Alberto Molgado

Quantum modified Regge–Teitelboim cosmology

The canonical quantization of the modified geodetic brane cosmology which is implemented from the Regge–Teitelboim model and the trace of the extrinsic curvature of the brane trajectory,

Polymeric quantum mechanics and the zeros of the Riemann zeta function

K

De Donder–Weyl Hamiltonian formalism of MacDowell–Mansouri gravity

K, is developed. As a second-order derivative model, on the grounds of the Ostrogradski Hamiltonian method and the Dirac’s scheme for constrained systems, we find suitable first- and second-class constraints which allow for a proper quantization. We also find that the first-class constraints obey a sort of truncated Virasoro algebra. The effective quantum potential emerging in our approach is exhaustively studied where it shows that an embryonic epoch is still present. The quantum nucleation is sketched where we observe that it is driven by an effective cosmological constant.

Hamiltonian analysis for linearly acceleration-dependent Lagrangians

We explore the cosmological implications provided by the geodetic brane gravity action corrected by an extrinsic curvature brane term, describing a codimension-1 brane embedded in a 5D fixed Minkowski spacetime. In the geodetic brane gravity action, we accommodate the correction term through a linear term in the extrinsic curvature swept out by the brane. We study the resulting geodetic-type equation of motion. Within a Friedmann?Robertson?Walker metric, we obtain a generalized Friedmann equation describing the associated cosmological evolution. We observe that, when the radiation-like energy contribution from the extra dimension is vanishing, this effective model leads to a self-(non-self)-accelerated expansion of the brane-like universe in dependence on the nature of the concomitant parameter ? associated with the correction, which resembles an analogous behaviour in the DGP brane cosmology. Several possibilities in the description for the cosmic evolution of this model are embodied and characterized by the involved density parameters related in turn to the cosmological constant, the geometry characterizing the model, the introduced ? parameter as well as the dark-like energy and the matter content on the brane.

Polysymplectic formulation for topologically massive Yang-Mills field theory

We analize the Berry-Keating model and the Sierra and Rodriguez-Laguna Hamiltonian within the polymeric quantization formalism. By using the polymer representation, we obtain for both models, the associated polymeric quantum Hamiltonians and the corresponding stationary wave functions. The self-adjointness condition provide a proper domain for the Hamiltonian operator and the energy spectrum, which turned out to be dependent on an introduced scale parameter. By performing a counting of semiclassical states, we prove that the polymer representation reproduces the smooth part of the Riemann-von Mangoldt formula, and introduces a correction depending on the energy and the scale parameter, which resembles the fluctuation behavior of the Riemann zeros.

Unruh effect detection through chirality in curved graphene

We analyse the emergence of the Unruh effect within the context of a field Lagrangian theory associated with the Pais–Uhlenbeck fourth order oscillator model. To this end, we introduce a transformation that brings the Hamiltonian bounded from below and is consistent with -symmetric quantum mechanics. We find that, as far as we consider different frequencies within the Pais–Uhlenbeck model, a particle together with an antiparticle of different masses are created and may be traced back to the Bogoliubov transformation associated with the interaction between the Unruh–DeWitt detector and the higher derivative scalar field. In contrast, whenever we consider the equal frequencies limit, no particle creation is detected as the pair particle/antiparticle annihilate each other. Further, following Moschella and Schaeffer, we construct a Poincare invariant two-point function for the Pais–Uhlenbeck model, which in turn allows us to perform the thermal analysis for any of the emanant particles.

Causal Poisson bracket via deformation quantization

We analyse the behaviour of the MacDowell–Mansouri action with internal symmetry group under the De Donder–Weyl Hamiltonian formulation. The field equations, known in this formalism as the De Donder–Weyl equations, are obtained by means of the graded Poisson–Gerstenhaber bracket structure present within the De Donder–Weyl formulation. The decomposition of the internal algebra allows the symmetry breaking , which reduces the original action to the Palatini action without the topological term. We demonstrate that, in contrast to the Lagrangian approach, this symmetry breaking can be performed indistinctly in the polysymplectic formalism either before or after the variation of the De Donder–Weyl Hamiltonian has been done, recovering Einsteins equations via the Poisson–Gerstenhaber bracket.

Deformation quantization of the Pais–Uhlenbeck fourth order oscillator

We study the constrained Ostrogradski-Hamilton framework for the equations of motion provided by mechanical systems described by second-order derivative actions with a linear dependence in the accelerations. We stress out the peculiar features provided by the surface terms arising for this type of theories and we discuss some important properties for this kind of actions in order to pave the way for the construction of a well defined quantum counterpart by means of canonical methods. In particular, we analyse in detail the constraint structure for these theories and its relation to the inherent conserved quantities where the associated energies together with a Noether charge may be identified. The constraint structure is fully analyzed without the introduction of auxiliary variables, as proposed in recent works involving higher order Lagrangians. Finally, we also provide some examples where our approach is explicitly applied and emphasize the way in which our original arrangement results in propitious for...