Related papers: Relativistic Brownian Motion in 3+1 Dimensions

Conformal geometry is considered within a general relativistic framework. An invariant distant for proper time is defined and a parallel displacement is applied in the distorted space-time, modifying Einstein's equation appropriately. A…

General relativity in three spacetime dimensions is used to explore three approaches to the ``problem of time'' in quantum gravity: the internal Schr\"odinger approach with mean extrinsic curvature as a time variable, the Wheeler-DeWitt…

The running of Newton's constant can be taken into account by considering covariant, non local generalizations of the field equations of general relativity. These generalizations involve nonanalytic functions of the d'Alembertian, as…

We construct relativistic-invariant spinning-particle Lagrangian without auxiliary variables. Spin is considered as a composed quantity constructed on the base of non-Grassmann vector-like variable. The variational problem guarantees both…

It is shown that nearly-flat 3+1D spacetime emerging from a dual quantum field theory in 2+1D displays quantum fluctuations from classical Euclidean geometry on macroscopic scales. A covariant holographic mapping is assumed, where plane…

This paper is the first of two papers devoted to formulation of quantum mechanics of a particle in a normal geodesic frame of reference in the general Riemannian space-time. Here canonical quantization of geodesic motion in the…

This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and…

Quantum gravity has long remained elusive from an observational standpoint. Developing effective cosmological models motivated by the fundamental aspects of quantum gravity is crucial for bridging theory with observations. One key aspect is…

We consider a primary model of ac-driven Brownian motors, i.e., a classical particle placed in a spatial-time periodic potential and coupled to a heat bath. The effects of fluctuations and dissipations are studied by a time-dependent…

We present a systematic expansion of Kramers equation in the high friction limit. The latter is expanded within an operator continued fraction scheme. The relevant operators include both temporal and spatial derivatives and a covariant…

In this study, we investigate the behavior of inertial active Brownian particles in a $d$-dimensional harmonic trap in the presence of translational diffusion. While the solution of the Fokker-Planck equation is generally challenging, it…

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that…

We survey Brownian manifolds -- manifolds that can parametrise Brownian motion -- and those that cannot. We consider covariances of space-time processes, particularly those when space is the sphere -- geo-temporal processes. There are…

The continued-fraction method to solve classical Fokker--Planck equations has been adapted to tackle quantum master equations of the Caldeira--Leggett type. This can be done taking advantage of the phase-space (Wigner) representation of the…

Aspects of a generalized representation theory of current algebras in $3+1$ dimensions are discussed in terms of the Fock bundle method, the sesquilinear form approach (of Langmann and Ruijsenaars), and Hilbert space cocycles.

We reconsider formulating $D$ dimensional gauge theories, with the focus on the case of gravity theories, in spacetimes with boundaries. We extend covariant phase space formalism to the cases in which boundaries are allowed to fluctuate. We…

This work studies the spatial derivatives of decoupling fields to strongly coupled forward-backward stochastic differential equations in a Brownian setting. We formally deduce the backward dynamics of the first and higher spatial…

The framework of relativistic energy density functionals is extended to include correlations related to restoration of broken symmetries and fluctuations of collective variables. A new implementation is developed for the solution of the…

We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…

Brownian motion is modelled by a harmonic oscillator (Brownian particle) interacting with a continuous set of uncoupled harmonic oscillators. The interaction is linear in the coordinates and the momenta. The model has an analytical solution…