Quantum orientation entanglement analysis of the interpolating helicity states between the instant form dynamics and the light-front dynamics

TL;DR

This paper investigates quantum orientation entanglement in relativistic helicity states interpolating between instant form and light-front dynamics, introducing a new expansion method and analyzing angular distributions in particle pair production.

Contribution

It introduces a novel expansion method for interpolating helicity states and analyzes the quantum orientation entanglement across different dynamical forms.

Findings

Identifies the critical interpolation angle bifurcating dynamical branches.

Provides explicit calculations of helicity amplitudes for vector particle pair production.

Discusses the underlying orientation entanglement in interpolating helicity amplitudes.

Abstract

The interplay between quantum orientation entanglement and Wigner rotation plays a fundamental role in understanding the behavior of spin angular momentum in quantum states. To analyze the quantum orientation entanglement of the relativistic helicity states interpolating between the Jacob-Wick helicity and the light-front helicity, we examine the relative angle between the particle's momentum direction and the spin orientation for the interpolating helicity states. For this analysis, we introduce a novel method for expanding the interpolating helicity states in terms of the Jacob-Wick helicity. The corresponding probabilistic coefficients follow the structure of the Wigner d-matrix elements, which we use for the interpretation of the quantum orientation entanglement manifested in the angular distributions of the interpolating scattering helicity amplitudes. As an explicit demonstration, we compute the interpolating helicity amplitudes for the pair production of spin-1 (vector) particles in the annihilation of two spin-0 (scalar) particles, focusing primarily on their contact interaction. In particular, we identify the critical interpolation angle that bifurcates the dynamical branches between the instant-form dynamics and the light-front dynamics and discuss the underlying orientation entanglement in the interpolating helicity amplitudes.