Superstatistics approach to path integral for a relativistic particle

Abstract

Superstatistics permits the calculation of the Feynman propagator of a relativistic particle in a novel way from a superstatistical average over non-relativistic single-particle paths. We illustrate this for the Klein-Gordon particle in the Feshbach-Villars representation, and for the Dirac particle in the Schroedinger-Dirac representation. As a byproduct we recover the worldline representation of Klein-Gordon and Dirac propagators, and discuss the role of the smearing distributions in fixing the reparametrization freedom. The emergent relativity picture that follows from our approach together with a novel representation of the Lorentz group for the Feshbach-Villars particle are also discussed.

25 pages, revtex 4, minor changes

References in corpus (22)

• Noncommutative Field Theory
• Superstatistics
• Nonstandard optics from quantum spacetime
• Testable scenario for Relativity with minimum-length
• Interpretation of the nonextensitivity parameter $q$ in some applications of Tsallis statistics and Lévy distributions
• Dynamical foundations of nonextensive statistical mechanics
• Perturbative Quantum Field Theory in the String-Inspired Formalism
• Quantum gravity corrections to neutrino propagation
• The IR/UV Connection in the Non-Commutative Gauge Theories
• From time series to superstatistics
• Spacetime foam as a quantum thermal bath
• Asymptotics of superstatistics
• Trace Anomalies from Quantum Mechanics
• Coarse-grained distributions and superstatistics
• Black Hole Thermodynamics and Lorentz Symmetry
• Superpositions of Probability Distributions
• Perturbation Expansion for Option Pricing with Stochastic Volatility
• Superstatistics from a different perspective
• Testing Nonperturbative Ansaetze for the QCD Field Strength Correlator
• Central limit theorem, deformed exponentials and superstatistics
• Recent developments in superstatistics
• Is 'superstatistics' really 'super'?

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• Transitions between superstatistical regimes: validity, breakdown and applications
• The classical ether-drift experiments: a modern re-interpretation
• Generalization of the Beck-Cohen superstatistics
• Cosmic Microwave Background and the issue of a fundamental preferred frame
• Kappa distribution from particle correlations in non-equilibrium, steady-state plasmas
• Path integral of the relativistic point particle in Minkowski space
• Symmetries of relativistic world-lines
• The stepwise path integral of the relativistic point particle
• Michelson-Morley Experiments: at the crossroads of Relativity, Cosmology and Quantum Physics
• First passage time for superstatistical Fokker-Planck models
• A hidden constraint on the Hamiltonian formulation of relativistic worldlines
• Relativistic Heat Equation via Lévy stable distributions: Exact Solutions
• Quantum Non-Locality and the CMB: what Experiments say
• Statistical mechanics of the vacuum
• Kappa distributions in the framework of superstatistics