What is the significance of S-Matrix in Quantum Field Theory?

[Ted Baas]

Can someone please explain Heisenberg's S-Matrix theory in simple terms. Minimals maths please. Please be as expansive as possible.

 

[Nugatory]

As with all questions of this sort, you will get better and more helpful answers if you can share what you've already studied and understood, and then pose a more specific question about the parts that you want help with.

 

[Ted Baas]

I am a novice to all fields of physics except Classical Mechanics. I understand(understand is perhaps too strong a word) Quantum Physics conceptually but not mathematically and I would like to learn about S-Matrix in its entirety(any information helps) but most specifically in its relation to String Theory.

 

[dextercioby]

You are venturing yourself into subjects you are not prepared to understand. Take your learning curve into the normal order: mathematical methods, classical mechanics (Newtonian, Lagrange, Hamilton, HJ), Electromagnetism, Quantum Mechanics. Typical QM curricula treat scattering theory (operator formalism) as their final chapter.

 

[strangerep]

[...] I understand (understand is perhaps too strong a word) Quantum Physics conceptually but not mathematically and I would like to learn about S-Matrix in its entirety [...]

Without maths, one cannot say much more about scattering theory except that it relates what goes "in" to a reaction and what comes "out". Think of scattering of classical bodies off a potential well in classical mechanics as a very simple example.

The term "S-Matrix" (i.e., "scattering matrix") means the expression of this idea in terms of quantum states (or fields) coming into a reaction, and those coming out. Vast amounts of knowledge can be gained from the S-Matrix in quantum field theory -- indeed it's hard to imagine any useful accelerator experiments being possible without an underpinning by S-Matrix theory.

But, as others have hinted, you'll need to start getting into QM on a mathematical level to get more out of the subject than the vague handwaving explanation above.