Spin operator in the Dirac theory

Abstract

We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii) eigenvalues of the projection of a spin operator on an arbitrary direction are independent of this direction (isotropy condition). We show that there are four such operators and all of them fulfill the standard su(2) Lie algebra commutation relations. Nevertheless, only one of them has a proper non-relativistic limit and acts in the same way on negative and positive energy states. We show also that this operator is equivalent to the Newton-Wigner spin operator and Foldy-Wouthuysen mean-spin operator. We also discuss another operators proposed in the literature.

9 pages

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• Relativistic Einstein-Podolsky-Rosen correlations and localization
• Dynamics of the relativistic electron spin in an electromagnetic field
• Effects of Lorentz boosts on Dirac bispinor entanglement
• Lorentz Invariant Quantum Concurrence for SU(2) x SU(2) spin-parity states
• Relativistic entanglement of two particles driven by continuous product momenta
• General form of the covariant field equations of arbitrary spin and the relativistic canonical quantum mechanics
• Thomas--Wigner rotation as a holonomy for spin-$1/2$ particles
• One and two spin$-1/2$ particles systems under Lorentz transformations
• Operators of quantum theory of Dirac's free field
• Spin dynamics in relativistic light-matter interaction
• Bundle Theoretic Descriptions of Massive Single-Particle State Spaces; With a view toward Relativistic Quantum Information Theory