Graduate Understanding the LSZ Reduction Formula in Quantum Field Theory

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The LSZ reduction formula connects scattering amplitudes to the vacuum expectation value of time-ordered products of fields in quantum field theory. It is essential for understanding how to compute physical processes in QFT. The discussion highlights a preference for Srednicki's explanation over those in Peskin & Schroeder and Zee's texts. The LSZ formula is not merely a propagator formula but a fundamental tool for relating theoretical calculations to observable quantities. Mastery of this formula is crucial for advancing in quantum field theory.
bengeof
My background is QM as done in Griffiths( So yes I have a background of operators, observables and scattering matrix), Classical fields as done in Goldstein and Particle physics as in Griffiths. Griffiths actually works out Feynman rules for QED and QCD. I've started QFT with Peskin and Schroeder and Zee's QFT in a nutshell. Need help in understanding LSZ reduction formula. Is it some sort of propagator formula ?
 
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The LSZ formula relates scattering amplitudes to the vacuum-expectation value of a time-ordered product of fields.

I prefer Srednicki's explanation of LSZ to P&S and Zee.
 
Time reversal invariant Hamiltonians must satisfy ##[H,\Theta]=0## where ##\Theta## is time reversal operator. However, in some texts (for example see Many-body Quantum Theory in Condensed Matter Physics an introduction, HENRIK BRUUS and KARSTEN FLENSBERG, Corrected version: 14 January 2016, section 7.1.4) the time reversal invariant condition is introduced as ##H=H^*##. How these two conditions are identical?

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