Related papers: Q*-normal spaces
A nonlocal generalization of quantum field theory in which momentum space is the space of continuous maps of a circle into $\mathbf{R}^4$ is proposed. Functional integrals in this theory are proved to exist. Renormalized quantum field model…
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
The aim of this paper is to extend the external characterization of I-favorable spaces. This allows us to obtain a characterization of compact I-favorable spaces in terms of quasi k-metrics. We also provide proofs of some author's results…
There has been much recent work on quantum inequalities to constrain negative energy. These are uncertainty principle-type restrictions on the magnitude and duration of negative energy densities or fluxes. We consider several examples of…
Quasinormal modes (QNMs) are essential for understanding the stability and resonances of open systems, with increasing prominence in black hole physics. We present here the first study of QNMs of optical potentials. We show that solitons…
Let X be a (connected and reduced) complex space. A q-collar of X is a bounded domain whose boundary is a union of a strongly q-pseudoconvex, a strongly q-pseudoncave and two flat (i.e. locally zero sets of pluriharmonic functions)…
The notion of an open quantum subgroup of a locally compact quantum group is introduced and given several equivalent characterizations in terms of group-like projections, inclusions of quantum group C*-algebras and properties of respective…
In this paper, we study some features of n-normed spaces with respect to norms of its quotient spaces. We define continuous functions with respect to the norms of its quotient spaces and show that all types of continuity are equivalent. We…
Weak measurement is a standard measuring procedure with two changes: it is performed on pre- and post-selected quantum systems and the coupling to the measuring device is weakened. The outcomes of weak measurements, ``weak values'' are very…
In this paper, we give new characterizations of algebraic regularity by using differential forms and difference quotients.
We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we…
In the first part of the paper we give a definition of G_q-function and we establish a regularity result, obtained as a combination of a q-analogue of the Andre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, \S 13]. In the second…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…
The quest for a consistent theory which describes the quantum microstructure of spacetime seems to require some departure from the paradigms that have been followed in the construction of quantum theories for the other fundamental…
We discuss some higher-loop studies of renormalization-group flows and fixed points in various quantum field theories.
The recent discoveries of new forms of quantum statistics require a close look at the under-lying Fock space structure. This exercise becomes all the more important in order to provide a general classification scheme for various forms of…
We study random compositions of transformations having certain uniform fiberwise properties and prove bounds which in combination with other results yield a quenched central limit theorem equipped with a convergence rate, also in the…
In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…
The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of…
There are two basic ways of weakening the definition of the well-known metric regularity property by fixing one of the points involved in the definition. The first resulting property is called metric subregularity and has attracted a lot of…