On the first quantization and quantum diversity of photons

TL;DR

This paper develops a first quantization framework for photons, deriving wave and Dirac equations, and explores the relationship between scalar and vector quantum mechanics, linking classical and quantum optical fields.

Contribution

It introduces a first quantization approach for photons, deriving fundamental equations and connecting classical and quantum descriptions of optical fields.

Findings

Derived Schrödinger-like and Dirac equations for photons.

Established relationships between scalar and vector quantum mechanics.

Proposed new equations for photon propagation in dispersive media.

Abstract

Quantum theory of photons based on the first quantization technique, similar to that used by Schroedinger in the formulation of quantum mechanics, is considered. First, scalar quantum mechanics of photons operating with the photon wave functions is discussed. Using the first quantization, the wave equation, the Schroedinger-like equations, and the Dirac equation for photons are derived. Then, vector quantum mechanics of photons is introduced, which defines the electromagnetic vector fields. Using the first quantization, the Maxwell equations for photons in magneto-dielectric medium are obtained. Since the photon electric and magnetic fields satisfy the Maxwell equations, all what is known about the classical optical fields can be directly transferred to photons demonstrating their quantum diversity. Relationships between the scalar and vector quantum mechanics of photons and between the Dirac and Maxwell equations are analyzed. To describe the propagation of photons in dispersive media novel equations are introduced.