The quantum mechanics of Einstein photons and generalized functions

TL;DR

This paper explores a quantum Lorentz covariant framework for Einstein photons, constructing Green functions, Schrödinger equations, and analyzing Casimir forces within a generalized quantum field approach.

Contribution

It introduces a novel interpretation of Majorana equations for Einstein photons and develops a generalized measure framework for photon path analysis.

Findings

Constructed Green functions for Einstein photons.

Developed Schrödinger equations for the photon field.

Calculated Casimir forces in the proposed quantum field model.

Abstract

The article consider an interpretation of Majorana equations as a quantum Lorentz covariant equations for the field of Einstein photon. A photon with "deinterlaced" spins (with diagonal Hamiltonian) is considered, its generalized Green function as a functional on finite test functions and its Schr\"{o}dinger equation are constructed. The generalized process corresponding to this Green function is continued to $\sigma$-additive quantum generalized measure on the space dual to the compact subspace of a photon paths in $L_{2}(-\infty,\infty)$. In this case, the filling of whole space by such quantum field instantly occurs in the evolutionary problem. The last part of the article gives the calculation of the "Casimir forces" arising in this field.