Related papers: Stochastic Quantization of $(\lambda\phi^{4})_d$ S…
In de Sitter space, scale invariant fluctuations give rise to infrared logarithmic corrections to physical quantities, which eventually spoil perturbation theories. For models without derivative interactions, it has been known that the…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
Quantization of electromagnetic fields is investigated in the framework of stochastic variational method (SVM). Differently from the canonical quantization, this method does not require canonical form and quantization can be performed…
Stochastic inflation is an effective theory describing the super-Hubble, coarse-grained, scalar fields driving inflation, by a set of Langevin equations. We previously highlighted the difficulty of deriving a theory of stochastic inflation…
Lattice Field theory allows to extract properties of particles in strongly coupled quantum field theories by studying Euclidean vacuum expectation values. When estimated from numerical Monte Carlo simulations these are typically affected by…
Covariant, self-interacting scalar quantum field theories admit solutions for low enough spacetime dimensions, but when additional divergences appear in higher dimensions, the traditional approach leads to results, such as triviality, that…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinskii's…
In this paper, we propose a quantized learning equation with a monotone increasing resolution of quantization and stochastic analysis for the proposed algorithm. According to the white noise hypothesis for the quantization error with dense…
Standard Model with a classical conformal invariance holds the promise to give a better understanding of the hierarchy problem and could pave the way for beyond the standard model physics. So, we give here a mathematical treatment of a…
We develop a Schr\"{o}dinger-picture formulation for a scalar quantum field driven by a Lorentz-invariant white-noise field. The quantum state of the system is described by a stochastic wave functional that evolves according to a stochastic…
Stochastic quantization provides a connection between quantum field theory and statistical mechanics, with applications especially in gauge field theories. Euclidean quantum field theory is viewed as the equilibrium limit of a statistical…
In a recent work [DDRZ20], it has been developed a novel framework aimed at studying at a perturbative level a large class of non-linear, scalar, real, stochastic PDEs and inspired by the algebraic approach to quantum field theory. The main…
A covariant quantization scheme employing reducible representations of canonical commutation relations with positive-definite metric and Hermitian four-potentials is tested on the example of quantum electrodynamic fields produced by a…
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…
During inflation explicit perturbative computations of quantum field theories which contain massless, non-conformal fields exhibit secular effects that grow as powers of the logarithm of the inflationary scale factor. Starobinski\u{\i}'s…
We develop an action formulation of stochastic dynamics in the Hilbert space. By generalizing the Wiener process into 1+3-dimensional spacetime, we define a Lorentz-invariant random field. By coupling the random to quantum fields, we obtain…
A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the…
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…
A stochastic field theory approach is applied to a coarse-grained polymer model that will enable studies of polymer behavior under non-equilibrium conditions. This article is focused on the validation of the new model in comparison to…