Related papers: Quaternions in mathematical physics (1): Alphabeti…
Spinors are used in physics quite extensively. The goal of this study is also the spinor structure lying in the basis of the quaternion algebra. In this paper, first, we have introduced spinors mathematically. Then, we have defined…
In this paper, we introduce the generalized Fibonacci-Lucas quaternions and we prove that the set of these elements is an order,in the sense of ring theory, of a quaternion algebra. Moreover, we investigate some properties of these…
The functional space of biquaternions is considered on Minkovskiy space. The scalar-vector biquaternions representation is used which was offered by W. Hamilton for quaternions. With introduction of differential operator - a mutual complex…
The paper aims to adopt the complex quaternion and octonion to formulate the field equations for electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition to combine some physics contents…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and…
In the 6th Int. Symposium on OPSFA there were several communications dealing with concrete applications of orthogonal polynomials to experimental and theoretical physics, chemistry, biology and statistics. Here I make suggestions concerning…
In this paper, we present a further generalization of the bi- periodic Fibonacci quaternions and octonions. We give the generating function, the Binet formula, and some basic properties of these quaternions and octonions. The results of…
The applications of quaternion in physics are discussed with an emphasis on elementary particle symmetry and interaction. Three colours of the quark and the quantum chromodynamics (QCD) can be introduced directly from the invariance of…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…
We give a simple and self contained introduction to quaternions and their practical usage in dynamics. The rigid body dynamics are presented in full details. In the appendix, some more exotic relations are given that allow to write more…
It is known that the groups of Euclidean rotations in dimension 3 (isometries of $S^2$), general Lorentz transformations in dimension 4 (Hyperbolic isometries in dimension 3), and screw motions in dimension 3 can be represented by the…
Various applications of quantum algebraic techniques in nuclear structure physics and molecular physics are briefly reviewed. Contains 81 references.
Some comments are made on the matrices which serve as the basis of a quaternionic algebra. We show that these matrices are related with the quaternionic action of the imaginary units from the left and from the right.
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
We consider Clifford algebras over the field of real or complex numbers as a quotient algebra without fixed basis. We present classification of Clifford algebra elements based on the notion of quaternion type. This classification allows us…
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 this note it is worked out a new set of Laplace-Like equations for quaternions through Riemann-Cauchy hypercomplex relations otained earlier \cite{BorgesZeMarcio}. As in the theory of functions of a complex variable, it is expected that…
Quaternions often appear in wide areas of applied science and engineering such as wireless communications systems, mechanics, etc. It is known that are two types of non-isomorphic generalized quaternion algebras, namely: the algebra of…
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous papers. On the basis of new classification of Clifford algebra elements it is possible to find out…