Stochastic Variational Method as Quantization Scheme I: Field Quantization of Complex Klein-Gordan Equation

Abstract

Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we discuss the complex Klein-Gordon equation. In this scheme, the Euler-Lagrangian equation for the stochastic fields leads to the functional Schroedinger equation, which in turn can be interpreted as the ideal fluid equation in the functional space. We show that the Fock state vector is given by the stationary solution of these differential equations and various results in the usual canonical quantization can be reproduced, including the effect of anti-particles. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, for example, in the definition of Noether charges.

38 pages, 4 figures, the errors of definitions are corrected and arguments are added

References in corpus (4)

• Variational Principles for Stochastic Fluid Dynamics
• Lieb-Thirring Bound for Schrödinger Operators with Bernstein Functions of the Laplacian
• Navier-Stokes, Gross-Pitaevskii and Generalized Diffusion Equations using Stochastic Variational Method
• Classicalization of Quantum Variables and Quantum-Classical Hybrids

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• Analytic Continuation of Stochastic Mechanics
• Simulating Nelsonian Quantum Field Theory
• Classical Statistical simulation of Quantum Field Theory
• Unification of Stochastic and Quantum Thermodynamics in Scalar Field Theory via a Model with Brownian Thermostat
• Torsion-Driven Nonlinearity in Spinless Quantum Mechanics