相关论文: Quaternions and Special Relativity

Quaternions have an (over a century-old) extensive and quite complicated interaction with special relativity. Since quaternions are intrinsically 4-dimensional, and do such a good job of handling 3-dimensional rotations, the hope has always…

Recently, [10,11], the Heisenberg Uncertainty relation and the No-Cloning property in Quantum Mechanics and Quantum Computation, respectively, have been extended to versions of Quantum Mechanics and Quantum Computation which are…

Different approaches to special relativity (SR) are discussed. The first approach is an invariant approach in which physical quantities in the four-dimensional spacetime are represented by true tensors or equivalently by coordinate-based…

We provide some guidance and examples to clear up common misconceptions about special relativity. These misconceptions often come from trying to express the truths of special relativity in Newtonian terms rather than in terms more natural…

Special geometry is most known from 4-dimensional N=2 supergravity, though it contains also quaternionic and real geometries. In this review, we first repeat the connections between the various special geometries. Then the constructions are…

The special theory of relativity is constructed demanding the retention of the rectilinear form of a trajectory and invariance of the wave equation under linear transformations of space and time coordinates. The usual approach to relativity…

We present a mathematical model for a physical theory that is compatible with Einstein's Special Relativity Theory. Our model consists of three pseudo-complex dimensions, representing three real dimensions of space, dual to what could be…

Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…

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 discuss the (right) eigenvalue equation for $\mathbb{H}$, $\mathbb{C}$ and $\mathbb{R}$ linear quaternionic operators. The possibility to introduce an isomorphism between these operators and real/complex matrices allows to translate the…

Within the framework of exterior algebra, the concept of time-like quaternions has been previously established. This paper advances beyond the existing structure by elucidating the procedure for constructing time-like quaternions with the…

Numerous attempts have been made to replicate the success of complex-valued algebra in engineering and science to other hypercomplex domains such as quaternions, tessarines, biquaternions, and octonions. Perhaps, none have matched the…

The paper explains how a unit generalized quaternion is used to represent a rotation of a vector in 3-dimensional space. We review of some algebraic properties of generalized quaternions and operations between them and then show their…

Different formulations of special relativity are theoretically discussed. First an invariant formulation, i.e., the ''true transformations (TT) relativity,'' is exposed. There a physical quantity is represented by a true tensor which…

A new formulation of what may be called the "fundamental theorem of the theory of relativity" is presented and proved in (3+1)-space-time, based on the full classification of special transformations and the corresponding velocity addition…

Special relativity turns out to be more than coordinate transformations in which the constancy of the speed of light plays the central role between two inertial reference frames. Special relativity, in essence, is a theory of…

This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding…

Numerical relativity is finally approaching a state where the evolution of rather general (3+1)-dimensional data sets can be computed in order to solve the Einstein equations. After a general introduction, three topics of current interest…

I show in this letter that it is possible to construct a Hamiltonian description for Lorentzian General Relativity in terms of two real $SO(3)$ connections. The constraints are simple polynomials in the basic variables. The present…

We develop quaternionic analysis using as a guiding principle representation theory of various real forms of the conformal group. We first review the Cauchy-Fueter and Poisson formulas and explain their representation theoretic meaning. The…