Related papers: Stochastic quantization of the linearized gravitat…

This is an introduction to quantum gravity, aimed at a fairly general audience and concentrating on what have historically two main approaches to quantum gravity: the covariant and canonical programs (string theory is not covered). The…

Stochastic quantization is applied to derivation of the equations for the Wilson loops and generating functionals of the Wilson loops in the large-N limit. These equations are treated both in the coordinate and momentum representations. In…

We consider a quantization of relativistic wave equations which allows to treat quantum fields together with interacting particles at a finite time. We discuss also a dissipative interaction with the environment. We introduce a stochastic…

We present a first analysis of a nonperturbative approach to quantum gravity based on a representation of quantum field theory in terms of stochastic processes. The stochastic description accommodates a physical Lorentz-invariant…

The problem of obtaining a realistic, relativistic description of a quantum system is discussed in the context of a simple (light-cone) lattice field theory. A natural stochastic model is proposed which, although non-local, is relativistic…

The non-perturbative, lattice field theory approach towards the quantization of Euclidean gravity is reviewed. Included is a tentative summary of the most significant results and a presentation of the current state of art.

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck's constant. Here we give a cursory…

Covariant classical particle dynamics is described, and the associated covariant relativistic particle quantum mechanics is derived. The invariant symmetric bracket is defined on the space of quantum amplitudes, and its relation to a…

Linearized Einstein gravity (with possibly nonzero cosmological constant) is quantized in the framework of algebraic quantum field theory by analogy with Dimock's treatment of electromagnetism [Rev. Math. Phys. 4 (1992) 223--233]. To…

Quantizing the gravitational field described by General relativity being a notorious difficult, unsolved and maybe meaningless problem I use in this essay a different strategy: I consider a linear theory in the framework of Special…

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…

We review some works of E M Lifshitz connected with gravity and cosmology and also some later works, connected with his ideas. The main topics of this review are the stochastic cosmology of an anisotropic universe and of an isotropic…

We propose to formulate a theory for Classical Stochastic Gravity for certain applications in Astrophysics and Cosmology.This involves the Langevin approach in curved spacetime, which is introduced here, in the form of a classical…

We present a first attempt to apply the approach of deformation quantization to linearized Einstein's equations. We use the analogy with Maxwell equations to derive the field equations of linearized gravity from a modified Maxwell…

We give a short update of our research program on nonequilibrium statistical field theory applied to quantum processes in the early universe and black holes, as well as the development of stochastic gravity theory as an extension of…

In this paper we have applied Bohmian quantum theory to the linear field approximation of gravity and present a self--consistent quantum gravity theory in the linear field approximation. The theory is then applied to some specific problems,…

Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin…

Stochastic semiclassical gravity is a theory for the interaction of gravity with quantum matter fields which goes beyond the semiclassical limit. The theory predicts stochastic fluctuations of the classical gravitational field induced by…

We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) and we discuss the relationships between these approaches…

The back-reaction of a classical gravitational field interacting with quantum matter fields is described by the semiclassical Einstein equation, which has the expectation value of the quantum matter fields stress tensor as a source. The…