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

Deepasika Dayananda, Chueng-Ryong Ji

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.

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

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.
Paper Structure (17 sections, 79 equations, 21 figures)

This paper contains 17 sections, 79 equations, 21 figures.

Table of Contents

  1. Introduction
  2. Orientation entanglement of Spin
  3. Non-Relativistic vs. Relativistic Helicity Formulations
  4. Spin Orientation of the Interpolating Helicity States
  5. Spin Orientation Relative to the Momentum Direction
  6. Interpolating Wigner-d matrix of helicity states
  7. Interpolating Helicity Amplitudes
  8. Interpolating helicity amplitudes: $M_{\delta}^{++}=M_{\delta}^{--}$
  9. Interpolating helicity amplitudes: $M_{\delta}^{+-}=M_{\delta}^{-+}$
  10. Interpolating helicity amplitudes: $M_{\delta}^{+0}= -M_{\delta}^{-0}=M_{\delta}^{0+}(\theta+\pi)=-M_{\delta}^{0-}(\theta+\pi)$
  11. Interpolating helicity amplitude: $M^{00}$
  12. SUMMARY AND CONCLUSION
  13. Interpolating Relations
  14. Orientation entanglement of interpolating spin-1/2 spinors
  15. Orientation entanglement of interpolating spin-1 spinors
  16. ...and 2 more sections

Figures (21)

  • Figure 1: Spin orientation ($\theta_s$) dependence on the particle's momentum direction ($\theta$) and the interpolation angle ($\delta$) for the helicity plus state
  • Figure 2: Spin direction dependence on the interpolation angle of helicity plus state when the particle is moving in the $-z$ direction.
  • Figure 3: Spin direction ($\theta_s$) dependence on particle moving direction ($\theta$) just before and after $\delta_c$, along with $\delta=0$ and $\delta=\pi/4$ profiles.
  • Figure 4: Interpolating helicity angle dependence on the particle's momentum direction for the plus helicity state.
  • Figure 5: Independent Wigner matrix elements $H^{1}_{\lambda,\lambda}$ of spin-1 helicity polarization vectors that depend on the interpolation angle and the particle's moving direction. Other Wigner matrix elements can be related by Eq. (\ref{['HWMP 1']}).
  • ...and 16 more figures