Related papers: Quaternionic Analysis and the Algebrodynamics
We consider the lagrangian of a self-interacting complex scalar field admitting generically Q-balls solutions. This model is extended by minimal coupling to electromagnetism and to gravity. A stationnary, axially-symmetric ansatz for the…
In the complete system of equations of evolution of the classical system of charges and the electromagnetic field generated by them, the field variables are excluded. An exact closed relativistic non-Hamiltonian system of nonlocal kinetic…
The gauge theories underlying gauged supergravity and exceptional field theory are based on tensor hierarchies: generalizations of Yang-Mills theory utilizing algebraic structures that generalize Lie algebras and, as a consequence, require…
A classical dynamical system in a four-dimensional Euclidean space with universal time is considered. The space is hypothesized to be originally occupied by a uniform substance, pictured as a liquid, which at some time became supercooled.…
Foundations of algebrodynamics based on earlier proposed equations of biquaternionic holomorphy are briefly expounded. Free Maxwell and Yang-Mills Eqs. are satisfied identically on the solutions of primary system which is also related to…
We introduce a new term into the Dirac equation based on the Lorentz symmetry violation background in order to make a theoretical description of the relativistic quantum dynamics of a spin-half neutral particle, where the wave function of…
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…
It is a well known fact that the usual complex structure on the real Clifford Algebra (CA) of Minkowski spacetime can be obtained by adding an extra time-like dimension, instead of the usual complexification of the algebra. In this article…
The perennial formalism is applied to the real, massive Klein-Gordon field on a globally-hyperbolic background space-time with compact Cauchy hypersurfaces. The parametrized form of this system is taken over from the accompanying paper. Two…
In this paper we study the quantum dynamics of a neutral particle in the presence of a topological defect. We investigate the appearance of a geometric phase in the relativistic quantum dynamics of neutral particle which possesses permanent…
For any given algebra of local observables in Minkowski space an associated scaling algebra is constructed on which renormalization group (scaling) transformations act in a canonical manner. The method can be carried over to arbitrary…
A general technique is presented for constructing a quantum theory of a finite number of interacting particles satisfying Poincar\'e invariance, cluster separability, and the spectral condition. Irreducible representations and…
We propose a model describing the scattering of hadrons as bound states of their constituent quarks. We analyze the role of simultaneity in measurements of the characteristics of different particles for the description of relativistic…
We define algebras of quasi-quaternion type, which are symmetric algebras of tame representation type whose stable module category has certain structure similar to that of the algebras of quaternion type introduced by Erdmann. We observe…
A non-associative Groenewold-Moyal plane is constructed using quaternion-valued function algebras. The symmetrized multi-particle states, the scalar product, the annihilation/creation algebra and d the formulation in terms of a Hopf algebra…
A representation of the Dirac algebra, derived from first principles, can be related to the combinations of unit charges which determine particle structures. The algebraic structure derives from a broken symmetry between 4-vectors and…
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…
Admitting non-Riemannian geometries, Double Field Theory extends the notion of spacetime beyond the Riemannian paradigm. We identify a class of singular spacetimes known in General Relativity with regular non-Riemannian geometries. The…
Relativistic quantum effects on physical observables of scalar charged particles are studied. Possible peculiarities of their behavior that can be verified in an experiment can confirm several fundamental conceptions of quantum mechanics.…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…