Related papers: Stochastic Quantization of Relativistic Theories

Over the past five years, there has been significant progress on the problem of quantization of diffeomorphism covariant field theories with {\it local} degrees of freedom. The absence of a background space-time metric in these theories…

This article continues and completes our previous work [14] J. Phys. Commun. 2 (2018) 025007. First of all, we present two methods of quantization associated with a linear connection given on a differentiable manifold, one of them being the…

The formulation of a consistent measurement theory for relativistic quantum fields has become a problem of growing foundational and practical significance. Standard non-relativistic measurement models fail to incorporate the essential…

The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a…

We revise the problem of the quantization of relativistic particle models (spinless and spinning), presenting a modified consistent canonical scheme. One of the main point of the modification is related to a principally new realization of…

The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…

We show that the noncritical string field theory developed from two-dimensional quantum gravity in the framework of causal dynamical triangulations can be viewed as arising through a stochastic quantization. This requires that the proper…

A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant…

A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality…

A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…

A subjective survey of stochastic models of quantum mechanics is given along with a discussion of some key radiative processes, the clues they offer, and the difficulties they pose for this program. An electromagnetic basis for deriving…

In quantizing gravity based on stochastic quantization method, the stochastic time plays a role of the proper time. We study 2D and 4D Euclidean quantum gravity in this context. By applying stochastic quantization method to real symmetric…

We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…

The Nelson stochastic mechanics is derived as a consequence of the basic physical principles such as the principle of relativity of observations and the invariance of the action quantum. The unitary group of quantum mechanics is represented…

There exists a two parameter action, the variation of which produces both the geodesic equation and the geodesic deviation equation. In this paper it is shown that this action can be quantized by the canonical method, resulting in equations…

Covariant stochastic partial (pseudo-)differential equations are studied in any dimension. In particular a large class of covariant interacting local quantum fields obeying the Morchio-Strocchi system of axioms for indefinite quantum field…

We describe an extension of the axioms of quantization to the case of 2-plectic manifolds. We show how such quantum spaces can be obtained as stable classical solutions in a zero-dimensional 3-algebra reduced model obtained by dimensional…

First of all we shortly illustrate how the symplectic quantization scheme [Gradenigo and Livi, 2021] can be applied to a relativistic field theory with self-interaction. Taking inspiration from the stochastic quantization method by Parisi…

Combination of a construction of unambiguous quantum conditions out of the conventional one and a simultaneous quantization of the positions, momenta, angular momenta and Hamiltonian leads to the geometric potential given by the so-called…

This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's…