Related papers: Poincar\'e et les quanta
This note studies the existence of quotients by finite set theoretic equivalence relations. May 18: Substantial revisions with a new appendix by C. Raicu
Two $(p,q)$-Laplace transforms are introduced and their relative properties are stated and proved. Applications are made to solve some $(p,q)$-linear difference equations.
The purpose of this paper is to present the notion of quotient of supergroups in different categories using the unified treatment of the functor of points and to examine some physically interesting examples.
The quantum-mechanical description of the world, including human observers, makes substantial use of entanglement. In order to understand this, we need to adopt concepts of truth, probability and time which are unfamiliar in modern…
This article is meant as a mathematical appendix or comment on [BT]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [BT] on bifurcation…
The interpretation of quantum mechanics has been discussed since this theme first was brought up by Einstein and Bohr. This article describes a proposal for a new foundation of quantum theory, partly drawing upon ideas from statistical…
A detailed study of the classical and quantum mechanics of a free particle on a double cone and the particle bounded to its tip by the harmonic oscillator potential is presented.
In ths paper we discuss the new concept of the q-extension of Genocchi numbers and give the some relations between q-Genocchi polynomials and q-Euler numbers.
The concept of uncertainty quanta for a general system is introduced and applied to some important problems in physics and mathematics. EPR paradox gives new clue to the further understanding of particle correlation which turns out to be…
We study the variances of the coordinates of an event considered as quantum observables in a Poincare' covariant theory. The starting point is their description in terms of a covariant positive-operator-valued measure on the Minkowski…
We discuss the status and some perspectives of relativistic quantum physics.
We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.
We propose a definition of a Poincar\'e algebra for a two dimensional space--time with one discretized dimension. This algebra has the structure of a Hopf algebra. We use the link between Onsager's uniformization of the Ising model and the…
The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
Two popular attempts to understand the quantum physics of gravitation are critically assessed. The talk on which this paper is based was intended for a general particle-physics audience.
This is a series of lecture notes explaining topos theory and its application in physics.
In this paper by using geometric techniques, we provide upper bounds for the Poincar\'e recurrence time of a quantum mixed state with discrete spectrum of energies. In the case of discrete but finite spectrum we obtain two type of upper…
Two types of Poisson pencils connected to classical R-matrices and their quantum counterparts are considered. A representation theory of the quantum algebras related to some symmetric orbits in $sl(n)^*$ is constructed. A twisted version of…
The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).
We solve two conjectures of Ceken-Palmieri-Wang-Zhang concerning discriminants and give some applications.