相关论文: Quaternions in University-Level Physics Considerin…
A proposal for the matrix model formulation of the M-theory on a space with a boundary is given. A general machinery for modding out a symmetry in M(atrix) theory is used for a Z_2 symmetry changing the sign of the X_1 coordinate. The…
Many professional physicists do not fully understand the implications of the Einstein equivalence principle of general relativity. Consequently, many are unaware of the fact that special relativity is fully capable of handling accelerated…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
We present a novel paradox in special relativity together with its solution. We call it the four particles paradox. The purpose of this paradox is pedagogical and therefore directed towards students and lecturers of physics. Even if most…
In this study, we introduce the concept of commutative quaternions and commutative quaternion matrices. Firstly, we give some properties of commutative quaternions and their Hamilton matrices. After that we investigate commutative…
In our joint papers [FL1-FL2] we revive quaternionic analysis and show deep relations between quaternionic analysis, representation theory and four-dimensional physics. As a guiding principle we use representation theory of various real…
Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
Special Relativity is often seen as a conceptually difficult topic, which in turn is difficult to effectively teach. This work focuses on the role of visualizations as a tool in teaching Special Relativity at the secondary or university…
Introducing Modern Physics represents an increasingly urgent need, towards which physics education concentrates many efforts. In order to contribute to this attempt, at the Department of Mathematics and Physics of Roma Tre University in…
Over the last decades quaternions have become a crucial and very successful tool for attitude representation in robotics and aerospace. However, there is a major problem that is continuously causing trouble in practice when it comes to…
The Principle of Relativity has so far been understood as the {\it covariance} of laws of Physics with respect to a general class of reference frame transformations. That relativity, however, has only been expressed with the help of {\it…
Probability theory can be modified in essentially one way while maintaining consistency with the basic Bayesian framework. This modification results in copies of standard probability theory for real, complex or quaternion probabilities.…
Dual quaternion algebra and its application to robotics have gained considerable interest in the last two decades. Dual quaternions have great geometric appeal and easily capture physical phenomena inside an algebraic framework that is…
Galilean Relativity and Einstein's Special and General Relativity showed that the Laws of Physics go deeper than their representations in any given reference frame. Thus covariance, or independence of Laws of Physics with respect to changes…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
This is a report of a course on modern physics designed and taught to undergraduate science and engineering students in the Spring of 2013. The course, meant for freshmen, attempts to integrate statistical mechanics into non-classical…
The paper aims to adopt the complex octonion to formulate the angular momentum, torque, and force etc in the electromagnetic and gravitational fields. Applying the octonionic representation enables one single definition of angular momentum…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
In the past, Kepler painstakingly derived laws of planetary motion using difficult to understand and hard to follow techniques. In 1843 William Hamilton created and described the quaternions, which extend the complex numbers and can easily…