All Questions
21
questions
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Lorentz transformation of Creation and Annihilation operators for a real scalar field theory - MIT OCW QFT I Problem set 3 [closed]
I have been working through the MIT OCW's QFT lecture notes and problem sets, but I have come to realize that I have a fundamental misunderstanding of what is meant by how objects transform under ...
1
vote
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
3
votes
1
answer
454
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Translation invariance in QFT
In P&S's QFT book, page 213, the book considered Heisenberg operator's translation under General interacting field:
$$ \begin{aligned}
\left\langle\Omega|\phi(x)| \lambda_{\mathbf{p}}\right\rangle ...
- 1,421
2
votes
1
answer
105
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Field exchange symmetry
I have a pheraps stupid doubt regarding the existence of a symmetry. Consider a theory such as:
$$\mathcal{L}= \frac{1}{2}(\partial_\mu\phi)^2+\frac{1}{2}(\partial_\mu\psi)^2+\phi^2\psi^2$$
With some ...
- 2,263
2
votes
1
answer
445
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Spontaneous symmetry breaking, massless bosons and the equations of motion
I am currently studying spontaneous symmetry breaking, and I don't entirely understand the implications of what we are doing at certain places. Consider the standard complex scalar field with the $\...
- 107
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1
answer
378
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Symmetry breaking for 4 scalar fields
So I've been trying to get familiar with concept of symmetry breaking with minimal experience with field theory and I've got stuck on, I think, a simple problem.
Let's consider four scalar fields $\...
- 3
7
votes
2
answers
824
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Spontaneous symmetry breaking and conservation laws revisited
Crystalline solids spontaneous break the continuous translational and rotational symmetries. According to this lecture by Steven Kivelson, this means that conservation laws such as momentum and ...
- 26.8k
1
vote
1
answer
174
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What is the difference between local and global symmetries in terms of properties of the particle spectrum?
I know that a global symmetry implies the presence of a conserved charge but how it does affect the particle spectrum? and in this sense what is the difference with a gauge symmetry?
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4
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2
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244
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What causes the evasion of the Goldstone theorem here?
For simplicity, I'll consider perhaps the simplest possible example of a gauge theory.
Consider a spontaneously broken ${\rm U(1)}$ gauge theory of a charged scalar field coupled to the ...
- 26.8k
3
votes
1
answer
153
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Vacuum Manifold of $U(1)$ theory and Goldstone theorem
I want to know if my understanding of the Goldstone theorem is correct.
What I know is that the number of Goldstone is equal to the rank of $G/H$ where $G$ is the symmetry of the Lagrangian before ...
- 311
12
votes
1
answer
534
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Trivial vs nontrivial TQFT
This question is inspired by Examples of "gauging a global symmetry" and answer to that question.
I list main statements from answer:
1) We start from free scalar field $\phi$ in d+1 ...
- 5,707
1
vote
0
answers
36
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Symmetry of theory on static electric field background
Let's consider complex scalar field in static homogeneous background electric field $E_z = E = const$, or in terms of vector potential $A_z = -Et$ or in another gauge $A_0 = -Ez$.
Without electric ...
- 5,707
4
votes
1
answer
761
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Parity Invariance Complex Scalar Field Lagrangian
I am trying to prove the parity invariance of some terms in a complex scalar field Lagrangian, for example $m^2 \; \phi^* \phi$ or $\partial_{\mu} \phi \;\partial^{\mu} \phi^*$. So what I want to ...
- 900
0
votes
0
answers
654
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Shift symmetry and vacuum expectation values
I have come across theories with a Nambu-Goldstone boson $\phi$ originating from a broken $U(1)$ symmetry where there is a leftover shift symmetry $\phi \rightarrow \phi + \alpha$ (and possibly other ...
- 780
6
votes
1
answer
2k
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Action of 1-form symmetry in Maxwell theory
I am reading Lectures on Gauge Theory by David Tong.
In 3.6.2 first example that the author talk about pure $U(1)$ gauge theory in 4D. In this example, he talk about two 1-form symmetries:
1) ...
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