Related papers: Subfactors and Mathematical Physics
The logical line is traced of formulation of theory of mechanics founded on the basic correlations of mathematics of hypercomplex numbers and associated geometric images. Namely, it is shown that the physical equations of quantum, classical…
Geometric formulation of Lagrangian relativistic mechanics in the terms of jets of one-dimensional submanifolds is generalized to Lagrangian theory of submanifolds of arbitrary dimension.
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
The relationship between mathematics and physics has long been an area of interest and speculation. Subscribing to the recent definition by Tegmark, we present a mathematical structure involving the only division rings - the real,…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
Physical quantities and physical dimensions are among the first concepts encountered by students in their undergraduate career. In this pedagogical review, I will start from these concepts and, using the powerful tool of dimensional…
A model about excited field of a particle is discussed. We found this model will give wave-particle duality clearly and its Lagrangian is consistent with Quantum Theory. A new interpretation of quantum mechanics but not statistical…
A physical theory is proposed that obeys both the principles of special relativity and of quantum mechanics. As a key feature, the laws are formulated in terms of quantum events rather than of particle states. Temporal and spatial…
This paper surveys some selected topics in the theory of conformal metrics and their connections to complex analysis, partial differential equations and conformal differential geometry.
The status of multifractional theories is reviewed using comparative tables. Theoretical foundations, classical matter and gravity dynamics, cosmology and experimental constraints are summarized and the application of the multifractional…
A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.
V. Drinfeld proposed conjectures on geometric Langlands correspondence and its quantum deformation. We refine these conjectures and propose their relationship with algebraic conformal field theory.
We briefly go through the problem of the quantum description of Brownian motion, concentrating on recent results about the connection between dynamics of the particle and dynamic structure factor of the medium.
Some conjectures and open problems in convex geometry are presented, and their physical origin, meaning, and importance, for quantum theory and generic statistical theories, are briefly discussed.
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
The phenomenon of quantum number fractionalization is explained. The relevance of non-trivial phonon field topology is emphasized.
The role of operational quantum mechanics, quantum axiomatics and quantum structures in general is presented as a contribution to a compendium on quantum physics, its history and philosophy.
This is intended as an introduction to and review of the work of V, Arnold and his collaborators on the theory of Lagrangian and Legendrian submanifolds and their associated maps. The theory is illustrated by applications to Hamilton-Jacobi…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…