Noncausality and Other Defects of Interaction Lagrangians for Particles with Spin One and Higher

1969/12/25 by G. Velo, Giorgio Velo, Daniel Zwanzinger · 320 citations
Physics and Astronomy · #Charge (physics) #Charged particle #Classical mechanics #Coupling (piping) #Degrees of freedom (physics and chemistry) #Dipole #Electromagnetic field #Equations of motion #Field (mathematics) #Magnetic dipole #Magnetic moment #Moment (physics) #Particle (ecology) #Physics #Quadrupole #Quantum Mechanics and Applications #Quantum and Classical Electrodynamics #Quantum chaos and dynamical systems #Quantum electrodynamics #Quantum mechanics #Spin (aerodynamics)

paper · doi:10.1103/physrev.188.2218

published in Physical Review 188(5), 2218-2222 (American Institute of Physics)

openalex publication_date 1969/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analyze critically what happens when various interaction terms are added to a Lagrangian describing a free particle with spin \ensuremath≥1. Good behavior results when the charged spin-one particle is coupled minimally to an external electromagnetic field or via a magnetic dipole moment. However, with an arbitrary electric quadrupole moment, the spin-one particle propagates noncausally (v>c) in an electrostatic field. Noncausal behavior is also found for the neutral vector field with self-coupling \ensuremathλ(W_\ensuremathμW^\ensuremathμ)². Another kind of disease appears when the spin-two particle is given a charge: A constraint is converted into an equation of motion, so that there are six degrees of freedom instead of the desired five.

Citations

• Propagation and Quantization of Rarita-Schwinger Waves in an External Electromagnetic Potential

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