All Questions
Tagged with quantum-field-theory symmetry
433
questions
0
votes
0
answers
31
views
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 ...
2
votes
2
answers
80
views
How does inserting an operator in the path integral change the equation of motion?
I am reading this review paper "Introduction to Generalized Global Symmetries in QFT and Particle Physics". In equation (2.43)-(2.47), the paper tried to prove that when
$$U_g(\Sigma_2)=\exp\...
- 133
1
vote
2
answers
108
views
Checks of anomaly cancellation
In a textbook I read that if $G$ is a global symmetry of the classical Lagrangian, then one has to check $G\times H^2$ anomalies, where $H$ is one of the SM gauge groups.
For example, when $G$ refers ...
- 51
4
votes
1
answer
209
views
Is gravitational particle production due to symmetry breaking?
A well-known fact about QFTs in curved spacetimes is that there is a phenomenon of particle production in expanding universes, these being described by the line element $$ds^2=-dt^2+b^2(t)d\vec x^2.$$
...
- 503
1
vote
2
answers
122
views
Confusion about Higgs mechanism
I am trying to understand the mass acquisition of particles in the Standard Model based on the book 'Fundamentals of Neutrino Physics and Astrophysics' by C. Giunti, and several doubts have arisen ...
- 161
1
vote
0
answers
38
views
What is a gauge transformation? How does it relate to Cauchy intial value problem and second functional derivative of the action?
I am having conceptual problems about 'gauge transformation'. I have well heard that gauge trnasformation is a 'local symmetry' and 'fake symmetry', but I want to understand it more precisely.
I am ...
- 99
1
vote
0
answers
28
views
Tenfold way symmetry classification for systems with pseudomomentum
For classifying Hamiltonians $H(\vec{k})$ of topological insulators/superconductors in the tenfold way, one has to see whether the Hamiltonians obeys (disobeys) symmetries of the following type (let's ...
- 21
1
vote
1
answer
78
views
What implements finite conformal transformations in two dimensions?
In a two dimensional conformal field theory I have two sets of generators giving a representation of the Virasoro algebra
$$L_n, \bar{L}_n, n \in \mathbb{Z}$$
$$[L_n,L_n] = (m-n) L_{m+n} + c\frac{m(m^...
- 420
3
votes
0
answers
116
views
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 ...
4
votes
1
answer
121
views
How do we know at the operator-level that the tadpole $\langle\Omega|\phi(x)|\Omega\rangle=0$ vanishes in scalar $\phi^4$ theory?
I'm a mathematician slowly trying to teach myself quantum field theory. To test my understanding, I'm trying to tell myself the whole story from a Lagrangian to scattering amplitudes for scalar $\phi^...
- 421
0
votes
2
answers
69
views
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 ...
0
votes
2
answers
63
views
Are loops counted twice in Feynman diagrams?
Consider the 2 point function in $\phi^4$ theory which is given as something proportional to
$$\int D(x-z) D(y-z) D(z-z) d^4 z,$$
where $D$ is the propagator. The corresponding Feynman diagram looks ...
- 3,350
2
votes
2
answers
85
views
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:
$$G_n=\langle\phi^n\rangle_{J=0}=\frac{1}{Z[0]}\frac{\delta^nZ[J]}{\delta J^n}|_{J\...
- 368
2
votes
0
answers
113
views
Confused about square of time-reversal operator $T$
I am reading An Introduction to Quantum Field Theory by Peskin & Schroeder, and I am confused about what is the square $T^2$ of time reversal operator $T$.
My guess is that for $P^2$, $C^2$ and $T^...
- 613
1
vote
1
answer
79
views
Lie group symmetry in Weinberg's QFT book
In Weinberg's QFT volume 1, section 2.2 and appendix 2.B discuss the Lie group symmetry in quantum mechanics and projective representation. In particular, it's shown in the appendix 2.B how a ...
- 399
0
votes
0
answers
53
views
What is the allowed operator in a global/ local theory?
While I'm reading Hong Liu's notes, it says:
Now we have introduced two theories:
(a)$$\mathcal{L}=-\frac{1}{g^2}Tr[\frac{1}{2}(\partial \Phi )^2+\frac{1}{4}\Phi^4]$$
(b)$$\mathcal{L}=\frac{1}{g^2_{...
- 368
6
votes
1
answer
355
views
Can we define topological order in the context of QFT?
Topological order is defined to be a phase that has ground state degeneracy (GSD) not described by the Landau SSB paradigm but exhibits some Long Range Entanglement property. Mathematically, it is ...
- 141
0
votes
2
answers
122
views
What symmetry present in a low energy theory is broken or not exact at high energies?
The opposite is quite common such as EWSB, SUSY or GUT. Is there any example where a certain symmetry emerges from a low energy effective theory but is not present in the high energy theory?
- 195
2
votes
1
answer
216
views
What's the meaning of this path integral measure?
I don't understand the meaning of following path integral measure
$$
\frac{[df]}{U(1)}
$$
What is the difference between $[df]$ and $[df]/U(1)$? A naive idea is the latter measure is more physical ...
- 53
2
votes
1
answer
199
views
Approximating the $U(1)$ Schwinger model with a $\mathbb{Z}_2$ symmetry
The Schwinger model or $(\text{QED})_2$ essentially is quantum electrodynamics defined in $1 + 1$ spacetime dimensions. In https://arxiv.org/abs/2305.02361 they use the Hamiltonian formulation to ...
- 119
4
votes
2
answers
131
views
Miraculous cancellations in a-priori non-renormalizable theories
Einstein's gravity is non-renormalizable since its coupling constant in 4D (I would like to limit the discussion to 4D) has negative mass dimension of -2.
Nevertheles it has been hoped that -- may be ...
- 9,778
0
votes
1
answer
196
views
Proper definition of spontaneously broken symmetry
I am currently working on generalized symmetries and i was reading https://arxiv.org/abs/2301.05261. In footnote 23 the authors state:
To
be precise, by spontaneous symmetry breaking, we mean
a phase ...
3
votes
0
answers
66
views
Consequences for symmetries of the equations of motion in QFT
In general, if a Quantum Field Theory is described by a Lagrangian $\mathcal{L}$, the symmetries of $\mathcal{L}$ lead to classically conserved currents along the equations of motion and Ward ...
- 370
2
votes
1
answer
243
views
Some question about the irreducible representation of Poincare group
I am writing a note about the Poincare group and I am trying to explain that argument that one-particle state transforms under irreducible unitary representations of the Poincare group. However, there ...
- 546
1
vote
1
answer
214
views
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
votes
1
answer
376
views
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
0
votes
0
answers
69
views
Quantum (higher-form) anomaly at finite temperature
At finite temperature, anomaly is generally known to be contaminated, and thus the 't Hooft anomaly matching does not work after thermal compactification. Meanwhile, I have read paper saying that ...
- 81
2
votes
1
answer
59
views
Why $|H_1(\Sigma,\mathbb{Z}_N)|$ can be interpreted as an 1+1d $\mathbb{Z}_2$ gauge theory?
I am reading the article https://arxiv.org/abs/2204.02407, and I am struggling with the definition of a condensation defect, which is given by
\begin{align}
S(\Sigma)=\frac{1}{\sqrt{|H_1(\Sigma,\...
- 451
2
votes
1
answer
198
views
Symmetry Factor and Wicks Theorem
I have a problem with a particular kind of exercise. The question is:
Consider $\phi^4$-theory with $\mathcal{L}_\text{int}=-\frac{\lambda}{4!}\phi^4$. Give the symmetry factors of the diagram and ...
- 23
4
votes
2
answers
510
views
Please help me to understand calculation of the symmetry factor of Feynman diagrams (Lancaster & Blundell's Quantum field theory)
I am reading the Lancaster & Blundell's Quantum field theory for the gifted amateur, p.183, Example 19.5 (Example of symmetry factors of several Feynman diagrams) and stuck at understanding ...
- 323