All Questions
18
questions
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
$$U_g(\Sigma_2)=\exp\...
- 133
2
votes
1
answer
216
views
What's the meaning of this path integral measure?
I don't understand the meaning of following path integral measure
$$
\frac{[df]}{U(1)}
$$
What is the difference between $[df]$ and $[df]/U(1)$? A naive idea is the latter measure is more physical ...
- 53
0
votes
1
answer
376
views
Ward identity of correlation function
For local observables $\{O_i(x_i)\}^n_{i = 1}$, one defines the Ward identity as
$$\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
1
vote
3
answers
233
views
What is a symmetry of the generating functional, and what is the significance?
I cannot find a definition for a symmetry of the generating functional in Quantum Field Theory:
$$ Z[J] = \int \mathrm d \mu \, \exp\left\lbrace i S[J] \right\rbrace \, .$$
I know it's a simple ...
- 1,387
14
votes
3
answers
3k
views
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
votes
1
answer
553
views
How to come up with Feynman rules: Proof of the multiplicity factor from functional derivative?
Consider $(\phi^*\phi)^2$ theory of complex scalar field. The goal is to come up with Feynman rules from functional derivatives, and the emphasis is on how does the symmetry factors or the ...
- 232
3
votes
1
answer
633
views
Path integral calculation in complex scalar field theory
I have some trouble understanding a particular expansion in my QFT lecture. Consider a complex scalar field $\phi$, with the Lagrangian
$$\mathcal{L} = \partial_\mu\phi^*\partial^\mu\phi-m^2\phi^*\phi....
- 1,215
4
votes
1
answer
721
views
Is there a formulation of Noether’s theorem for the path integral formalism?
The notion that conserved quantities (or quantities for which there is something like a continuity equation) correspond to symmetries of the action of a physical system can be formulated in various ...
- 6,763
2
votes
0
answers
258
views
Confusion about chiral anomaly (Fujikawa's method)
I am reading Fujikawa's method for calculating chiral anomaly, see this wiki page.
The method can be described as follows.
It starts with the path integral
\begin{equation}
Z=\int\mathcal{D}\psi\...
- 995
5
votes
0
answers
171
views
Symmetries in quantum field theory and anomalies
Suppose we have a lagrangian quantum field theory, thus a theory where we can write an action in the form
\begin{equation}
S = \displaystyle \int d^4 x \; \mathcal L \, \left( \partial_{\mu} \phi , \...
- 141
5
votes
0
answers
109
views
New symmetries upon quantization
In standard field theory texts, a “classical symmetry” is defined to be a transformation $\phi\to\phi’$ such that the corresponding action is left invariant. The symmetry is said to survive ...
- 8,490
6
votes
2
answers
194
views
Symmetries in QFT preserving only combination of action and measure
Could we list examples of symmetries that preserve only the combination of the measure $\mathcal{D}\phi$ together with $e^{-S}$ but not each on their own? (That is, symmetries which have no classical ...
- 867
5
votes
1
answer
1k
views
Calculating the numerical factor from Feynman diagram
I kind of understood the symmetry factor quite well. However, I just do not understand how one can relate the Feynman diagram to the term (especially the numerical factor in front of it) in the ...
- 518
17
votes
2
answers
441
views
Quantum symmetries: $S$ or $Z$?
Let $I$ be the action of some QFT (gauge-fixed and including all the necessary counter-terms); $S$ the associated scattering-matrix; and $Z$ the partition function (in the form of, say, a path ...
12
votes
3
answers
924
views
Why is there no anomaly when particle mechanics is quantized?
We know that if one or more symmetries of the action of a classical field theory is violated in its quantized version the corresponding quantum theory is said to have anomaly.
Is this a sole feature ...
- 26.8k