Questions tagged [gauge-invariance]
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.
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Gauge invariance in General relativity [duplicate]
Suppose a theoretical physicist wants to construct a theory to explain some newly discovered phenomenon. The new theory is expected to follow certain rules or fundamental principles. There are four ...
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8 votes
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Are there two meanings of small gauge transformations and why must we restric ourselves to transformations small in the first sense?
For the sake of context suppose a euclidean pure Yang Mills theory with gauge group SU(2) for the rest of this question. The terms large and small gauge transformations are used around in two ...
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Why does the boundary behavior of Lagrange multipliers matter for gauge vs global symmetries?
In Henneaux & Teitelboim (Quantization of Gauge Systems, p. 30), they discuss the variation of a dynamical variable $$ \delta F = \int d^nx\, u(x)\,\{F, C(x)\}_{PB},\tag{1.62} $$ where $C(x)$ is a ...
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Gauge Invariance and Degrees of Freedom [duplicate]
According to Wigner's classification, any massless particle (except for scalars) has 2 degrees of freedom i 4D. This reduction is usually understood in terms of gauge invariance. For instance, a ...
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$U(1)$: Gauge invariance
In Special Relativity, is it mathematically possible for a local, gauge-invariant field theory to have only one vector field $A_\mu$ and to have $U(1)$ symmetry, assuming the vector field $A_\mu$ and/...
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Could local charge conservation be violated by a moving point charge?
The charge density $\rho(\mathbf{x},t)$ and current density $\mathbf{j}(\mathbf{x},t)$ due to a point charge $q$ following a trajectory $\mathbf{r}(t)$ with velocity $\mathbf{v}(t)=d\mathbf{r}/dt$ is ...
2 votes
1 answer
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Why are classical gauge theories insensitive to large gauge transformations, while quantum gauge theories are affected by them?
In a previous question regarding large gauge transformations, one of the answers mentions that large gauge transformations are true redundancies for classical gauge theories, while they contain ...
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8 votes
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Why isn't gauge symmetry a symmetry while global symmetry is?
A typical opinion is that a gauge transformation doesn't change physical states, but a global transformation does. However, it's clear that global transformation is a subset of gauge transformation, ...
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Understanding the use of the Ward identities (in general and for an explicit example)
As the title suggests I am trying to understand the idea behind these identities and in order to do so, I will describe below, an example provided to us in the lecture. Once I understand how these ...
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1 vote
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Are there local transformations which leave the action invariant but are not gauge transformations?
For the sake of generality, I am not considering any specific scenario or field theory in particular. Instead, if we consider some arbitrary field theory of choice and also global and local ...
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2 votes
2 answers
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Unitary gauge and how to obtain a real representation from a complex one
I was reading an article by Weinberg that introduced the unitary gauge ("General Theory of Broken Local Symmetries", 1) at the classical level for a lagrangian $L$ of standard model-type, ...
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3 votes
1 answer
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Explanation of statement concerning static gauge in flat metric
I am reading Tong's notes about string theory, the second chapter, and I encountered this part that I don't know how is derived. We are considering the worldsheet $(\tau,\sigma)$ whose gauge we set to ...
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Quantum Electrodynamics from local gauge symmetry of Dirac Equation
I'm taking at look at QED foundations, and started thinking about how it relates to Dirac's Equation. Dirac spinors are invariant under a global phase transformation $\psi(x)\mapsto e^{i\alpha}\psi(x)$...
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6 votes
2 answers
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What constitutes an admissable gauge?
Consider the Lorenz gauge condition \begin{equation} \partial_\mu A^\mu = 0. \tag{1} \end{equation} Suppose there exists a field configuration $B^\mu$ that satisfies the Lorenz gauge, and another ...
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4 votes
2 answers
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Emergence of gauge invariance in QFT
This question is related to different motivations for the need of gauge invariance in QFT. I was introduced to gauge invariance in the following way. Consider a vector field $A^\mu(x)$, with $x\equiv ...
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