Symplectic quantization I: dynamics of quantum fluctuations in a relativistic field theory

Abstract

We propose here a new symplectic quantization scheme, where quantum fluctuations of a scalar field theory stem from two main assumptions: relativistic invariance and equiprobability of the field configurations with identical value of the action. In this approach the fictitious time of stochastic quantization becomes a genuine additional time variable, with respect to the coordinate time of relativity. This proper time is associated to a symplectic evolution in the action space, which allows one to investigate not only asymptotic, i.e. equilibrium, properties of the theory, but also its non-equilibrium transient evolution. In this paper, which is the first one in a series of two, we introduce a formalism which will be applied to general relativity in the companion work "Symplectic quantization II".

arXiv comment7 pages

References in corpus (6)

• Parton Physics on Euclidean Lattice
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Von Neumann Algebra Automorphisms and Time-Thermodynamics Relation in General Covariant Quantum Theories
• Ultra-slow-roll inflation with quantum diffusion
• Localization transition in the Discrete Non-Linear Schrödinger Equation: ensembles inequivalence and negative temperatures
• Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant

Cited by in corpus (4)

• Symplectic quantization II: dynamics of space-time quantum fluctuations and the cosmological constant
• Symplectic quantization III: Non-relativistic limit
• Symplectic Quantization: numerical results for the Feynman propagator on a 1+1 lattice and the theoretical relation with Quantum Field Theory
• Symplectic Quantization and Minkowskian Statistical Mechanics: simulations on a 1+1 lattice