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

In this paper we study a class of functions that appear naturally in some equidistribution problems and that we call $F$-harmonic. These are functions of the universal cover of a closed and negatively curved which possess an integral…

Exact non-perturbative partition functions of coupling constants and external fields exhibit huge hidden symmetry, reflecting the possibility to change integration variables in the functional integral. In many cases this implies also some…

Let $\Omega$ be a sufficiently regular bounded open connected subset of $\mathbb{R}^n$ such that $0 \in \Omega$ and that $\mathbb{R}^n \setminus \mathrm{cl}\Omega$ is connected. Then we take $q_{11},..., q_{nn}\in ]0,+\infty[$ and $p \in…

We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…

Using properties of the determinant line bundle for a family of elliptic boundary value problems, we explain how the Fock space functor defines an axiomatic quantum field theory which formally models the Fermionic path integral. The 'sewing…

We present a new class of topological conformal field theories (TCFT) characterized by a rational $W$ potential, which includes the minimal models of A and D types as its subclasses. An explicit form of the $W$ potential is found by solving…

Let $K$ be a field, and let $f\in K(z)$ be rational function. The preimages of a point $x_0\in P^1(K)$ under iterates of $f$ have a natural tree structure. As a result, the Galois group of the resulting field extension of $K$ naturally…

We work out the perturbative expansion of quantum Liouville theory on the pseudosphere starting from the semiclassical limit of a background generated by heavy charges. By solving perturbatively the Riemann-Hilbert problem for the Poincare'…

In the determination of alpha_s from tau decays several different moments of the hadronic spectral functions have been used. In a recent work, we performed an analysis of their perturbative behaviour under two different assumptions for the…

In this paper we prove some characterizations of the matrix orthogonal polynomials whose derivatives are also orthogonal, which generalize other known ones in the scalar case. In particular, we prove that the corresponding orthogonality…

Constrained symplectic quantization is a functional formulation of quantum field theory in which quantum fluctuations are sampled through a deterministic Hamiltonian flow in an auxiliary intrinsic time $\tau$. In this paper we extend the…

Many observables in quantum field theories are involved non-analytic functions of the parameters of the theory. However, it is expected that they are not arbitrarily wild, but rather have only a finite amount of geometric complexity. This…

We study the class of functions on Lipschitz-graph domains satisfying a differential-oscillation condition and show that such functions are $\epsilon$-approximable. As a consequence we obtain the quantitative Fatou theorem in the spirit of…

This article summarises the theory of several bounded functional calculi for unbounded operators that have recently been discovered. The extend the Hille--Phillips calculus for (negative) generators $A$ of certain bounded $C_0$-semigroups,…

In this paper, we aim at characterizing generalized functionals of discrete-time normal martingales. Let $M=(M_n)_{n\in \mathbb{N}}$ be a discrete-time normal martingale that has the chaotic representation property. We first construct…

Under unitary evolution, a typical macroscopic quantum system is thought to develop wavefunction branches: a time-dependent decomposition into orthogonal components that (1) form a tree structure forward in time, (2) are approximate…

We characterize completely the Gneiting class of space-time covariance functions and give more relaxed conditions on the involved functions. We then show necessary conditions for the construction of compactly supported functions of the…

Using a particular Hilbert space representation of minimum-length deformed quantum mechanics, we show that the resolution of the wave-function singularities for strongly attractive potentials, as well as cosmological singularity in the…

We construct 3-dimensional once-Extended Topological Quantum Field Theories (ETQFTs for short) out of (possibly non-semisimple) modular categories, and we explicitly identify linear categories and functors in their image. The circle…

Quantum field theory (QFT) on fractal spacetimes is a program aiming at quantizing the gravitational interaction consistently at all energy scales thanks to an intrinsically or dynamically induced multiscale or multifractal-like spacetime…