相关论文: Physical Space as a Quaternion Structure, I: Maxwe…

The mathematical structure of the Born-Infeld field equations was analyzed from the point of view of the symmetries. To this end, the field equations were written in the most compact form by means of quaternionic operators constructed…

In this paper we introduce a new algebraic device, which enables us to treat the quaternions as though they were a commutative field. This is of interest both for its own sake, and because it can be applied to develop an "algebraic…

There must exist a reformulation of quantum field theory, even at low energies, which does not depend on classical time. The octonionic theory proposes such a reformulation, leading to a pre-quantum pre-spacetime theory. The ingredients for…

The paper focuses on applying the octonions to explore the influence of the external torque on the angular momentum of fluid elements, revealing the interconnection of the external torque and the vortices of vortex streets. J. C. Maxwell…

The goal of this paper is to sketch a broader outline of the mathematical structures present in the Nonlinear Maxwell Theory in continuation of work presented in my previous articles. In particular, I display new types of both dynamic and…

We analyse the problem of defining a Poisson bracket structure on the space of solutions of the equations of motions of first order Hamiltonian field theories. The cases of Hamiltonian mechanical point systems (as a (0 + 1)-dimensional…

On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local…

Maxwell equations (Faraday and Ampere-Maxwell laws) can be presented as a three component equation in a way similar to the two component neutrino equation. However, in this case, the electric and magnetic Gauss's laws can not be derived…

A transparent linear magneto-dielectric material in free space that is illuminated by a finite quasimonochromatic field is a thermodynamically closed system, definitively, regardless of what field and material subsystems that one defines.…

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…

A four-vector field in flat space-time, satisfying a gauge-invariant set of second-order differential equations, is considered as a unified field. The model variational principle corresponds to the general covariance idea and gives rise to…

This paper challenges some of the common assumptions underlying the mathematics used to describe the physical world. We start by reviewing many of the assumptions underlying the concepts of real, physical, rigid bodies and the translational…

Mechanics can be founded in a principle stating the uncertainty in the position of an observable particle delta-q as a function of its motion relative to the observer, expressed in a trajectory representation . From this principle,…

When four-dimensional general relativity is embedded in an unconstrained man-ner in a fifth dimension, the physical quantities of spacetime can be interpreted as geometrical properties related to the extra dimension. It has become…

The fact that a temperature and an entropy may be associated with horizons in semi-classical general relativity has led many to suspect that spacetime has microstructure. If this is indeed the case then its description via Riemannian…

The state of a thermodynamic system being characterized by its set of extensive variables $q^{i}(i=1,...,n) ,$ we write the associated intensive variables $\gamma_{i},$ the partial derivatives of the entropy $ S(q^{1},...,q^{n}) \equiv…

Based on the explicit knowledge of a Hamiltonian of mean force, the classical statistical mechanics and equilibrium thermodynamics of open systems in contact with a thermal environment at arbitrary interaction strength can be formulated.…

Four-dimensional mass is determined in four-dimensional pseudo-Euclidean space as a physical invariant of that space. That invariant is discussed as an invariant of electromagnetic type. Finally, equations of Maxwell type are obtained for…

We show that classical thermodynamics has a formulation in terms of Hamilton-Jacobi theory, analogous to mechanics. Even though the thermodynamic variables come in conjugate pairs such as pressure/volume or temperature/entropy, the phase…

We considered the thermodynamics in spaces with deformed commutation relation leading to existence of the minimal length. We developed a classical method of the partition function evaluation. We calculated the partition function and heat…