All Questions
11
questions
4
votes
1
answer
249
views
Symmetry implies Ward identity
I am thinking about symmetries and that their "quantum" consequences are Ward identities of the form $$<\beta|[Q,S]|\alpha>=0,$$ where $Q$ is the conserved charge associated with the ...
- 3,992
0
votes
0
answers
180
views
Proof of Weinberg effective field theorem?
In the book Effective field theory at page 6 there is this Weinberg's theorem
To any given order in perturbation theory, and for a given set of asymptotic states, the most general possible ...
- 445
4
votes
0
answers
97
views
Is crossing symmetry reliant on using the Feynman propagator?
If one used the advanced or retarded propagator instead of the Feynman propagator would crossing symmetry necessarily be violated in some scattering amplitudes?
- 2,270
0
votes
1
answer
196
views
Particle Creation by a Source
I am currently self-studying Quantum Field Theory and am using the textbook Introduction to Quantum Field Theory by Peskin and Schroeder. Currently I am in chapter 4, and am doing the first problem in ...
user261609
1
vote
0
answers
74
views
Why do we demand that symmetries commute with $S$-matrix?
I am working in the context of Wightman Quantum Field Theory, and under a symmetry group I understand a group together with a unitary projective representation on the projective Hilbert space, unitary ...
- 329
4
votes
0
answers
83
views
Time-independent source and quantum field theory
Can anyone explain the fundamental reason of why time-independent sources cannot emit or absorb energy. Does it have to do with time-translation symmetry and Noether's theorem?
I was studying the ...
- 369
4
votes
1
answer
185
views
Weinberg's Coleman-Mandula theorem proof sufficient condition for isomorphism?
In Weinberg's QFT Volume 3 book on Supersymmetry, he presents his own proof of the Coleman-Mandula theorem. As part of the proof, he proves that the only possible internal symmetry generators must ...
- 3,514
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 ...
3
votes
1
answer
167
views
Unit determinant for relevant symmetry groups in QFT
When treating QFT we want our theory to be invariant under different symmetry groups, for example, the Standard Model is a non-abelian gauge theory with the symmetry group $U(1)×SU(2)×SU(3)$. Moreover,...
- 975
6
votes
2
answers
488
views
If the S-matrix has symmetry group $G$, must the fields be representations of $G$?
If the fields in QFT are representations of the Poincare group (or generally speaking the symmetry group of interest), then I think it's a straight forward consequence that the matrix elements and ...
- 8,523
16
votes
2
answers
2k
views
CFT and the Coleman-Mandula Theorem
The Coleman-Mandula theorem states that under certain seemingly-mild assumptions on the properties of the S-matrix (roughly: one particle states are left invariant and the amplitudes are analytic in ...
- 161