Related papers: Classical and stochastic L\"owner-Kufarev equation…
We generalize the Kolmogorov continuity theorem and prove the continuity of a class of stochastic fields with the parameter. As an application, we derive the continuity of solutions for nonlocal stochastic parabolic equations driven by…
We try to develop a coherent picture on Liouville theory as a two-dimensional conformal field theory that takes into account the perspectives of path-integral approach, bootstrap, canonical quantization and operator approach. To do this, we…
Understanding the demarcation line between classical and quantum is an important issue in modern physics. The development of such an understanding requires a clear picture of the various concurrent notions of `classicality' in quantum…
Canonical coordinates for the Schr\"odinger equation are introduced, making more transparent its Hamiltonian structure. It is shown that the Schr\"odinger equation, considered as a classical field theory, shares with Liouville completely…
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…
Considering stationary states of continuous-variable systems undergoing an open dynamics, we unveil the connection between properties and symmetries of the latter and the dynamical parameters. In particular, we explore the relation between…
In classical stochastic theory, the joint probability distributions of a stochastic process obey by definition the Kolmogorov consistency conditions. Interpreting such a process as a sequence of physical measurements with probabilistic…
We trace the history of conformal bootstrap from its early days to our times - a great example of unity of physics. We start by describing little-known details about the origins of conformal field theory in the study of strong interactions…
Obtaining explicit stability estimates in classical functional inequalities like the Sobolev inequality has been an essentially open question for 30 years, after the celebrated but non-constructive result of G. Bianchi and H. Egnell in…
Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide…
In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and…
This book is devoted to review two of the most relevant approaches to the study of classical field theories of first order, say k-symplectic and k-cosymplectic. In the last part, we relate the k-symplectic and k-cosymplectic manifolds with…
The relation between the distribution of work performed on a classical system by an external force switched on an arbitrary timescale, and the corresponding equilibrium free energy difference, is generalized to quantum systems. Using the…
Schauder theory is a basic tool in the study of elliptic and parabolic PDEs, asserting that solutions inherit the regularity of the coefficients. It plays a central role in establishing higher regularity for solutions to a broad class of…
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
A review on the main results concerning the algebraic and differential properties of the averaging and coordination operators and the properties of the space-time averages of macroscopic gravity is given. The algebraic and differential…
Deterministic dynamical models are discussed which can be described in quantum mechanical terms. -- In particular, a local quantum field theory is presented which is a supersymmetric classical model. The Hilbert space approach of Koopman…
Moment problems and orthogonal polynomials, both meant in a single real variable, belong to the oldest problems in Classical Analysis. They have been developing for over a century in two parallel, mostly independent streams. During the last…