Causality and relativistic localization in one-dimensional Hamiltonians
- Intense Laser Physics Theory Unit and Department of Physics, Illinois State University, Normal, Illinois 61790-4560 (United States)
We compare the relativistic time evolution of an initially localized quantum particle obtained from the relativistic Schroedinger, the Klein-Gordon and the Dirac equations. By computing the amount of the spatial probability density that evolves outside the light cone we quantify the amount of causality violation for the relativistic Schroedinger Hamiltonian. We comment on the relationship between quantum field theoretical transition amplitudes, commutators of the fields and their bilinear combinations outside the light cone as indicators of a possible causality violation. We point out the relevance of the relativistic localization problem to this discussion and comment on ideas about the supposed role of quantum field theory as a vehicle of making a theory causal by introducing antiparticles.
- OSTI ID:
- 21550031
- Journal Information:
- Physical Review. A, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevA.83.062106; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANTIPARTICLES
CAUSALITY
COMMUTATORS
COMPARATIVE EVALUATIONS
DIRAC EQUATION
HAMILTONIANS
KLEIN-GORDON EQUATION
LIGHT CONE
ONE-DIMENSIONAL CALCULATIONS
PARTICLES
PROBABILITY DENSITY FUNCTIONS
QUANTUM FIELD THEORY
RELATIVISTIC RANGE
SCHROEDINGER EQUATION
TRANSITION AMPLITUDES
AMPLITUDES
ANTIMATTER
DIFFERENTIAL EQUATIONS
ELEMENTARY PARTICLES
ENERGY RANGE
EQUATIONS
EVALUATION
FIELD EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICAL OPERATORS
MATTER
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE-TIME
WAVE EQUATIONS