Lorentz-covariant spinor wave packet

TL;DR

This paper introduces a new Lorentz-covariant spinor wave-packet basis that resolves mixing issues under Lorentz transformations and provides a complete, covariant expansion of free spinor fields, including a Lorentz-invariant zero-point energy expression.

Contribution

It presents a novel, manifestly Lorentz-covariant spinor wave-packet basis that addresses mixing problems and enables covariant field expansion.

Findings

Resolves mixing issues under Lorentz transformations.

Provides a complete, covariant basis for spinor fields.

Derives a Lorentz-invariant zero-point energy expression.

Abstract

We propose a novel formulation for a manifestly Lorentz-covariant spinor wave-packet basis. The traditional definition of the spinor wave packet is problematic due to its unavoidable mixing with other wave packets under Lorentz transformations. Our approach resolves this inherent mixing issue. The wave packet we develop constitutes a complete set, enabling the expansion of a free spinor field while maintaining Lorentz covariance. Additionally, we present a Lorentz-invariant expression for zero-point energy.