1
vote
1answer
62 views

Scattering theory textbooks

I am looking for a possibly extensive list of great textbooks on elastic and inelastic scattering of particles within quantum field theory. So far I am familiar with: Peskin and Schroeder: An ...
7
votes
2answers
214 views

How to replace $T$-product with retarded commutator in LSZ formula?

I am reading Itzykson and Zuber's Quantum Field Theory book, and am unable to understand a step that is made on page 246: Here, they consider the elastic scattering of particle $A$ off particle $B$: ...
0
votes
1answer
77 views

Green functions in QFT

What is the sense of Green function $$ \langle | \hat {T}(u_{1}(x_{1})...u_{n}(x_{n})\hat {S})|\rangle , \quad \hat {S} = \hat{T}e^{i\int \hat {L}(x)d^{4}x} ? $$ How is it connected with scattering ...
1
vote
1answer
107 views

quantum theory of light

What's the scattering matrix for a PBS (polarization beam splitter) ? Is it just unitary ? If one polarization never couples into another polarization (then there's a lot of zeroes in that 4x4 matrix) ...
2
votes
2answers
105 views

Lippman-Schwinger Equation with Outgoing Solutions

I'm reading about Green's functions and how the Lippmann-Schwinger equation eventually leads to the textbook expression for the form of scattered wavefunctions by a central potential in the far ...
4
votes
1answer
125 views

A question about the energy of turning on and off interaction adiabatically in QFT

I read a saying as follows: In a theory with no particles which decay and no bound states, the turning on and off of the interactions merely serves to limit the effective range of forces. In this ...
1
vote
0answers
75 views

Scattering theory of Dirac equation in curved space-time in presence of a strong magnetic field

What is the exact solution of the Dirac equation in curved space-time in the presence of a strong magnetic field? The solution should be in momentum space for simplicity to calculate scattering cross ...
8
votes
1answer
193 views

There are two definitions of S operator (or S matrix) in quantum field theory. Are they equivalent?

I read several textbooks of QFT and found that there are two kinds of definition of $S$ operator (or S matrix). First kind: Define $\hat{S}$ is map from out space to in space ...
2
votes
1answer
96 views

Materials about S-matrix and S-matrix theory

What is the best book or paper to learn about analytical structures of S-matrix and S-matrix theory? I already know books as The Analytic S-matrix by RJ Eden, PV Landshoff, DI Olive, JC P and Quantum ...
8
votes
1answer
417 views

Green's function in path integral approach (QFT)

After having studied canonical quantization and feeling (relatively) comfortable with it, I have now been studying the path integral approach. But I don't feel entirely comfortable with. I have the ...
2
votes
1answer
68 views

Any difference between “Mueller matrix” and “Scattering matrix”?

I find in some references 4x4 Mueller matrix and in other references 4x4 Scattering matrix. Are they different or identical? If they are different, I would like to know the book or any research ...
2
votes
3answers
286 views

Naive question about the S-matrix

In quantum field theory, the elements of the S-matrix are defined as the amplitude describing the transition from an initial $n$-particle state (the "in" state) to an final $m$-particle state: ...
4
votes
1answer
281 views

Connected and strongly connected Feynman diagrams

Recently I read, that only connected Feynman diagrams give contribution of nonzero values into the scattering amplitude. Why it is so and what is the physical sense of connected diagrams (due to ...
4
votes
2answers
140 views

What is the sense of introducing generating functional to the summands of expansion of S-matrix?

Let's have generating functional $Z(J)$: $$ Z(J) = \langle 0|\hat {T}e^{i \int d^{4}x (L_{Int}(\varphi (x)) + J(x) \varphi (x))}|0 \rangle , \qquad (1) $$ where $J(x)$ is the functional argument ...
2
votes
0answers
344 views

Radial Wave Function for Spherical Squared Well Potential and $S$-Matrix

I have a problem with this exercise because I really don't know how to proceed. It's related with the "S-matrix". In class we saw this example: Consider the spherically symmetric potential: ...
2
votes
0answers
97 views

Møller scattering: twisted?

I am studying the Møller scattering, but I don't know how to get the twisted diagram from the S-matrix. Has anybody a good explanation?
2
votes
1answer
192 views

Virtual particles and S-matrix

One of methods of introducing of virtual particles is using perturbation theory. We say that scattering matrice amplitude $M_{in \to out}$ contains of $\delta(P_{out} - P_{in})$, which realizes ...
3
votes
1answer
58 views

String total cross sections at asymptotically high energy

I only have a vague understanding of string theory, but a solid understanding of particle physics. At asymptotically high energy (Regge limit), the string cross section is dominated by the exchange ...
2
votes
0answers
50 views

Origin of crossing relations in relativistic scattering amplitudes

What is the origin of crossing relations in relativistic scattering amplitudes? At first I thought it was CPT, but then it turned out that was not correct. That is, what is the formal reason that ...
2
votes
0answers
34 views

How to write down the detailed balance (microreversed) amplitude

I know that time-reversal of a reaction and the detailed balance (microreversed, or reciprocal) reaction are different. Textbooks on scattering theory explain how to relate the S-matrix elements of a ...
5
votes
2answers
362 views

Can scattering amplitudes be simplified with 1PI diagrams?

I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
3
votes
1answer
107 views

What are anomalous threshold singularities

In the papers of the 1950s and 1960s, I see reference to anomalous threshold singularities. What are these? Is there a good reference that discusses this subject?
11
votes
2answers
1k views

What is the physical interpretation of the S-matrix in QFT?

A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers. Given a quantum field theory when ...
16
votes
2answers
755 views

Does the exact string theory $S$-matrix describe all physics there is?

Suppose someone manages to evaluate the string theory $S$-matrix to all orders for any and all vertex operator insertions including non-perturbative contributions from world-sheet instantons and ...
9
votes
1answer
559 views

When we define the S-matrix, what are “in” and “out” states?

I have seen the scattering matrix defined using initial ("in") and final ("out") eigenstates of the free hamiltonian, with $$\left| \vec{p}_1 \cdots \vec{p}_n \; \text{out} \right\rangle = S^{-1} ...
4
votes
3answers
686 views

Unitarity of S-matrix in QFT

I am a beginner in QFT, and my question is probably very basic. As far as I understand, usually in QFT, in particular in QED, one postulates existence of IN and OUT states. Unitarity of the S-matrix ...
7
votes
4answers
339 views

Different kinds of S-matrices?

It seems to me that the notion of an "S-matrix" refers to several different objects One construction you can find in the literature is allowing the coupling constant to adiabatically approach 0 in ...