Feynman's transition amplitudes in the space Sn?

David Carfì

Abstract


In this paper we propose a rigorous formulation for Feynman’s propagator of Quantum Mechanics; the space in which we build up the propagator is the space of tempered distributions S0n . The goals of the paper are the following ones: 1) a rigorous and operative definition of Feynman’s propagator in S0n; 2) the basic indications for a straightforward and not-ambiguous calculus for the propagators, easy to teach and use; 3) a rigorous formulation and proof of the famous Feynman’s Transition Amplitudes Theorem, in the space of tempered distributions; and of one its original generalization.

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DOI: http://dx.doi.org/10.1478/C1A0701007