All Questions
42
questions
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What is a gauge transformation? How does it relate to Cauchy intial value problem and second functional derivative of the action?
I am having conceptual problems about 'gauge transformation'. I have well heard that gauge trnasformation is a 'local symmetry' and 'fake symmetry', but I want to understand it more precisely.
I am ...
- 99
0
votes
2
answers
69
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Variation in the context of symmetries
I’m rephrasing a suggestion as a question because there was an aspect to it where I wanted to know more as well.
I have studied both general relativity and particle physics, though in both cases my ...
2
votes
2
answers
85
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Why $n-1$ point function vanishes in $D=0$ scalar theory?
If we consider a $D=0$ theory with the Lagrangian:
$$\mathcal{L}[\phi]=g\phi^n+J\phi$$
And its Green functions:
$$G_n=\langle\phi^n\rangle_{J=0}=\frac{1}{Z[0]}\frac{\delta^nZ[J]}{\delta J^n}|_{J\...
- 368
1
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1
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214
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Symmetry groups breaking for the lagrangian of two complex scalar fields
Suppose we have a generic non-interacting Lagrangian of two complex scalar fields,
\begin{align}
\mathcal{L} &= (\partial^\mu \Phi^\dagger)(\partial_\mu \Phi) - \Phi^\dagger\mathbb{M}^2\Phi \tag{1}...
- 1,783
0
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1
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376
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Ward identity of correlation function
For local observables $\{O_i(x_i)\}^n_{i = 1}$, one defines the Ward identity as
$$\partial_{\mu}\langle j^{\mu}(x)\prod^n_{i = 1}O(x_i)\rangle = \sum^n_{i = 1}\delta(x-x_i)\langle O_1(x_1)\cdots\...
user361492
1
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0
answers
40
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Does Elitzur's theorem say anything about theories which are NOT gauge theories?
Does Elitzur's theorem say anything about theories which are NOT gauge theories? I was wondering what happens if one considers scalar sector, or massive spin-1 field with a bare mass included in the ...
- 153
1
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3
answers
204
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Why the symmetry of $\phi^4$ excludes the odd diagams?
I have a follow-up question from this post:
Suppose
$$
L\supset \lambda\phi^4
$$
This term is invariant under $\phi\rightarrow-\phi$, Peskin and Schroeder (p.323) said this implies that all amplitudes ...
- 1,783
2
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0
answers
52
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Do Ward identities imply that there is an (effective) Lagrangian invariant under the symmetry?
In usual perturbative QFT, if the UV Lagrangian is invariant under a symmetry $G$ and the regularization of the path integral does not break $G$, the Feynman rules are explicitly invariant under $G$. ...
- 461
14
votes
3
answers
3k
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How are anomalies possible?
From Matthew D. Shwartz Quantum Field Theory textbook, he writes:
"Most of the time, a symmetry of a classical theory is also a symmetry of the quantum theory based on the same Lagrangian. When ...
- 2,599
5
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2
answers
318
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Symmetry factors in two interacting fields
Red and blue colored lines represent the two different fields.
At 1st order, by the exchange of the blue legs and red legs we get $\frac{1}{4}$ factor and in one of the 2nd order term drawn above, ...
- 3,464
-1
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1
answer
161
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Is the Standard Model, in some sense, special relativity plus everything possible?
I found this intro to QFT on YouTube really helpful (and apparently I'm not the only one). Let my try to summarize it:
We start with Minkowski space. We want to add a field to it, but there are only ...
- 2,475
3
votes
1
answer
327
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How can Chiral symmetry protect the mass of a fermion if it's broken by quantization?
Suppose we have a Lagrangian invariant under Chiral symmetry, such as QED with massless fermions:
$$ \mathscr{L} = -\frac{1}{4} F_{\mu \nu} F^{\mu \nu} + \bar{\psi} i \gamma^{\mu} D_{\mu} \psi .$$
In ...
1
vote
1
answer
223
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Symmetry protects against symmetry-breaking counterterms in renormalization
My lecturer said that when we renormalize a theory (any theory, not necessarily a renormalizable one) we can do so by adding counterterms to the original Lagrangian $\mathscr{L}_B$, turning it into $\...
0
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1
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195
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$\phi^4$ theory in 5 dimensions
$\phi^4$ theory is not perturbatively renormalizable in 5 dimensions.
I have come across literature where renormalizability is discussed w.r.t $N$, for fields obeying $O(N)$ symmetry. But it is not ...
- 1,023
2
votes
1
answer
741
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What is an accidental symmetry?
Wikipedia describes an accidental symmetry as
a symmetry which is present in a renormalizable theory only because the terms which break it have too high a dimension to appear in the Lagrangian
but I ...
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