Stochastic Interpretation of Relativistic Quantum Equations

Masao Nagasawa, Hiroshi L. TANAKA

A. Frigerio, Marco Ruzzier

We propose a relativistic version of quantum stochastic calculus based on the relativistic properties of test functions; these properties are determined on the basis of the interpretation of test functions as interaction rate amplitudes, and lead to the relativistic transformations of the quantum stochastic differential equations and of the reduced dynamics. We obtain for the latter the relativistic time dilatation Proposition d'une version relativiste du calcul stochastique quantique basee sur les proprietes relativistes des fonctions test. Determination des proprietes par l'interpretation des fonctions test comme des amplitudes de taux d'interaction, ce qui conduit aux transformations relativistes des equations differentielles stochastiques quantiques et a la dynamique reduite. Pour cette derniere, on obtient la dilatation temporelle relativiste

Eduard Prugovečki

James A. Brooke

Maurizio Serva

A stochastic interpretation of Klein-Gordon equation is proposed. The starting point is the construction of relativistically covariant diffusions satisfying a property similar but not identical to the Markov property. It is then shown that the continuity equation associated with these processes together with the relativistic version of mean Newton equation are equivalent to the Klein-Gordon equation On propose une interpretation stochastique de l'equation de Klein Gordon. Le point de depart est la construction d'une diffusion relativiste covariante qui satisfait une propriete semblable (mais pas identique) a la propriete de Markov. On montre ensuite que l'equation de continuite associee a ce processus plus la version relativiste de l'equation de Newton en moyenne sont equivalentes a l'equation de Klein-Gordon

Partha Ghose

A process-theoretic approach to electrodynamics based on persistent Kac-type stochastic processes is developed. Finite-velocity stochastic propagation is taken as primary, while relativistic wave equations arise as emergent descriptions after analytic continuation of Telegrapher-type dynamics. The Dirac and Maxwell equations are interpreted as arising from closely related persistent propagation structures differing only in spin representation. The framework is not intended to modify the successful empirical predictions of quantum electrodynamics, but to provide a different underlying ontology. Particles and fields are not treated as primitive entities with fixed intrinsic properties. Instead, relativistic particle and field structures emerge as stable collective modes of coupled persistent stochastic dynamics. Mass and charge acquire interpretations respectively as persistence and stochastic coupling scales. Stationary bound states are interpreted as metastable persistent stochastic modes with nontrivial internal sector dynamics. Spontaneous emission is viewed as stochastic destabilization of such modes, while stimulated emission arises through resonant synchronization of persistent transition currents by incident radiation. Gauge interactions are introduced at the level of propagation-sector amplitudes prior to the emergence of observable probabilities. Radiative effects, including the anomalous magnetic moment of the electron, are interpreted as effective stochastic dressing of coupled matter--radiation processes. Some comments on gauge symmetry, equilibration and the Standard Model are also included.