相关论文: Quaternionic Analysis, Representation Theory and P…
We express the real connective $K$ theory groups of the quaternion QL group of order $2^j\ge8$ in terms of the representation theory of by showing $ko_{4k-1}(BQL)=KSp(S^{4k+3}/\tau QL)$ where $tau$ is any fixed point free representation of…
Using octonions, more specifically, using a 4 x 4 matrix representation of octonions obtained with the help of algebraic properties of quaternions, we obtain the fully symmetric Maxwell's equations (Maxwell's equations with electric and…
Quasi-conformal actions were introduced in the physics literature as a generalization of the familiar fractional linear action on the upper half plane, to Hermitian symmetric tube domains based on arbitrary Jordan algebras, and further to…
We first prove a Cauchy's integral theorem and Cauchy type formula for certain inhomogeneous Cimmino system from quaternionic analysis perspective. The second part of the paper directs the attention towards some applications of the…
We study the computational complexity of converting one representation of real numbers into another representation. Typical examples of representations are Cauchy sequences, base-10 expansions, Dedekind cuts and continued fractions.
In honor of Minkowski's great contribution to Special Relativity, celebrated at this conference, we first review Wigner's theory of the projective irreducible representations of the inhomogeneous Lorentz group. We also sketch those parts of…
The first and second representation theorems for sign-indefinite, not necessarily semi-bounded quadratic forms are revisited. New straightforward proofs of these theorems are given. A number of necessary and sufficient conditions ensuring…
Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed in unique, simple and consistent manner. It has been shown that this theory is extended consistently to time-harmonic…
The contribution emphasizes the geometric modeling point of view on Minkowski point set operations. In this paper, the Minkowski product is specified as the quaternionic product. Selected point sets are visualized using double orthogonal…
We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant…
A monoid structure on families of representations of a quiver is introduced by taking extensions of representations in families, i.e. subvarieties of the varieties of representations. The study of this monoid leads to interesting…
Analysis of the logical foundations of quantum mechanics indicates the possibility of constructing a theory using quaternionic Hilbert spaces. Whether this mathematical structure reflects reality is a matter for experiment to decide. We…
In the last one and a half centuries, the analysis of quaternions has not only led to further developments in mathematics but has also been and remains an important catalyst for the further development of theories in physics. At the same…
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable…
In a general and non metrical framework, we introduce the class of co-CR quaternionic manifolds, which contains the class of quaternionic manifolds, whilst in dimension three it particularizes to give the Einstein-Weyl spaces. We show that…
Quaternionic formulation of supersymmetric quantum mechanics has been developed consistently in terms of Hamiltonians, superpartner Hamiltonians, and supercharges for free particle and interacting field in one and three dimensions.…
In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal…
I compare the matrix representation of the basic statements of Special Relativity with the conventional vector space representation. It is shown, that the matrix form reproduces all equations in a very concise and elegant form, namely:…
We study a one-component quaternionic wave equation which is relativistically covariant. Bi-linear forms include a conserved 4-current and an antisymmetric second rank tensor. Waves propagate within the light-cone and there is a conserved…
A representation theorem for non-semibounded Hermitian quadratic forms in terms of a (non-semibounded) self-adjoint operator is proven. The main assumptions are closability of the Hermitian quadratic form, the direct integral structure of…