In QFT when performing path integral, why don’t we divide it by the volume of Poincaré group, as what we did for gauge group?
When performing path integral in gauge theory, we naively want to compute
$$
Z = \int DA \exp(iS[A])
$$
But we noticed, that because the action is the same for gauge equivalent conditions, we should ...
- 99
1
vote
0
answers
81
views
Why can't we gauge the Lorentz group? (Or can we?)
One of the (many different, somewhat independent) routes to gauge theory is to start from a global symmetry of some kind and "gauge" it, which involves promoting it to a local symmetry and ...
- 858
2
votes
4
answers
271
views
What is the physical significance of $\mathbf{E}^2-\mathbf{B}^2$ in E and M?
Choosing nice units, i.e $c=1$, the electromagnetic energy density is:
$$u=\frac{1}{2}\left(\mathbf{E}^2+\mathbf{B}^2\right).$$
This is not Lorentz invariant, which makes sense since our ...
- 269
5
votes
0
answers
215
views
Embedding $h = \pm 2$ gravitons into the $\left(1,1\right)$ Lorentz representation
I've read from Figueroa-O'Farrill's The Theory of Induced Representations in Field Theory and this answer that massless particles of helicity $h$ must be associated with fields transforming under the $...
- 737
1
vote
0
answers
105
views
Lorentz invariance of Quantum Electrodynamics [closed]
In chapter 5 of Weinberg QFT (Vol.$1$), in section 5.9, Weinberg demonstrated through an explicit calculation that there cannot be a massless vector field with helicities $\pm 1$. In fact, Weinberg ...
- 789
0
votes
1
answer
472
views
How local gauge invariance explain charge conservation and electromagnetic force appearance?
Without electromagnetic coupling, the QM charged particle wave function is not invariant under a local gauge transformation — one with a phase that depends
on space (space-time):
\begin{equation}
\psi ...
- 2,635
2
votes
0
answers
135
views
Cauchy problem of classical Maxwell equations in Minkowski spacetime
I'm wondering a bit about the classical Maxwell equations in flat spacetime and their Cauchy problem. For the following, I suppose that the sources are already given and don't react to their own ...
- 7,592
1
vote
0
answers
29
views
Can we study invariance of field theories under local Lorentz transformations?
Local internal symmetry transformations, where the group parameters are allowed to become functions of spacetime, has led to successful quantum field theories of electromagnetic, weak and strong ...
- 11.8k
9
votes
1
answer
1k
views
General relativity as a gauge theory of the Poincaré algebra
Let the Poincaré algebra be given without any factors of i as
$[P_\mu,P_\nu]=0$,
$[M_{\rho \sigma},P_\mu]=\eta_{\sigma\mu}P_\rho-\eta_{\rho\mu}P_\sigma$,
$[M_{\mu\nu},M_{\rho\sigma}]=\eta_{\nu\rho}...
- 1,031
1
vote
0
answers
77
views
Lorenz Gauge and Pauli-Lubanski vector
I am trying to understand the origin of the gauge condition $\partial^{\mu}A_{\mu}=0$. For the polarization 4-vector, $\epsilon_{\mu}$, the equivalent statement would be $k^{\mu} \epsilon_{\mu}=0$, ...
- 329
11
votes
1
answer
2k
views
Connection between gauge invariance and Lorentz invariance
This question is presented in the context of Weinberg's QFT book treatment, in particular considering the electromagnetism chapter.
It begins in Chapter 3 where Weinberg argues that in order to have ...
- 36.4k
0
votes
1
answer
199
views
Does the Vector Potential Coil and Transformer Violate Special Relativity?
"Vector Potential Coil and Transformer" by M. Diabo et al reports the induction of voltage by a time varying curl free vector potential. A refinement reported in "Vector-Potential Coil and ...
- 1,357
0
votes
0
answers
190
views
Gauge invariant and Lorentz invariant in Weinberg's QFT textbook (eq. 8.1.5)
In Weinberg's QFT textbook, using a gauge transformation $$A_{\mu}(x) \rightarrow A_{\mu}(x) + \partial_{\mu}\epsilon(x)\tag{8.1.3},$$ it has:
$$\delta I_{M} = \int d^4 x \frac{\delta I_{M}}{\delta A_{...
