Mathematica A Mathematical Physics Question

eljose79

Let be the propagators for the Schroedinguer,Klein-Gordon and Dirac?...are they hermitian operators?..are their eigenfunctions ortogonal?...

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shchr

Hi! This is my first post.
Do you mean "propagators are Unitary"? I think a propagator is an operator which governs time evolution of an eigenstate. In order that total of probability obtained from the integration of the eigenstate's inner product remains 1 in the course of time evolution, time evolution operator should be Unitary. If so, I think propagators are Green's function used to solve a problem by perturbation method. So although a time evolution operator of an exact solution of the problem should be Unitary, propagators are not neccesarily Unitary, I think. Propagators are not the operators which should be diagonalized by eigenfunctions in order to solve the problem. I heard that S matrix which is constructed by a propagator is Unitary, though. How do you think about this.

jeff

Propagators are usually defined not as operators but as amplitudes for particles to be created at some given point and annhilated at another.

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shchr

Thank you! jeff. Propagators are not operators. However, I found that Feynman propagator was defined by an expectation value in vaccum of two time ordered field operators in quantum field theory. Is this what you mean?

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