Geometrical properties of Riemannian superspaces, observables and physical states

Classical and quantum aspects of physical systems that can be described by Riemannian non degenerate superspaces are analyzed from the topological and geometrical points of view. For the N=1 case the simplest supermetric introduced in [Physics Letters B \textbf{661}, (2008),186] have the correct number of degrees of freedom for the fermion fields and the super-momentum fulfil the mass shell condition, in sharp contrast with other cases in the literature where the supermetric is degenerate. This fact leads a deviation of the 4-impulse (e.g. mass constraint) that can be mechanically interpreted as a modification of the Newton's law. Quantum aspects of the physical states and the basic states and the projection relation between them, are completely described due the introduction of a new Majorana-Weyl representation of the generators of the underlying group manifold. A new oscillatory fermionic effect in the $B_{0}$ part of the vaccum solution involving the chiral and antichiral components of this Majorana bispinor is explicitly shown.Comment: 16 pags. 3 figures. To Anna Grigorievna Kartavenko and Academic Professor Alexei Norianovich Sissakian, in memoria

Algebraic structures, physics and geometry from a Unified Field Theoretical framework

Starting from a Unified Field Theory (UFT) proposed previously by the author, the possible fermionic representations arising from the same spacetime are considered from the algebraic and geometrical viewpoint. We specifically demonstrate in this UFT general context that the underlying basis of the single geometrical structure P (G,M) (the principal fiber bundle over the real spacetime manifold M with structural group G) reflecting the symmetries of the different fields carry naturally a biquaternionic structure instead of a complex one. This fact allows us to analyze algebraically and to interpret physically in a straighforward way the Majorana and Dirac representations and the relation of such structures with the spacetime signature and non-hermitian (CP) dynamic operators. Also, from the underlying structure of the tangent space, the existence of hidden (super) symmetries and the possibility of supersymmetric extensions of these UFT models are given showing that Rothstein's theorem is incomplete for that description. The importance of the Clifford algebras in the description of all symmetries, mainly the interaction of gravity with the other fields, is briefly discussed.Comment: To be published in IJTP, last corrected version. This work is devoted to the memory of the Prof. Academician Vladimir Georgievich Kadyshevsky. 21 pages, no figures. References added and misprints/typos correcte

Coherent states, vacuum structure and infinite component relativistic wave equations

It is commonly claimed in the recent literature that certain solutions to wave equations of positive energy of Dirac-type with internal variables are characterized by a non-thermal spectrum. As part of that statement, it was said that the transformations and symmetries involved in equations of such type correspond to a particular representation of the Lorentz group. In this paper we give the general solution to this problem emphasizing the interplay between the group structure, the corresponding algebra and the physical spectrum. This analysis is completed with a strong discussion and proving that: i) the physical states are represented by coherent states; ii) the solutions in previous references [1] are not general, ii) the symmetries of the considered physical system in [1] (equations and geometry) do not correspond to the Lorentz group but to the fourth covering: the Metaplectic group Mp(n).Comment: To be published in the IJGMMP, 12 pages , no figure

Quantum particle on a Mobius strip, coherent states and projection operators

The coherent states for a quantum particle on a M\"{o}bius strip are constructed and their relation with the natural phase space for fermionic fields is shown. The explicit comparison of the obtained states with previous works where the cylinder quantization was used and the spin 1/2 was introduced by hand is given, and the relation between the geometrical phase space, constraints and projection operators is analyzed and discussed.Comment: 14 pgs., no figure

Charge dynamics and "in plane" magnetic field I: Rashba-Dresselhauss interaction, Majorana fermions and Aharonov-Casher theorems

The 2-dimensional charge transport with parallel (in plane) magnetic field is considered from the physical and mathematical point of view. To this end, we start with the magnetic field parallel to the plane of charge transport, in sharp contrast to the configuration described by the theorems of Aharonov and Casher where the magnetic field is perpendicular. We explicitly show that the specific form of the arising equation enforce the respective field solution to fulfil the Majorana condition. Consequently, as soon any physical system is represented by this equation, the rise of fields with Majorana type behaviour is immediately explained and predicted. In addition, there exists a quantized particular phase that removes the action of the vector potential producing interesting effects. Such new effects are able to explain due the geometrical framework introduced, several phenomenological results recently obtained in the area of spintronics and quantum electronic devices. The quantum ring as spin filter is worked out in this framework and also the case of the quantum Hall effect.Comment: Accepted in International Journal of Geometric Methods in Modern Physics (IJGMMP) Vol. 12 (2015), no figures. General references added, english improved. arXiv admin note: text overlap with arXiv:quant-ph/0701076, arXiv:1302.3641 by other author