Using the recently developed groupoidal description of Schwinger’s picture Quantum Mechanics, a new approach to Dirac’s fundamental question on role Lagrangian in Mechanics is provided. It shown that function [Formula: see text] groupoid configurations (or kinematical groupoid) quantum system determines state von Neumann algebra histories system. This function, which we call q-Lagrangian, can b...

This paper is a personal look at some issues in the representation theory of Lie groups having to do with the role of commutative hypergroups, bi-modules, and the construction of representations. We begin by considering Frobenius’ original approach to the character theory of a finite group and extending it to the Lie group setting, and then introduce bi-modules as objects intermediate between c...

are uniform expanders. Nikolov [N] proved that every classical group is a bounded product of SLn(q)’s (with possible n = 2, but the proof shows that if the Lie rank is sufficiently high, say ≥ 14, one can use SLn(q) with n ≥ 3). Bounded product of expander groups are uniform expanders. Thus together, their results cover all classical groups of high rank. So, our Theorem is new for classical gro...

The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them relies on the action of the orthogonal or symplectic group on a space of tensors, while the second is provided by the action of this group on the symmetric algebra of the corresponding Lie algebra. We c...

‎in this paper, we formulate the fourth order sturm-liouville problem (fslp) as a lie group matrix differential equation. by solving this ma- trix differential equation by lie group magnus expansion, we compute the eigenvalues of the fslp. the magnus expansion is an infinite series of multiple integrals of lie brackets. the approximation is, in fact, the truncation of magnus expansion and a gauss...

In this review, we give a basic introduction to the κ-deformed relativistic phase space and free quantum fields. After review of κ-Poincaré algebra, illustrate construction classical particle using tools Lie bi-algebras Poisson–Lie groups. We then discuss how construct scalar field theory on non-commutative κ-Minkowski associated group valued nature momenta affects propagation.