Stochastic Quantization of Relativistic Theories
arXiv:2103.02501 · doi:10.1063/5.0057720
Abstract
It was shown recently that stochastic quantization can be made into a well defined quantization scheme on (pseudo-)Riemannian manifolds using second order differential geometry, which is an extension of the commonly used first order differential geometry. In this letter, we show that restrictions to relativistic theories can be obtained from this theory by imposing a stochastic energy-momentum relation. In the process, we derive non-perturbative quantum corrections to the line element as measured by scalar particles. Furthermore, we extend the framework of stochastic quantization to massless scalar particles.
arXiv commentv1: 12 pages. v2: clarifications added. v3: appendix added, to appear in J.Math.Phys
References in corpus (13)
- On the Renormalizability of Horava-Lifshitz-type Gravities
- Quantum Theory from Quantum Gravity
- Relating Field Theories via Stochastic Quantization
- The Schroedinger Problem, Levy Processes Noise in Relativistic Quantum Mechanics
- MARKOV DIFFUSIONS IN COMOVING COORDINATES AND STOCHASTIC QUANTIZATION OF THE FREE RELATIVISTIC SPINLESS PARTICLE
- Stochastic Emergent Quantum Gravity
- Stochastic Quantization and AdS/CFT
- On the stochastic mechanics of the free relativistic particle
- Stochastic mechanics and the Feynman integral
- Stochastic Quantization on Lorentzian Manifolds
- Stochastic Foundation of Quantum Mechanics and the Origin of Particle Spin
- Variational Principle of Hydrodynamics and Quantization by Stochastic Process
- Equivalence of quantum harmonic oscillators and classical oscillators subject to random forces