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Physics

Questions tagged [gauge-invariance]

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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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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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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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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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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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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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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 ...
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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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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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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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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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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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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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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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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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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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