Relativistic massive particle with spin-1/2, a vector bundle point of view

Abstract

Recently, in the context of Relativistic Quantum Information Theory (RQI) of massive spin-1/2 particles, it has been suggested that it is impossible to perform a momentum-independent spin measurement, showing the inadequacy of the spin reduced density matrix as a legitimate information resource. This is because there is an unavoidable ambiguity in the definition of the spin of a moving particle. In this paper, by introducing a vector bundle theoretic way to view the single-particle state space, we try to rule out this ambiguity. The discrete degree of freedom of the resulting representation space contains information about the Pauli-Lubansky four-vector of the particle instead of the ambiguous spin. Comparing this representation with the standard one used in the RQI literature, we show that the discrete degree of freedom of the standard representation space attains the meaning of the Newton-Wigner spin. Also using this viewpoint, we give a mathematical proof of why the spin reduced density matrix is meaningless, which is stronger than the previous claims in that it asserts that the matrix is void of any meaning at all, not just in terms of the impossibility of measurement or Lorentz non-covariance. We give a way (which turns out to be the only way) to modify it to obtain the Pauli-Lubansky reduced density matrix, which is covariant under Lorentz transformations.

This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in [Heon Lee, "Relativistic massive particle with spin-1/2: A vector bundle point of view", J. Math. Phys. 63, 012201 (2022) https://doi.org/10.1063/5.0064409] and may be found at https://aip.scitation.org/doi/abs/10.1063/5.0064409

References in corpus (5)

• Lorentz-covariant reduced spin density matrix and EPR-Bohm correlations
• Relativistic corrections to the algebra of position variables and spin-orbital interaction
• Spin and localization of relativistic fermions and uncertainty relations
• Quantum Helicity Entropy of Moving Bodies
• Quantum state of a free spin-1/2 particle and the inextricable dependence of spin and momentum under Lorentz transformations

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• Lorentz-Covariant Spin Operator for Spin 1/2 Massive Fields As a Physical Observable
• Thomas--Wigner rotation as a holonomy for spin-$1/2$ particles
• Bundle Theoretic Descriptions of Massless Single-Particle State Spaces; How do we perceive a moving quantum particle
• Relativistic entanglement in muon decay
• Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory