All Questions
Tagged with correlation-functionss-matrix-theory
89 questions
0votes
2answers
71views
Diagrammatic interpretation of the four-point correlation function in momentum space
In Peskin & Schroeder's book (chapter 7.2,p227), they claim that the exact 4-point function, expressed by $$ \left( \prod_{i=1}^{2} \int d^4 x_i \, e^{i p_i \cdot x_i} \right) \left( \prod_{i=1}^{...
- 726
10votes
0answers
254views
Why can we extract the value of $S$-matrix element by simply analyzing the pole of correlation function?
In Peskin & Schroeder's book (Chapter 7.2, p.223-226), they analyze the pole of the correlation function by discarding the exponential term. They first calculate the accurate value of the ...
- 726
0votes
1answer
84views
Dividing multi-particle states into a sum of states with particles of definite number
In Peskin & Schroeder's book (7.1 , p212) in the studying of the analytic structure of two-point correlation function, they generalize the completeness relationship of 1 particle states $$ \left( ...
- 726
4votes
2answers
202views
Renormalization constant $Z$ in LSZ formula and field renormalization
In the demonstration of the formula LSZ it is assumed that the fields in the Heisenberg representation tend to the asymptotic fields multiplied by a constant $\sqrt{Z}$; through the Källén-Lehmann ...
1vote
0answers
25views
Zero-component of quadri-momenta and dispersion relation for 2-to-2 scattering
I posted this question yesterday, Complex integral (residue method) in lattice quantum field theory and I found out a way the integral will be solved as in the reference, but to do that, I should ...
2votes
0answers
59views
Complex integral (residue method) in lattice quantum field theory
I was studying this reference https://arxiv.org/abs/1901.00483 and i'm stucked on this passage: at page 5 it defines $\mathcal{M}_{2L}$ in a $\lambda\phi^4$ theory and then he says to perform the ...
1vote
0answers
40views
The Optical theorem: P&S section 7.3 [closed]
I'm studying about the optical theorem in QFT with P&S textbook. I was trying to find the discontinuity of $\mathcal{M}(s)$ in $\phi^4$- theory (p.233). More specifically, I was calculating the ...
1vote
0answers
63views
Does vacuum expectation values of field operators contain all the information of the quantum field theory?
It is a very general question in the field theory context. It means whether anything that we can compute with a canonically quantized Hamilton, can be computed from the generating functional with an ...
- 401
4votes
0answers
84views
Analytic continuation of $\mathcal{M}$ in Peskin and Schroeder QFT book
In Peskin and Schroeder QFT book on page 232 they define $\mathcal{M}(s)$, the $S$-matrix element, to be defined by the Feynman rules, where $s=E^2_{cm}$ can have complex values. Let $s_0$ be the ...
- 543
1vote
1answer
74views
Do all possible theories of quantum gravity have amplitudes?
There are many possible models of quantum gravity, some more developed than others (including: String theory, M-theory, supergravity, loop quantum gravity, causal sets, causal dynamical triangulation, ...
- 3,018
1vote
0answers
109views
Reflection positivity and $i\epsilon$ in Green's function
There are several ways to tell you why there is $i\epsilon$ in physical Green function, like from direct derivation of $\langle\Omega|\text{T}{\phi(x)\phi(y)}|]\Omega\rangle$, or from path integral ...
- 976
2votes
1answer
174views
Schrodinger's picture and Heisenberg's picture in finding interaction ground state and two-point correlator
In section 4.2 of An Introduction to Quantum Field Theory by M.E.Peskin and others, it derives interaction ground state by observing the time evolution of ground state in free field theory (pg.86), ...
- 976
3votes
0answers
297views
LSZ reduction formula and connected Feynman diagrams in Peskin & Schroeder [duplicate]
I don't understand why in the LSZ reduction formula I need to consider only connected Feynman diagrams when I compute scattering amplitudes. From what I read in Peskin & Schroeder it seems that ...
- 421
1vote
0answers
60views
How to apply multiple Klein-Gordon operators to products of propagators?
I have the 4-point correlation function for a scalar free field $$ \langle{0} | T \phi_1 \phi_2 \phi_3 \phi_4 | 0 \rangle = -\left[ \Delta_F(x_1-x_2) \Delta_F(x_3-x_4) + \Delta_F(x_1-x_3) \Delta_F(x_2-...
- 611
19votes
2answers
1kviews
What physical processes other than scattering are accounted for by QFT? How do they fit into the general formalism?
For background, I'm primarily a mathematics student, studying geometric Langlands and related areas. I've recently been trying to catch up on the vast amount of physics knowledge I'm lacking, but I've ...
- 191
