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2
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42 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} ...
1
vote
2answers
110 views

Derivation of the full generator of the lorentz transformations

Let us study the subgroup of the Poincare group that leaves the point $x=0$ invariant, that is the Lorentz group. The action of an infinitesimal Lorentz transformation on a field $\Phi(0)$ is $L_{\mu ...
7
votes
2answers
181 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
82 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) ...
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0answers
47 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 ...
3
votes
1answer
107 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 ...
2
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0answers
41 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 ...
0
votes
1answer
64 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 ...
2
votes
1answer
55 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) = ...
1
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0answers
39 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
1answer
109 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 ...
3
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1answer
124 views

Quantum Field Theory without LSZ, how is it possible?

Most modern texts spend some time deriving the LSZ reduction formula that connects S matrix elements to time ordered field correlation functions. It seems essential, and really helps clear up what you ...
2
votes
3answers
276 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: ...
2
votes
1answer
48 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 $U(1)×SU(2)×SU(3)$. ...
2
votes
2answers
72 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 ...
4
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1answer
72 views

Does the LSZ reduction method prove gauge-independence in massless gauge theories?

I've been working my way through L. Baulieu's excellent paper [Perturbative gauge theories, Physics Reports, Volume 129, Issue 1, December 1985, Pages 1-74]. Towards the end, he goes on to prove that ...
8
votes
1answer
369 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
2answers
90 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 ...
3
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1answer
250 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 ...
3
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1answer
88 views

S-operator lorentz invariance

How to show that $\hat {S}$-operator must be lorentz-invariant operator? $$ |\Psi (t)\rangle = \hat {S} | \Psi (0) \rangle , \quad \hat {S} = \hat {T}e^{-i\int \hat {H}_{I}d^{4}x}. $$ I have read ...
2
votes
1answer
37 views

A question about propagator of Maxwell field in different gauge

The propagator of Maxwell theory is different, depending on the gauge fixing procedure used. Then why will the S-matrix elements be the same for the same process in different gauges?
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0answers
71 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 ...
2
votes
1answer
79 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
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1answer
182 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 ...
6
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0answers
115 views

Are there any serious alternatives to QCD nowadays?

I've read several posts here where people talk about the history of the developement of the theory of strong interactions. And they mention Regge theory, pomerons, S-matrix and so on. I'm confused ...
7
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3answers
322 views

Applications of analytic continuation to physics

I posted this on math.SE, but didn't get much response. It might fit better on this site. Holomorphic functions have the property that they can be uniquely analytically continued to (almost) the ...
2
votes
1answer
60 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
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0answers
47 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
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0answers
317 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
1answer
135 views

S-Matrix, String theory, Matrix mechanics and Quantum Mechanics

I'm trying to learn theoretical physics up to string theory. I know linear algebra, calculus 1+2, complex analysis. I know the basics of homology, homotopy, group theory and differential geometry. Now ...
6
votes
1answer
206 views

Basic question about the S-Matrix, Unitarity and Effective Field Theory

Consider scattering some particles in a state collectively denoted by $i$ to a final state denote by $f$. The scattering amplitude, S-matrix is then defined by: $S_{fi}\equiv \langle ...
2
votes
0answers
90 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?
4
votes
2answers
129 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 ...
4
votes
1answer
498 views

Help with Cutkosky cutting rules for fermions

I know that a cut boson propagator is replaced with the mass shell delta function. But what happens when you cut a fermion propagator? Do you just replace the denominator with a mass shell delta ...
2
votes
1answer
183 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
57 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
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0answers
106 views

S-Matrix and normalization of states

I'm trying to understand what is the S-matrix in QFT. People say that it has to be a unitary matrix, but that I guess will change with a different normalization of the incoming and outgoing states. My ...
3
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0answers
75 views

How to check the unitarity of the theory by having field equation?

Let's have some field equation of some field corresponding to particles with mass $m$ and spin $s$. How to check the unitarity of the theory? May I do it without getting $S$-matrix? May the scalar ...
16
votes
2answers
748 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 ...
3
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0answers
97 views

S-matrix and it's exponential form

By using Dyson series for the representation of the $S$-matrix, it's expression can be written in a form $$ \hat {S}(\infty , -\infty) = \sum_{n = 0}^{\infty}\frac{(-i)^{n}}{n!}\int ...
2
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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 ...
12
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2answers
576 views

Equivalence Theorem of the S-Matrix

as far as I know the equivalence theorem states, that the S-matrix is invariant under reparametrization of the field, so to say if I have an action $S(\phi)$ the canonical change of variable $\phi \to ...
6
votes
1answer
155 views

Flat Space Limit of AdS/CFT is S-Matrix Theory

In an answer to this question, Ron Maimon said: The flat-space limit of AdS/CFT boundary theory is the S-matrix theory of a flat space theory, so the result was the same--- the "boundary" ...
2
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0answers
33 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
359 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 ...
11
votes
1answer
311 views

Witten's constrained S-matrix and Coleman-Mandula Theorem

I remember reading somewhere that Witten argued that if the Poincaré symmetry of spacetime were nontrivially combined with internal symmetries, then the S-matrix would be so constrained that the ...
16
votes
1answer
264 views

Is string theory local?

By locality I mean something like the Atiyah-Segal axioms for Riemannian cobordisms (see e.g. http://ncatlab.org/nlab/show/FQFT). I.e. to any (spacelike) hypersurface in the target we associate a ...
4
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3answers
647 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 ...
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4answers
325 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 ...
6
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1answer
103 views

Why is there no double counting of $s$- and $t$-channels in string theory?

In string theory for the four particle tree diagram exchange, why is there some mysterious crossing duality between the $s$- and $t$- and $u$-channels? Why isn't there a double counting in the Feynman ...