Related papers: Nonperturbative Stochastic Quantization of the Hel…

We propose a generalization of the stochastic gauge fixing procedure for the stochastic quantization of gauge theories where not only the drift term of the stochastic process is changed but also the Wiener process itself. All gauge…

We study the stochastic quantization of the system with first class constraints in phase space. Though the Langevin equations of the canonical variables are defined without ordinary gauge fixing procedure, gauge fixing conditions are…

It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…

Mathematical models for complex systems under random fluctuations often certain uncertain parameters. However, quantifying model uncertainty for a stochastic differential equation with an $\alpha$-stable L\'evy process is still lacking.…

We show how to obtain all covariant field equations for massless particles of arbitrary integer, or half-integer, helicity in four dimensions from the quantization of the rigid particle, whose action is given by the integrated extrinsic…

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are…

We consider a nonlinear pendulum whose suspension point undergoes stochastic vibrations in its plane of motion. Stochastic vibrations are constructed by stochastic differential equations with random periodic solutions. Averaging over these…

A non-perturbative effective model is derived for the Higgs sector of the standard model, described by a simple scalar theory. The renormalized couplings are determined by the derivatives of the Gaussian Effective Potential that are known…

Using stochastic quantization method we derive gauge-invariant equations, connecting multilocal vacuum correlators of nonperturbative field configurations immersed into the quantum background. Three alternative methods of stochastic…

In this paper we consider stabilised finite element methods for hyperbolic transport equations without coercivity. Abstract conditions for the convergence of the methods are introduced and these conditions are shown to hold for three…

The Lie-Poisson structure of non-Abelian Thirring models is discussed and the Hamiltonian quantization of these theories is carried out. The consistency of the Hamiltonian quantization with the path integral method is established. It is…

The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major…

Stochastic quantisation normally involves the introduction of a fictitious extra time parameter, which is taken to infinity so that the system evolves to an equilibrium state.In the case of a locally supersymmetric theory, an interesting…

A simpler method of quantization is given for massive gauge theories. This method gives the same results as those of the conventional massive gauge theory with ghost and Higgs fields under the Higgs mass. Besides, we point out physical…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

We discuss the quantization of an unstable field through the construction of a "one-particle Hilbert space." The system considered here is a neutral scalar field evolving over a globally hyperbolic static spacetime and subject to a…

Stochastic quantization is applied to derivation of equations connecting multilocal gauge-invariant correlators in different field theories. They include Abelian Higgs Model, QCD with spinless quarks at T=0 and T>0 and QED, where spin…

We study the classical motion of a particle subject to a stochastic force. We then present a perturbative schema for the associated Fokker-Planck equation where, in the limit of a vanishingly small noise source, a consistent dynamical model…

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical…

We construct a relativistically covariant stochastic model for systems of non-interacting spinless particles whose number undergoes random fluctuations. The model is compared with the canonical quantization of the free scalar field in the…