Consistent formulation of relativistic dynamics for massive spin-zero particles in external fields

Journal Article · Wed Nov 15 00:00:00 EST 1978 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.18.3655· OSTI ID:6465268

Prugovecki, E

It is shown that in the context of stochastic-phase-space formulations of quantum mechanics a nonlocal type of nonrelativistic as well as relativistic dynamics for a massive spin-zero particle moving in an external electromagnetic field can be formulated in L/sup 2/(GAMMA) space. In a sharp-point limit S ..-->.. + 0 the nonrelativistic dynamics merges into the conventional local model. The relativistic dynamics is gauge invariant, it can be formulated covariantly in the relativistic phase space M/sub m/, it possesses a covariant propagator, it leaves the space of positive-energy solutions of the Klein-Gordon equation invariant, and it gives rise to a covariant and conserved probability current on stochastic phase space. Furthermore, for states describing a particle moving at nonrelativistic speeds in relation to a given inertial frame, the relativistic propagation contracts into its nonrelativistic counterpart. The sharp-point limit s ..-->.. + 0 of the relativistic S matrix also exists in each such inertial frame. The necessity of interactions acting at nonsharp configuration points for a consistent formulation of covariant relativistic one-particle dynamics is traced to the question of the nonexistence of covariant position operators in relativistic theories. The mandatory character of this feature is shown to be firmly rooted in the theory of quantum measurement.

• Research Organization: Department of Mathematics, University of Toronto, Toronto, Canada M5S 1A1
• OSTI ID: 6465268
• Journal Information: Phys. Rev., D; (United States), Vol. 18:10
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
PARTICLE KINEMATICS
GAUGE INVARIANCE
DIRAC EQUATION
ELECTROMAGNETIC FIELDS
FOLDY-WOUTHUYSEN TRANSFORM
KLEIN-GORDON EQUATION
QUANTUM MECHANICS
RELATIVISTIC RANGE
SPACE-TIME
SPIN
WAVE EQUATIONS
ANGULAR MOMENTUM
CANONICAL TRANSFORMATIONS
DIFFERENTIAL EQUATIONS
ENERGY RANGE
EQUATIONS
INVARIANCE PRINCIPLES
MECHANICS
PARTICLE PROPERTIES
645202* - High Energy Physics- Particle Interactions & Properties-Theoretical- Electromagnetic Interactions & Properties
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics