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Results tagged with gauge-invariance
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user 47373
Invariance of a physical system (its action) under a continuous group of local transformations underlain by a global symmetry whose group parameters fixed in space-time have now been extended to vary in space-time instead. Use for buildup of the invariance, fixing the gauge, and accounting for the corresponding changes in the functional measure of the system.
2
votes
0
answers
115
views
Unitarity Gauge : how to undo the gauge transformation
I will simplify the argument.
Let's consider a Gauge Boson (like the gauged one of U(1), $A_\mu$). Then, consider the Higgs boson with exponential representation, then $$H = e^{i\pi(x)/v}\left(\begin …
- 2,237
5
votes
1
answer
3k
views
Conserved current in scalar QED
Consider a theory of a free massless complex scalar $\phi$ which undergoes global $U(1)$ transformations. The conserved current associated to this symmetry is the usual scalar current
$$
J^\mu = i\le …
- 2,237
6
votes
1
answer
725
views
Non-local field redefinition and effects on path-integral measure
Consider the partition function
$$
Z[0] = \int \left[\mathcal{D}A_\mu\right]\left[\mathcal{D}\pi\right] e^{-i \int d^4x \left(-\frac{1}{2}(\partial\pi)^2-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+ \frac{a}{M^2 …
- 2,237
4
votes
Why do the right-handed up quark and down quark not form an $SU(2)$ doublet?
An important feature of the models you need to specify is the symmetry group and the representations under which the fields transform. The absence of $SU(2)_R$ doublets in the Standard Model can be se …
- 2,237
7
votes
1
answer
3k
views
Why do we impose de Donder gauge?
In the field language, a massless particle corresponds to irreducible representations of the Lorentz group. In particular, given a spin-2 massless particle, we can embed the creation and annihilation …
- 2,237
7
votes
Why do we impose de Donder gauge?
Actually this is not possible.
To impose the gauge $h=0$, I have to solve
$$
2\partial\cdot \epsilon = -h\,,\qquad\qquad (1)
$$
which always admits solutions.
This partial gauge fixing leaves a redund …
- 2,237