We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant aspect of
continuity in the analytic foundations of Wigner work. We conclude the paper by reviewing the connection between continuity, the possibility of defining certain local groups, and their relation to projective representations.
Bearing in mind the Lounesto spinor classification, we connect the expansion coefficients of well behaved fermionic quantum field, i.e., a local field within a full Lorentz covariant theory, with and only with a given subclass of Type-2 spinors accor
ding to Lounesto. We comment on theoretical possibilities as well as physical outputs for the other cases.
We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic
spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to prevent the Dirac operator to be injective, allowing the existence of non-trivial solutions.
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping structure
among them and the conditions under which sets of such dual maps do form a group. We also study the covariance of bilinear quantities constructed with the several possible duals, the invariant eigenspaces of those group elements and its connections with spinors classification, as well as dual maps defined as elements of group algebras.
We investigate a braneworld model generated by a global monopole in the context of Brans-Dicke gravity. After solving the dynamical equations we found a model capable to alleviate the so-called hierarchy problem. The obtained framework is described b
y a hybrid compactification scheme endowed with a seven-dimensional spacetime, in which the brane has four non-compact dimensions and two curled extra dimensions. The relevant aspects of the resulting model are studied and the requirements to avoid the well known seesaw-like behavior are discussed. We show that under certain conditions it is possible to circumvent such a pathological behavior that characterizes most of the models that exhibit hybrid compactification. Lastly, we deepen our analysis by considering possible extensions of this model to a setup with multiple branes and orbifold-like extra dimension. For this, we compute the consistency conditions to be obeyed by this more general configuration as predicted by the braneworld sum rules formalism. This study indicates the possibility of exclusively positive brane tensions in the model.
By exploring a spinor space whose elements carry a spin 1/2 representation of the Lorentz group and satisfy the the Fierz-Pauli-Kofink identities we show that certain symmetries operations form a Lie group. Moreover, we discuss the reflex of the Dira
c dynamics in the spinor space. In particular, we show that the usual dynamics for massless spinors in the spacetime is related to an incompressible fluid behavior in the spinor space.
We study the conditions under which a non-standard Wigner class concerning discrete symmetries may arise for massive spin one-half states. The mass dimension one fermionic states are shown textcolor{red}{to} constitute explicit examples. We also show
how to conciliate these states with the current criticism due to the Lee and Wick, and Weinberg formulation.
In this paper we proceed into the next step of formalization of a consistent dual theory for mass dimension one spinors. This task is developed approaching the two different and complementary aspects of such duals, clarifying its algebraic structure
and the so called $tau-$deformation. The former regards the mathematical equivalence of the recent proposed Lorentz preserving dual with the duals of algebraic spinors, from Clifford algebras, showing the consistency and generality of the new dual. Moreover, by revealing its automorphism structure, the hole of the $tau-$deformation and contrasting the action group orbits with other Lorentz breaking scenarios, we argue that the new mass dimension one dual theory is placed over solid and consistent basis.
Observation shows that the velocities of stars grow by approximately 2 to 3 orders of magnitude when the distances from the centers of the galaxies are in the range of $0.5$ kpc to $82.3$ kpc, before they begin to tend to a constant value. Up to know
, the reason for this behavior is still a matter for debate. In this work, we propose a model which adequately describes this unusual behavior using a (nearly) cylindrical symmetrical solution in the framework of a scalar-tensor-like (the Brans-Dicke model) theory of gravity.
The so called Inomata-McKinley spinors are a particular solution of the non-linear Heisenberg equation. In fact, free linear massive (or mass-less) Dirac fields are well known to be represented as a combination of Inomata-McKinley spinors. More recen
tly, a subclass of Inomata-McKinley spinors were used to describe neutrino physics. In this paper we show that Dirac spinors undergoing this restricted Inomata-McKinley decomposition are necessarily of the first type, according to the Lounesto classification. Moreover, we also show that this type one subclass spinors has not an exotic counterpart. Finally, implications of these results are discussed, regarding the understanding of the spacetime background topology.
