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arXiv:2603.18208

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

Deepasika Dayananda, Chueng-Ryong Ji

hep-thquant-phSubmitted Mar 18, 2026• Announced Mar 20, 2026
arXivHTMLPDF

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.

Journal reference
Physical Review D 113, 116038 (2026)
DOI
10.1103/3t9t-9v5g
Comments
26 pages. 21 figures

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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.
In this paper, we calculate the helicity rotation angle induced by Lorentz boosts. This is relevant for the study of Lorentz boost effects on quantum entanglement encoded in pairs of massive fermions, which are described in terms of positive energy solutions of the Dirac equation with definite helicity. A Lorentz boost describing the change to an inertial frame moving at uniform speed will in general rotate the particle’s helicity. We obtain the coefficients of the helicity superposition in the boosted frame and specialize our results for a perpendicular boost geometry. We verify that the helicity rotation angle can be obtained in terms of the Wigner rotation angle for spin [Formula: see text] states, bridging the framework considered in our previous works to the one of the Wigner rotations. Finally, we calculate the boost-induced spin-parity entanglement for a single particle.
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We examine the behaviour of the maximally entangled Bell state of two spin 1 massive particles under relativistic transformations. On the basis of explicit calculations of the Wigner rotation and the use of transformation properties of Dirac spinors, we establish that the constituent particles of the Bell state undergo momentum dependent rotation of the spin orientations characterized by the Wigner angle φW = tan −1 sinhsinh τ cosh � +cosh τ . However, since local unitarity is retained in the process, the corresponding entanglement fidelity is not lost. c
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Abstract: We examine the behaviour of the maximally entangled Bell state of two spin 12 massive particles under relativistic transformations. On the basis of explicit calculations of the Wigner rotation and the use of transformation properties of Dirac spinors, we establish that the constituent particles of the Bell state undergo momentum dependent rotation of the spin orientations characterized by the Wigner angle φW = tan−1 sinh sinh τcosh+cosh τ. However, since local unitarity is retained in the process, the corresponding entanglement fidelity is not lost.