Related papers: Stochastic quantization of Born-Infeld field
A large class of quantum and statistical field theoretical models, encompassing relevant condensed matter and non-abelian gauge systems, are defined in terms of complex actions. As the ordinary Monte-Carlo methods are useless in dealing…
We analyze three classical field theories based on the wave equation: scalar field, electrodynamics and linearized gravity. We derive certain generating formula on a hyperboloid and on a null surface for them. The linearized Einstein…
Stochastic quantization in physics has been considered to provide a path integral representation of a probability distribution for Ito processes. It has been indicated that the stochastic quantization can involve a potential term, if the…
The statistical linearization method known in nonlinear mechanics and random vibrations theory has been applied to stochastically quantized fields in finite temperature. It has been shown that even in its simplest form the method yields…
This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.
We consider the stochastic quantization equation associated with the weighted exponential quantum field model (or the H{\o}egh-Krohn model) on the two dimensional torus. Unlike in the case of the usual (unweighted) exponential model, the…
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…
We present a new non-abelian generalization of the Born-Infeld Lagrangian. It is based on the observation that the basic quantity defining it is the generalized volume element, computed as the determinant of a linear combination of metric…
We consider the mean field theory of the Random Field Ising Model obtained by weighing the many solutions of the mean field equations with Boltzmann-like factors. These solutions are found numerically in three dimensions and we observe…
The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…
A succinct presentation of the algebraic structure of the quantized Klein-Gordon field can be given in terms of a Lorentz invariant inner product. A presentation of a classical Klein-Gordon \emph{random} field at non-zero temperature can be…
In this work, we propose a new non-abelian generalization of the Born- Infeld lagrangian. It is based on a geometrical property of the abelian Born-Infeld lagrangian in its determinantal form. Our goal is to extend the abelian second type…
We propose a microscopic stochastic approach to improve description of nuclear dynamics beyond the mean-field approximation at low energies. It is shown that, for small amplitude fluctuations, the proposed model gives a result for the…
We argue that the quantized non-Abelian gauge theory can be obtained as the infrared limit of the corresponding classical gauge theory in a higher dimension. We show how the transformation from classical to quantum field theory emerges and…
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 investigate the application of Parisi-Wu stochastic quantization to the construction of random fields within the sublinear expectation framework. Using the semigroup approach and the infinite dimensional $G$-Ornstein Uhlenbeck process,…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We consider a stochastic lattice Cahn-Hilliard equation with nonautonomous nonlinear noise. First, we prove the existence of pullback random attractors in $\ell^2$ for the generated nonautonomous random dynamical system. Then, we construct…
Gaussian random field on general ultrametric space is introduced as a solution of pseudodifferential stochastic equation. Covariation of the introduced random field is computed with the help of wavelet analysis on ultrametric spaces. Notion…
In the present paper we consider the problem of description of an arbitrary generalized quantum measurement with outcomes in a measurable space. Analyzing the unitary invariants of a measuring process, we present the most general form of a…