Related papers: Some new considerations about the $\nu$-function
This paper describes how the structure of the state space of the quantum harmonic oscillator can be described by an adjunction of categories, that encodes the raising and lowering operators into a commutative comonoid. The formulation is an…
In this paper, the generalized coherent state for quantum systems with degenerate spectra is introduced. Then, the nonclassicality features and number-phase entropic uncertainty relation of two particular degenerate quantum systems are…
In this pedagogically structured article, we describe a generalized harmonic formulation of the Einstein equations in spherical symmetry which is regular at the origin. The generalized harmonic approach has attracted significant attention…
A method of proving local continuity of concave functions on convex set possessing the $\mu$-compactness property is presented. This method is based on a special approximation of these functions. The class of $\mu$-compact sets can be…
The axiomatic formulation of quantum field theory (QFT) of the 1950's in terms of fields defined as operator valued Schwartz distributions is re-examined in the light of subsequent developments. These include, on the physical side, the…
Definition of Feynman integrals as solutions of some well defined systems of differential equations is proposed. This definition is equivalent to usual one but needs no regularization and application of $R$-operation. It is argued that…
The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…
This paper is devoted to the proof Gauss' divergence theorem in the framework of "ultrafunctions". They are a new kind of generalized functions, which have been introduced recently [2] and developed in [4], [5] and [6]. Their peculiarity is…
Reduction is shown to be a possible consequence of the basic principles of quantum mechanics, involving no branching of the quantum state of the universe. The key feature of a measurement is attributed to the creation of macroscopic germs…
Geometric quantization is a natural way to construct quantum models starting from classical data. In this work, we start from a symplectic vector space with an inner product and -- using techniques of geometric quantization -- construct the…
The aim of this work is to define a continuous functional calculus in quaternionic Hilbert spaces, starting from basic issues regarding the notion of spherical spectrum of a normal operator. As properties of the spherical spectrum suggest,…
We consider an ordinary nonlinear differential equation with generalized coefficients as an equation in differentials in algebra of new generalized functions. Then the solution of such equation will be a new generalized function. In the…
We define a series $\mathcal{F}_{M,N}$ as a certain generalization of $q$-hypergeometric function. We study its duality and the system of $q$-difference nonlinear equations which admits particular solutions in terms of $\mathcal{F}_{1,M}$.
We review realistic models that reproduce quantum theory in some limit and yield potentially new physics outside that limit. In particular, we consider deterministic hidden-variables theories (such as the pilot-wave model) and their…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
The classical limit for generalized partition functions is obtained using coherent states. In this framework it is presented a general procedure to obtain all the corrections to the classical limit. In particular, the first and second order…
The a-function is a proposed quantity defined for quantum field theories which has a monotonic behaviour along renormalisation group flows, being related to the beta-functions via a gradient flow equation involving a positive definite…
The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
We propose a new formalism of quantum subsystems which allows to unify the existing and new methods of reduced description of quantum systems. The main mathematical ingredients are completely positive maps and correlation functions. In this…
The geometric quantization problem is considered from the point of view of the Davies and Lewis approach to quantum mechanics. The influence of the measuring device is accounted in the classical and quantum case and it is shown that the…