New answers tagged gauge-invariance
1
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Is First-Class Constraint Generator of matter Gauge Symmetry in EM example?
The solution to OP's problem is to include a pertinent matter sector in the E&M Lagrangian (3) (in OP's case: a complex scalar $\phi$). This produces the source term in the first-class secondary ...
- 207k
2
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Is First-Class Constraint Generator of matter Gauge Symmetry in EM example?
From @Andrew's comment, I know how to solve it.
In scalar QED, EM field would couple to current $J^{\mu}(x) = \phi^{\star}(x)\partial^{\mu}\phi(x) - \phi(x)\partial^{\mu}\phi^{\star}(x)$, and the ...
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Independence of $S$-matrix of $\xi$-gauge in QED
As far as I know, the rigorous proof of the LSZ formula fails in QED because of the photon cloud. Nevertheless, it still seems to work! We just have to physically assume that at $t\to\pm\infty$ the ...
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3
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Accepted
Analog between Electromagnetism and Gravity
In electromagnetism, if you have a
$$
\mathcal{L} = -\frac{1}{4} F^2 + A_\mu J^\mu
$$
where $F^2=F_{\mu\nu}F^{\mu\nu}$ is the Maxwell term ($F_{\mu\nu}=\partial_\mu A_\nu-\partial_\nu A_\mu$), the ...
- 51.2k
1
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Accepted
Writing gauge transformation of the gauge fields explicitly in terms of coordinates
Assume a field $\psi(x)$ transforming with respect to some arbitrary representation $$U(x)=e^{-i \alpha_a(x) T_a}, \qquad [T_a,T_b]= i f_{abc}T_c$$ of your gauge group. Defining the matrix-valued ...
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Writing gauge transformation of the gauge fields explicitly in terms of coordinates
Your derivative term should be
$$
(\partial_\mu g) g^{-1}.
$$
This combination is an element of the Lie algebra,and so expressible as a sum of the $t^\alpha$, unlike the group element $g$ itself.
It'...
- 54.5k
0
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How to find a covariant gauge derivative from a field transformation
I'll give the example for SU(N):
Consider a field $\Phi$ in the fundamental representation of SU(N) which means that $\Phi \to U \Phi$, with $U \in SU(N)$. Now consider how its ordinary derivative ...
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Misconceptions in spontaneous symmetry breaking
For completeness let us write down the potential
$$V(\phi)=-\mu^2\phi^2+\lambda \phi^4$$
In what follows we will use the term "invariant", which means: "does not change".
The ...
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