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Using equations of motion with the anisotropic dissipative term for quantum particle and quantum-mechanical commutation rules, the general Maxwell-type differential equations are derived. The direct modifications of the well-known Maxwell…
We give an overview of the first integrals of motion of particles in the presence of external gauge fields in a covariant Hamiltonian approach. The special role of St\"ackel-Killing and Killing-Yano tensors is pointed out. Some nontrivial…
Here is discussed generalization of Clifford algebras, l^n-dimensional Weyl-Clifford algebras T(n,l) with n generators t_k satisfying equation $(\sum_{k=1}^n a_k t_k)^l = \sum_{k=1}^n a_k^l$. It is originated from two basic and well known…
To simulate open boundaries within finite computation domain, real-function coordinate transformation in the framework of generally covariant formulation of Maxwell equations is proposed. The mapping--realized with arctangent function…
This paper aims to review our recent results on exploring the capabilities of non-quantum field theory as a possible tool for describing single photon-like objects, considered as massless time-stable spatially finite physical entities with…
The covariant Maxwell equations are derived from the continuity equation for the electric charge. This result provides an axiomatic approach to Maxwell's equations in which charge conservation is emphasized as the fundamental axiom…
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…
In this paper, we apply the generalized integration constants method in field theory to quantize Maxwell and the Klein-Gordon free fields. The study is performed in both position and momentum spaces, to obtain equal-time Dirac brackets…
For an elliptic complex of first order differential operators on a smooth manifold, we define a system of two equations which can be thought of as abstract Maxwell equations. The formal theory of this system proves to be very similar to…
We study the integrability of two-dimensional theories that are obtained by a dimensional reduction of certain four-dimensional gravitational theories describing the coupling of Maxwell fields and neutral scalar fields to gravity in the…
Teleparallel gravity can be seen as a gauge theory for the translation group. As such, its fundamental field is neither the tetrad nor the metric, but a gauge potential assuming values in the Lie algebra of the translation group. This gauge…
The determination of the quantum state of a single system by protective observation is used to justify operationally a formulation of quantum theory on the quantum state space (projective Hilbert space) $\cal P$. Protective observation is…
The quantum theory of the Maxwell free field in Coulomb gauge on the de Sitter expanding universe is completed with the technical elements needed for building a coherent quantum theory of redshift. Paying a special attention to the…
A new local and gauge invariant quantum vortex operator is constructed in three-dimensional gauge field theories. The correlation functions of this operator are evaluated exactly in pure Maxwell theory and by means of a loop expansion in…
Charges are everywhere because most atoms are charged. Chemical bonds are formed by electrons with their charge. Charges move and interact according to Maxwell's equations in space and in atoms where the equations of electrodynamics are…
Maxwell's equations are considered in metric-free form, with a local but otherwise arbitrary constitutive law. After splitting Maxwell's equations into evolution equations and constraints, we derive the characteristic equation and we…
Distributional and neural approaches to natural language semantics have been built almost exclusively on conventional linear algebra: vectors, matrices, tensors, and the operations that accompany them. These methods have achieved remarkable…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real…
Complementary idempotent paravectors and their ordered compositions, are used to represent multivector basis elements of geometric Clifford algebra for 3D Euclidean space as the states of a geometric byte in a given frame of reference. Two…