A Positive-Definite Scalar Product for Free Proca Particle
V. Jakubsky, J. Smejkal
TL;DR
This paper develops a Lorentz-invariant positive-definite scalar product for the Proca equation, enabling a consistent quantum mechanical description of massive spin-one particles within pseudo-Hermitian frameworks.
Contribution
It introduces a one-parameter family of scalar products that are Lorentz invariant and positive-definite for the Proca equation, advancing the mathematical foundation of relativistic quantum mechanics.
Findings
Derived a family of scalar products for Proca solutions
Ensured Lorentz invariance of the scalar products
Provided a positive-definite inner product framework
Abstract
We implement recent results of pseudo-Hermitian quantum mechanics to description of relativistic massive particle with spin-one. We derive a one-parameter family of Lorentz invariant positive-definite scalar products on the space of solutions of Proca equation.
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