Related papers: The Cumulant Bijection and Differential Forms
Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented and used to classify…
We investigate the relation between Cartan decompositions of the unitary group and discrete quantum symmetries. To every Cartan decomposition there corresponds a quantum symmetry which is the identity when applied twice. As an application,…
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. For the fractional harmonic oscillator, the corresponding q-number is derived.…
The equivalence group is determined for systems of linear ordinary differential equations in both the standard form and the normal form. It is then shown that the normal form of linear systems reducible by an invertible point transformation…
A method is proposed for defining an arbitrary number of differential calculi over a given noncommutative associative algebra. As an example the generalized quantum plane is studied. It is found that there is a strong correlation, but not a…
This paper deals with quon algebras or deformed oscillator algebras, for which the deformation parameter is a root of unity. We show the interest of such algebras for fractional supersymmetric quantum mechanics, angular momentum theory and…
A certain notion of canonical equivalence in quantum mechanics is proposed. It is used to relate quantal systems with discrete ones. Discrete systems canonically equivalent to the celebrated harmonic oscillator as well as the quartic and…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic…
Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the…
This document is an extended abstract for two articles in preparation. Recently, framing lattices were introduced to generalize many classical lattices such as the Tamari lattice and the weak order on the symmetric group. We define bricks…
We describe a decomposition of the Lie group of unitary evolutions for a bipartite quantum system of arbitrary dimensions. The decomposition is based on a recursive procedure which systematically uses the Cartan classification of the…
On conformally compact manifolds of arbitrary signature, we use conformal geometry to identify a natural (and very general) class of canonical boundary problems. It turns out that these encompass and extend aspects of already known…
An algebraic formalism for the study of a system of charged particles interacting with an external quantum field is developed. The notion of monoidal categories with duality is used for the description of composite systems and corresponding…
Cosmological correlation functions are central observables in modern cosmology, as they encode properties of the early universe. In this paper, we derive novel canonical differential equations for wavefunction coefficients in power-law FRW…
Quantum algebras are a mathematical tool which provides us with a class of symmetries wider than that of Lie algebras, which are contained in the former as a special case. After a self-contained introduction to the necessary mathematical…
Defects are a useful tool in the study of quantum field theories. This is illustrated in the example of two-dimensional conformal field theories. We describe how defect lines and their junction points appear in the description of symmetries…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
Generalized differential forms are used in discussions of metric geometries and Einstein's vacuum field equations. Cartan's structure equations are generalized and applied. In particular flat generalized connections are associated with any…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…