Talk:S-matrix

message: Would it be useful to move the stuff about Wick's theorem to another page? --HappyCamper 16:05, 4 September 2006 (UTC)
replies: text: I agree with this. Wick's theorem is far more general than something that is used to evaluate S-matrix elements. PhysicsBob 09:19, 26 July 2007 (UTC)
replies: text: I copied the section there (it was a redirect here) as a start on that article.  Now it alos needs some work and this section can be trimmed. RJFJR 13:48, 2 November 2007 (UTC)
thread_title: Wick's Theorem

message: The article at present seems to read like a page of mathematics rather than an encyclopedia entry. The LSZ reduction section especially reads like a mathematical proof. Perhaps someone who is competent in these matters could insert more explanation about the underlying ideas and applications of the S-matrix. Unfortunately, I don't know much about this kind of thing. PhysicsBob 16:19, 26 July 2007 (UTC)
replies: text: The LSZ reduction formula has its own article; is there any reason why it needs a separate section here?  --Starwed 19:25, 29 October 2007 (UTC)
replies: text: I feel there is no reason why the section on the LSZ reduction and Wick's theorem should remain in the main article, since they are techniques used to evaluate S-matrix elements, rather than being part of the defintion of the S-matrix. Perhaps a 'see also' section would be more appropriate? PhysicsBob (talk) 06:45, 11 June 2008 (UTC)
thread_title: Reorganization of Article

message: Towards the end of "mathematican definition" there is a list of properties that the S matrix "must" have. There is no mathematical need for these, as I understand it, but they are rather connected to (admittedly very reasonable) physical properties.
like:
unitarity <--> conservation of probability
does not change vacuum <-- energy conservation <--> time independence of lagrangian
S|k> = |k> <--> stable (non-decaying) particle
momentum conservation <--> space independence of lagrangian
most of these are related to Noethers theorem, which could be linked to. In fact, most of these are properties of the lagrangian rather than properties of the S-matrix imo, although they are tightly connected. Not really sure how to organise this article...
Art.cascade (talk) 16:50, 25 November 2011 (UTC)
thread_title: Properties

message: In the paragraph "Use of S-matrices", it seems to me that is is not the "Heisenberg" picture, but the "interaction" picture, isn't it ?  — Preceding unsigned comment added by 31.33.159.210 (talk) 13:03, 26 July 2012 (UTC)
thread_title:  "Heisenberg" picture 

message: Weinberg describes things seemingly very differently. The in-states and the out-states inhabit the same Hilbert space. The scattering matrix is then the set of inner products of suitable basis vectors (well defined free multi-particle like Lorentz transformation properties) between them. These states are eigenstates of the full Hamiltonian. Then there is the S operator. This is defined such that it's matrix elements between free particle states equal the S-matrix elements. I.e. free</sub>|S|afree> = Sba = out</sub>|ain>. [This presupposes a suitable subdivision of the Hamiltonian in free and interacting parts.] Is this the same thing as described in this article? YohanN7 (talk) 14:07, 28 January 2013 (UTC)
replies: text: \left \langle F,\beta | I,\alpha\right\rangle,
(from article) doesn't make sense unless the states inhabit the same Hilbert space. YohanN7 (talk) 14:19, 28 January 2013 (UTC)
thread_title:  Definition 

message: When we have to calculate reflection and transmission coefficient,we have to take mod value of that ratio.Phase information is lost.Matrix elements of the S-matrix has phase.So matrix elements of S-matrix is not reflection coefficient and transmission coefficient.Sorry for this.Thank you for correcting me.
As S-matrix elements are not reflection and transmission coefficient,so to specify S-matrix we have to specify four real number.
To specify a 2 by 2 unitary symmetric matrix we need 3 real parameter.whereas to specify unitary matrix we need 4 real parameter. So it does not mean that the information is smaller in S-matrix ,it only means that one information is related to other by one more constraint(symmetric constrained).
In optical theorem the departure from free particle S-matrix is described by two complex function.So it has 4 real parameter.But there is a real relation.So the number of parameters is 3.
Here the S-matrix is given for a particular value of wave vector.That is why the S-matrix is 2 by 2.As there is infinite number of wave vector, the S-matrix is in general infinite dimensional block diagonal matrix.Each block is 2 by 2,correspond to particular value of wave vector.Dibyendum (talk) 09:44, 1 December 2014 (UTC)
thread_title: Answer

message: It looks like the odd conventions of this section, namely  S→symplectic metric, instead of the identity, for the free theory (T=0) may well confuse the reader who has just read that S→I in the preceding sections.  
Specifically, assuming a universal time-dependence by a phase exp(−iωt)  in ψ, A describes an in right-mover and C an out-right mover; while D an in left-mover and B an out left-mover. So, interchanging B with C in  ψout while leaving  ψin alone, has the effect of interchanging the two rows of the S-matrix written at present, so that the free case is, indeed, the identity, as advertised above this section.  
In this way, the optical theorem could present less deformed, indeed, bizarre, and the missing further relation for the imaginary part of r would be apparent. Cuzkatzimhut (talk) 02:03, 2 December 2014 (UTC)
replies: text: But this convention is used in Eugen Merzbacher quantum mechanics book.Dibyendum (talk) 09:13, 2 December 2014 (UTC)
replies: text: (It's common practice to indent replies.) This is the perfect example of where you need to put in a literature reference as a footnote. I'll do this one. YohanN7 (talk) 09:34, 2 December 2014 (UTC)

text: Done. Feel free to fill out with page number or anything. The ref-tag creates a popup, and the template harvnb connects to the reference list and places the actual popup text under "Notes". It takes a while to get used to the system, but it works. YohanN7 (talk) 09:45, 2 December 2014 (UTC)
thread_title: Conventions of the S-matrix in one-dimensional quantum mechanics section

message: I think the new section should be moved closer to the top since it is relatively accessible. Some reorganization is required for this. But I don't know exactly what that reorganization would be. Just an idea. YohanN7 (talk) 08:06, 2 December 2014 (UTC)
thread_title:  New section closer to top? 

message: Sanity-check for the intro to the new section appreciated. I think the "continuous matrix" can be formalized rigorously, but that would be gross overkill to do here. YohanN7 (talk) 15:26, 2 December 2014 (UTC)
thread_title:  Intro 

message: Substituted at 05:09, 30 April 2016 (UTC)
thread_title: Assessment comment

message: Should the "S" in "S-matrix" be italicized. Usually mathematical variables (that do not spell a word) are written in italics. Should this apply to all "S-matrix" in this article?--ReyHahn (talk) 16:28, 28 June 2021 (UTC)
replies: text: Looking at some of the sources the last two, Mussardo (1992) and Zamolodchikov (1979)  both have the S in italics. The others are books I don't have access to. --Salix alba (talk): 18:40, 28 June 2021 (UTC)
replies: text: The Peskin and Griffiths too, I will proceed to make the changes soon.--ReyHahn (talk) 19:25, 28 June 2021 (UTC)
thread_title:  Title style