All Questions
21
questions
3
votes
0
answers
116
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Relation between chiral symmetry in condensed matter and chiral symmetry in QFT？
In QFT the chiral transformation (also called axial transformation) is:
$$\psi \rightarrow e^{-\theta \gamma_5}\psi$$
It is a global continuous phase transformation, where $\theta$ is an arbitrary ...
1
vote
0
answers
85
views
Global form of flavour symmetry groups in gauge theories
How do we work out the global nature of a flavour symmetry group? To be concrete, consider the simplest example of QED, preferably in D dimensions, with $N$ flavours of fermions with Lagrangian
$$\...
- 51
1
vote
1
answer
222
views
Is there (emergent) higher form spontaneous symmetry breaking in classical statistical field theory?
I was wondering if there are examples of (emergent) higher form spontaneous symmetry breaking (SSB) in classical statistical physics (finite temperature). I believe the deconfined phase of gauge ...
- 978
1
vote
2
answers
334
views
Why is a hole a time-reversed electron?
I am trying to understand a paper where the hole wavefunction is transformed into the electron wavefunction in a semiconductor using the time-reversal operator. None of my books mention this concept ...
- 2,122
3
votes
0
answers
69
views
Calculation of commutation relations in the SYK model
I'm reading this paper (https://arxiv.org/abs/1604.07818). And I'm having trouble showing an equality. We consider the following $SL(2,R)$ generators.
\begin{align}
D=-t\partial_t-\frac{1}{4},\ P=\...
- 125
7
votes
2
answers
824
views
Spontaneous symmetry breaking and conservation laws revisited
Crystalline solids spontaneous break the continuous translational and rotational symmetries. According to this lecture by Steven Kivelson, this means that conservation laws such as momentum and ...
- 26.8k
1
vote
0
answers
207
views
Action of 1-form symmetry
1) Free scalar field
Let me start with simple illustration, how charge constructed from current and how charge acts:
$$
S = \int d^dx\; \partial_\mu \phi \partial^\mu \phi
$$
We have obvious global ...
- 5,707
1
vote
0
answers
86
views
One Goldstone boson from breaking of two different symmetries
I am looking for examples where only one Goldstone boson appears after spontaneous breaking of 2 different symmetries.
In this post there is an answer why there are no Goldstone bosons for rotational ...
- 5,707
12
votes
1
answer
534
views
Trivial vs nontrivial TQFT
This question is inspired by Examples of "gauging a global symmetry" and answer to that question.
I list main statements from answer:
1) We start from free scalar field $\phi$ in d+1 ...
- 5,707
2
votes
0
answers
97
views
Relation between chiral symmetry and chiral material
There seems to be two types of chiral.
One chiral is usually referred to in terms of chiral symmetry or its breaking. It can be in the context of field theories where mass generation mixes left &...
- 3,701
0
votes
2
answers
764
views
How can we prove that correlation function depends only on the spatial difference if Hamiltonian is translationally invariant?
If $H$ is a translationally invariant Hamiltonian, how can I convince myself that the correlation function (on the ground state $\left|G\right\rangle$) $\left\langle G|\psi(x)\psi(x’)|G\right\rangle$ ...
- 43
5
votes
1
answer
218
views
Symmetry of a quantum Hamiltonian.
Consider the quantum Heisenberg model:
$$H=-J\sum_{\left< \vec r,\vec r'\right>} \hat S_\vec r\cdot \hat S_{\vec r'}\tag{1}$$
according to David Bar Moshe's answer on a related question this is ...
13
votes
2
answers
356
views
What is the physical implication(s) of the isomorphism between ${\rm SO}(2)$ and $\mathbb{R}/\mathbb{Z}$?
In the book Mathematical physics by V. Balakrishnan, he says (on page 329) that the isomorphism between ${\rm SO}(2)$ and $\mathbb{R}/\mathbb{Z}$, and the fact that $\mathbb{R}$ is the universal ...
- 26.8k
-1
votes
1
answer
341
views
Why the term 'hidden symmetry' is preferred compared to 'spontaneously broken symmetry'?
The word hidden symmetry gives me the impression that the symmetry is not actually broken. Let us consider the liquid to crystalline solid transition. It is quite clear that the continuous group of ...
- 26.8k
3
votes
1
answer
700
views
Are Goldstone bosons necessarily spin-0 particles?
EDIT: Bosonic fields with spin $s>0$ transform non-trivially under Lorentz transformation. Hence, if any of them acquires a VEV, that would violate Lorentz invariance as I learnt from the posts 1 , ...
- 26.8k