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2
votes
1answer
61 views

How exactly to show that s-matrix elements diverges because time-ordering is not well determined?

Let's have s-matrix: $$ S_{\alpha \beta} = \langle \alpha | \hat {S} | \beta \rangle , $$ $$\hat{S} = \hat{T}e^{-i\int \hat{L}(x)d^{4}x}, \quad \hat{T} \left( \hat{\Psi}(t) \hat{\Psi}(t') \right) = ...
2
votes
2answers
84 views

Gauge symmetry for p-forms

It is well known that the Lorentz invariance of the S-matrix implies Gauge redundancy for 1-forms,'photons'. Does this argument go through to p-forms? That is does lorentz invariance of s-matrix of ...
2
votes
1answer
136 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 ...
2
votes
0answers
119 views

Perturbation theory : quadratic external field

I'm trying to derive the explicit form of S-matrix of an interaction Hamiltonian $$H' = \frac{1}{2} \lambda \left[ \int d^3 x \rho({\vec x}) \phi({\vec x}, t)\right]^2\tag{1}$$ Even though the ...
2
votes
1answer
51 views

Green's Functions from Gell-Mann and Low Theorem

What I want to do: $\newcommand{\ket}[1]{\left|#1\right\rangle}$ $\newcommand{\bra}[1]{\left\langle#1\right|}$ $\newcommand{\braket}[1]{\left\langle#1\right\rangle}$ The Gell-Mann Low Theorem tells ...
2
votes
0answers
15 views

Main differences between elastodynamic and light scattering when using S-matrix to find bound states

What are the main differences (top 5 if question is too broad), for using the S-matrix to find bound states, between elastodynamic and light scattering? (if it facilitates a higher quality ...
2
votes
0answers
75 views

What's the difference between correlation functions and S-matrix, and between in-in formalism (or “closed time path formalism”) and in-out formalism?

I was reading the "in-in" formalism (or "closed time path formalism" used in condensed matter physics) in cosmology created by Schwinger in 1961, and there is a saying: "they care about correlation ...
2
votes
0answers
69 views

S-Matrix Generating Functional (Problem 4.1 in Weinberg)

I'm currently working through Weinberg's QFT book, but I'm somewhat stuck at problem 4.1, which states: Define generating functionals for the S-matrix and its connected part: \begin{equation} ...
2
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0answers
51 views

One question about renormalization

The idea of renormalization of "naked" perturbation theory is in principal possibility of addition counterterms which reduce infinity when calculating matrix elements. But I have met such concepts as ...
2
votes
1answer
88 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
0answers
66 views

What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
2
votes
0answers
521 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
138 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
0answers
58 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
39 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 ...
1
vote
1answer
101 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
70 views

Relation between scattering matrix and an effective Hamiltonian

Could somebody provide the proof (or reference to some accessible literature) of relation $$S(E) = 1 + 2πiW^{†} (H_M − E − iπW W^{†} )^{−1} W \tag{2}$$ of arXiv:0806.4889, which relates $S$-matrix to ...
1
vote
1answer
44 views

What does it mean to have a degenerate $S$-matrix?

The Coleman-Mandula theorem $D>2$ assumes that the quantum field theory may not have a degenerate $S$-matrix. But what does it mean to have a degenerate $S$-matrix? The $S$-matrix if I got it ...
1
vote
2answers
167 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 ...
1
vote
1answer
114 views

The n-point Green functions and Heisenberg picture

Let's have the S-matrix: $$ S_{\beta \alpha} = \langle \beta | \hat{S} | \alpha\rangle . $$ Here $|\alpha \rangle , | \beta \rangle$ are $t \to \mp \infty$ limit of the free states, $\hat {S} = ...
1
vote
1answer
133 views

Why do we need an old perturbation theory?

There are two types of perturbation theory corresponding to explicit lorentz-covariance of amplitudes. The first one is called Rayleigh-Schrodinger perturbation theory. It is based on following ...
1
vote
0answers
59 views

Potential of S-Matrix Theory to lead to breakthrough in GUT [closed]

I was told by a former physicist that he thinks that the now dormant S-Matrix Theory has the potential to lead to a breakthrough in formulating a Grand Unified Theory. He stated several reasons for ...
1
vote
0answers
74 views

Probability and the propagator

Due to the Wiki article, "...In quantum mechanics and quantum field theory, the propagator gives the probability amplitude for a particle to travel from one place to another in a given time, or to ...
1
vote
0answers
49 views

Spin matrix for various spacetime fields

Let $V^{\mu}$ be a vector field defined in a Minkowski spacetime and suppose it transforms under a Lorentz transformation $V'^{\mu} = \Lambda^{\mu}_{\,\,\,\nu}V^{\nu}$. We can write this like ...
1
vote
2answers
188 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) - ...
1
vote
0answers
89 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 ...
0
votes
0answers
40 views

What to do when finite counterterms are undetermined?

Suppose I have some theory of "new physics" which involves interaction of some gauge boson with Standard model. For this theory I have some loop-mediated process with this new gauge boson whose matrix ...
0
votes
0answers
33 views

Differential Cross sections from amplitude scattering matrix

How can I get the differential cross sections from the amplitude scattering matrix, $S$ (2x2 matrix)? I've seen this in a Mie solution solver: Parallel Polarized Light: dCsdOp = $\frac{2}{\pi k} ...
0
votes
1answer
30 views

scattering by weak potential and the adiabatic hypothesis

In Ryder QFT, regarding the calculation of the scattering amplitude by a weak potential $V$, the potential is assumed to be switched on and off slowly using the adiabatic hypothesis. But there is a ...