All Questions
Tagged with group-theory quantum-field-theory
263
questions
2
votes
0
answers
35
views
A reference for the fact that the second cohomology of the full Poincare algebra is zero
S. Weinberg in his book "The quantum theory of fields" vol. I says in page 86 that the full Poincare algebra is not semi-simple but its central charges can be eliminated (as he showed in the ...
- 374
1
vote
0
answers
44
views
One-Loop beta function for gauge couplings
I am currently doing my homework on Standard Model one-loop correction. When I am reading Quantum Field Theory by Mark Srednicki and Journeys Beyond the Standard Model by Pierre Ramond, I notice some ...
- 81
3
votes
1
answer
58
views
Why semi-simple and compact Gauge Group in YM Theory? [duplicate]
I'm studying the Yang-Mills theory, with the Action:
$$
S=-\frac{1}{2}\int\mathrm{tr}_{\rho}(\mathcal{F}\wedge\star\mathcal{F})
$$
where $\mathcal{F}:=\mathrm{d} \mathcal{A}+\frac{1}{2}[\mathcal{A},\...
- 77
0
votes
1
answer
95
views
In QFT when performing path integral, why don’t we divide it by the volume of Poincaré group, as what we did for gauge group?
When performing path integral in gauge theory, we naively want to compute
$$
Z = \int DA \exp(iS[A])
$$
But we noticed, that because the action is the same for gauge equivalent conditions, we should ...
- 99
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
2
votes
0
answers
95
views
Why representations? [duplicate]
I've been studying Talagrand's What is a Quantum Field Theory? lately and I have some questions regarding the scheme he presents.
Essentially the state of affairs as of where I am in the book is that ...
- 873
9
votes
6
answers
2k
views
What exactly is a quantum field?
As I understand it, a relativistic quantum field is an operator-valued function of spacetime that transforms under some finite dimensional irreducible representation of the Lorentz* group:
\begin{...
- 904
2
votes
1
answer
126
views
In what sense are fields representations of the Poincare group?
As far as I know, a representation is a homomorphism from the group to a vector space $V$ which preserves the group multiplication, i.e., if $(\pi,V)$ is a representation of the group $G$, then ...
- 904
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
0
votes
1
answer
127
views
Simple definition for the generator of an infinitesimal transformation
Studying quantum mechanics, or QFT, the concept of generator $G$ of an infinitesimal transformation $T$ keeps showing up. My problem is that I don't have in mind a solid (dare I say "rigorous&...
- 4,577
0
votes
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187
views
Represent the Pauli 4-vector $\sigma^\mu$ as hermitian matrix of matrices due to the $SL(2,C)$ universal double cover of $SO^+(3,1)$
It's known that it's possible to map a 4-vector $x^\mu=(t,x,y,z)$, here i use $c=1$, into a 2x2 hermitian matrix as linear combination of Pauli matrices, thus the mapping $x^\mu \leftrightarrow X$. ...
- 310
0
votes
0
answers
47
views
Why are the expressions of the Skyrme Model related with a kinetic and a mass term?
I was reading about the Syrme Model Lagrangian,
$$
\mathcal{L} =-f^2_\pi/4 Tr(L_\mu L^\mu) + 1/32e^2 Tr([L_\mu,L_\nu]^2)- \frac{\mu^2}{2} Tr(1-U)
$$
where $L_\mu=U^\dagger \partial_\mu U$. I've read ...
- 161
3
votes
1
answer
112
views
Quantization of charge from the path integral
Consider a complex scalar field, with the usual Lagrangian:
$$
\mathcal{L} = | \partial_{\mu} \phi|^2 - V(|\phi|^2).
$$
This theory has a $U(1)$ symmetry, $\phi \to e^{i \alpha} \phi$, and the ...
- 3,098
1
vote
0
answers
76
views
Why do we need to consider the full Poincare group to get unitary representations?
I am trying to study and understand QFT from the perspective of symmetries. I was referred to this super helpful answer by @ACuriousMind : https://physics.stackexchange.com/a/174908/50583. I still ...
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