New symmetry properties of pointlike scalar and Dirac particles

TL;DR

This paper uncovers new symmetry properties of scalar and Dirac particles in curved spacetimes, deriving Hermitian forms of their equations and identifying conformal symmetries unaffected by electromagnetic interactions.

Contribution

It introduces new conformal symmetries for scalar and Dirac particles and derives Hermitian forms of their equations in arbitrary curved spacetimes, including electromagnetic interactions.

Findings

Hermitian form of Klein-Gordon equation in arbitrary spacetimes

New conformal symmetries for scalar and Dirac particles

Conformal symmetries remain unchanged with electromagnetic interactions

Abstract

New symmetry properties are found for pointlike scalar and Dirac particles (Higgs boson and all leptons) in Riemannian and Riemann-Cartan spacetimes in the presence of electromagnetic interactions. A Hermitian form of the Klein-Gordon equation for a pointlike scalar particle in an arbitrary n-dimensional Riemannian (or Riemann-Cartan) spacetime is obtained. New conformal symmetries of initial and Hermitian forms of this equation are ascertained. In the above spacetime, general Hamiltonians in the generalized Feshbach-Villars and Foldy-Wouthuysen representations are derived. The conformal-like transformation conserving these Hamiltonians is found. Corresponding conformal symmetries of a Dirac particle are determined. It is proven that all conformal symmetries remain unchanged by an inclusion of electromagnetic interactions.