A S-Matrix in Quantum Field Theory

gremory
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Usage of the S-matrix
Hello, i need help with the S-matrix. From what i understand, with the S-matrix i would be able to compute the scattering amplitude of some processes, is that correct? If so, how would i be able to do that if i have some field ##\phi(x,t)## in hands? Is that possible?
 
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Study Peskin & Schroeder... :rolleyes:
 
gremory said:
i need help with the S-matrix.
That is more help than is within the scope of a PF thread. You are basically asking for a course in S matrix theory, and for that you need a textbook (such as the one @strangerep suggested), not a PF thread.

gremory said:
From what i understand, with the S-matrix i would be able to compute the scattering amplitude of some processes, is that correct?
Yes. However...

gremory said:
If so, how would i be able to do that if i have some field ##\phi(x,t)## in hands? Is that possible?
It's certainly possible, but as above, learning how to do it takes one or more full-time courses in S-matrix theory. It's not something we're going to be able to teach you in a PF thread.

If, after taking some time to study a textbook, you have particular questions about what you are reading, by all means open a new thread with a much more specific focus. In the meantime, this thread is closed.
 
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The lesser Green's function is defined as: $$G^{<}(t,t')=i\langle C_{\nu}^{\dagger}(t')C_{\nu}(t)\rangle=i\bra{n}C_{\nu}^{\dagger}(t')C_{\nu}(t)\ket{n}$$ where ##\ket{n}## is the many particle ground state. $$G^{<}(t,t')=i\bra{n}e^{iHt'}C_{\nu}^{\dagger}(0)e^{-iHt'}e^{iHt}C_{\nu}(0)e^{-iHt}\ket{n}$$ First consider the case t <t' Define, $$\ket{\alpha}=e^{-iH(t'-t)}C_{\nu}(0)e^{-iHt}\ket{n}$$ $$\ket{\beta}=C_{\nu}(0)e^{-iHt'}\ket{n}$$ $$G^{<}(t,t')=i\bra{\beta}\ket{\alpha}$$ ##\ket{\alpha}##...

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