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Itzhak the cat
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I am looking for simple explanation for the idea of LSZ representation in quantum fields theory.
thanks in advance
thanks in advance
dextercioby said:I don't know what you mean by "representation",but I'm sure there's no simple explanation of this issue.Heavy mathematics is needed.
I infer you to chapters 13 & 14 from Bogolubov's book [1] for a serious treatment.
Daniel.
[1]N.N.Bogolubov et al.,"Introduction to Axiomatic Quantum Field Theory",Benjamin/Cummings,1975.
selfAdjoint said:Let me try this coarse overview. Corrections always welcome.
First of all interactive quantum field theory is not well-defined. It has as many Hilbert spaces as there are points on a line, which is not physically meaningful. This is Haag's theorem. This problem shows up as a shaky vacuum state condition for interactive QFT; field states that should be over and gone continue to affect the vacuum. The LSZ formalism intends to work around this by going into the remote past and seeking "asymptotically localized" solutions of the theory. These will than be used as the incoming particles to the intreractions defined, e.g., by Feynman diagrams. As Daniel said, the math of doing this is very non-trivial, and Bogoliubov's book is a good intro to it. See also R. Haag, Local Quantum Physics, p. 81 ff.
Itzhak the cat said:This is the reduction formalism. I am more interested in the spectrum- why the masses are the poles of the propagator
LSZ representation is a mathematical framework used in quantum field theory to calculate the scattering amplitudes of particles.
LSZ representation allows for the calculation of scattering amplitudes in quantum field theory, which is necessary in order to make predictions about the behavior of particles in high-energy collisions.
LSZ representation uses a mathematical technique called "operator product expansion" to express correlation functions in terms of the interactions between particles.
LSZ representation is limited to perturbative calculations, meaning it can only be used to calculate the behavior of particles in weak interactions rather than strong interactions.
Yes, LSZ representation has been applied to other areas of physics such as condensed matter physics and statistical mechanics, where it is used to calculate correlation functions and transport coefficients.