Related papers: Brackets
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects…
We introduce and study a construction of higher derived brackets generated by a (not necessarily inner) derivation of a Lie superalgebra. Higher derived brackets generated by an element of a Lie superalgebra were introduced in our earlier…
We provide a general framework to study invariant properties of various gradient-like and Laplace-like differential operators naturally associated to geometric structures on $\mathbb{R}^n$, which encompass Euclidean, Minkowski,…
We consider odd Laplace operators arising in odd symplectic geometry. Approach based on semidensities (densities of weight 1/2) is developed. The role of semidensities in the Batalin--Vilkovisky formalism is explained. In particular, we…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
The geometry of jets of submanifolds is studied, with special interest in the relationship with the calculus of variations. A new intrinsic geometric formulation of the variational problem on jets of submanifolds is given. Working examples…
Classical limits of quantum systems are shown to lead to different conceptions of spaces different from the classical one underlying the process of quantization of such systems. The accent is put in situations where traces of…
The Weltanschauung emerging from quantum theory clashes profoundly with our classical concepts. Quantum characteristics like superposition, entanglement, wave-particle duality, nonlocality, contextuality are difficult to reconcile with our…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
We provide a general definition of Toda brackets in a pointed model categories, show how they serve as obstructions to rectification, and explain their relation to the classical stable operations.
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…
This paper classifies the splints of the root system of classical Lie superalgebras as a superalgebraic conversion of the splints of classical root systems. It can be used to derive branching rules, which have potential physical application…
Wigner's "unreasonable effectiveness of mathematics" in physics can be understood as a reflection of a deep and unexpected unity between the fundamental structures of mathematics and of physics. Some of the history of evidence for this is…
The concept of Lagrange structure allows one to systematically quantize the Lagrangian and non-Lagrangian dynamics within the path-integral approach. In this paper, I show that any Lagrange structure gives rise to a covariant Poisson…
We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level accessible to scientists from…
We give a review of classical, thermodynamic and quantum properties of black holes relevant to fundamental physics.
Geometrization of physical theories have always played an important role in their analysis and development. In this contribution we discuss various aspects concerning the geometrization of physical theories: from classical mechanics to…
This paper points out the usefulness of the concept of derivation along a map in many problems in Geometry and Physics. In particular it will be shown that this approach allows us to translate the usual concepts arising in Geometrical…
The Rankin--Cohen brackets provide a basic example of ``non-elementary" differential symmetry breaking operators. They can be interpreted as bi-differential operators remarkable for reflecting the structure of fusion rules for holomorphic…