相关论文: A novel class of functionals for perturbative alge…

Open quantum systems can display periodic dynamics at the classical level either due to external periodic modulations or to self-pulsing phenomena typically following a Hopf bifurcation. In both cases, the quantum fluctuations around…

We study non-linear additive functionals of stationary Gaussian fields over anisotropically growing domains in $\mathbb{R}^d$, including spatiotemporal settings, and establish Gaussian and non-Gaussian limit theorems under non-separable…

We delve into the in-in formalism and derive general expressions for the computation of n-point functions for a self-interacting scalar field by means of a probability density functional (PDF). Even though in typical situations these…

We extend the category of (super)manifolds and their smooth mappings by introducing a notion of microformal or "thick" morphisms. They are formal canonical relations of a special form, constructed with the help of formal power expansions in…

Let $Q(x)$ denote a periodic function on the real line. The Schr\"odinger operator, $H_Q=-\partial_x^2+Q(x)$, has $L^2(\mathbb{R})-$ spectrum equal to the union of closed real intervals separated by open spectral gaps. In this article we…

We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative…

We review here the quantum mechanics of some noncommutative theories in which no state saturates simultaneously all the non trivial Heisenberg uncertainty relations. We show how the difference of structure between the Poisson brackets and…

The main aim of this work is to relate integrability in QFT with a complete particle interpretation directly to the principle of causal localization, circumventing the standard method of finding sufficiently many conservation laws. Its…

The primary objective of this paper is to establish an algebraic framework for the space of weakly slice regular functions over several quaternionic variables. We recently introduced a $*$-product that maintains the path-slice property…

A recurrent theme in functional analysis is the interplay between the theory of positive definite functions, and their reproducing kernels, on the one hand, and Gaussian stochastic processes, on the other. This central theme is motivated by…

In this article, using the language of jet space, we propose a functional class space for pseudo-local functionals. We test this functional class proposal in a number of examples ranging from string-field-theory to AdS/CFT dualities.…

Using the quadrature bases that incorporate the spatiotemporal degrees of freedom, we develop a Wigner functional theory for quantum optics, as an extension of the Moyal formalism. Since the spatiotemporal quadrature bases span the complete…

According to \textit{effective realism}, scientific theories give us knowledge about the unobservable world, but not at the fundamental level. This view is justified by the well-received \textit{effective-field-theory} (EFT) approach to…

In the category of sets and partial functions, $\mathsf{PAR}$, while the disjoint union $\sqcup$ is the usual categorical coproduct, the Cartesian product $\times$ becomes a restriction categorical analogue of the categorical product: a…

We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…

We establish natural splittings for the values of global Mackey functors at orthogonal, unitary and symplectic groups. In particular, the restriction homomorphisms between the orthogonal, unitary and symplectic groups of adjacent dimensions…

We establish a new, real-space formula for the Zak phase for one dimensional periodic Jacobi operators in terms of the Weyl $m_+$-function that does not rely on Floquet-Bloch theory. This novel representation highlights the dependence of…

This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust…

This paper is devoted to the multivariable $H^\infty$ functional calculus associated with a finite commuting family of sectorial operators on Banach space. First we prove that if $(A_1,\ldots, A_d)$ is such a family, if $A_k$ is…

We revise the technique of semiclassical effective dynamics, in particular reexamining the evaluation of Poisson structure of the so-called central moments capturing quantum corrections, providing a systematic, pedagogical, and efficient…