Scalar product in relativistic quantum mechanics

E. Ruiz

I. Gottlieb

Eduard Prugovečki

It is shown that the new interpretation of the scalar product in Hilbert space recently proposed by Aharanov, Albert, and Au is in fact the one underlying the stochastic phase-space formulation of nonrelativistic quantum mechanics. The extrapolation of this interpretation to the relativistic domain and its relationship to the program of geometrizing quantum theory and quantizing space-time are discussed.

Konstantin K. Likharev

Damião Pedro Meira Filho, Eliesio Alves da Silva, Railene Martins de Araujo +3 more

The objective of the present work is to didactically analyze, in the context of relativistic quantum mechanics, the algebraic structuring of the dot product between two quantum wavefunctions relative to a spin-0 quantum particle, assuming the light cone coordinates. For that, the linear momentum tensor is used in four dimensions, considering the description of the operational and quantum character of energy and linear momentum in three dimensions, as well as defining a pseudo volumetric probability density from which the product is reached scalar, properly written in terms of light cone coordinates.

Yu.V. Novozhilov