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In this conceptual paper we construct a local version of Shape Dynamics that is equivalent to General Relativity in the sense that the algebras of Dirac observables weakly coincide. This allows us to identify Shape Dynamics observables with…
The similarity renormalization group is used to transform Dirac Hamiltonian into a diagonal form, which the upper (lower) diagonal element becomes an operator describing Dirac (anti-)particle. The eigenvalues of the operator are verfied to…
We study expectation values of observables in three-dimensional spinfoam quantum gravity coupled to Dirac fermions. We revisit the model introduced by one of the authors and extend it to the case of massless fermionic fields. We introduce…
We obtain classes of two dimensional static Lorentzian manifolds, which through the supersymmetric formalism of quantum mechanics admit the exact solvability of Dirac equation on these curved backgrounds. Specially in the case of a modified…
We provide a brief overview of what is known about Quadratic Gravity, which includes terms quadratic in the curvatures in the fundamental action. This is proposed as a renormalizeable UV completion for quantum gravity which continues to use…
We review some results on the complete coupling between tensor and vector multiplets in six-dimensional $(1,0)$ supergravity.
We report on the construction of four dimensional gauged supergravity models that can be interpreted as type IIB orientifold compactification in presence of 3-form fluxes and D3--branes. We mainly address our attention to the symplectic…
We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex $\ell^p$-potentials for $1\leq p\leq\infty$. As a corollary, subsets of the essential spectrum free of embedded…
It is shown that Einstein's equations on the brane can be received from the multi-dimensional vector field equations in pseudo-Euclidean space. The idea is based on the observation that the brane geometry can be equivalently described by…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that…
By mean of generalized Fourier series and Parseval's equality in weighted $L^{2}$--spaces, we derive a sharp energy estimate for the wave equation in a bounded interval with a moving endpoint. Then, we show the observability, in a sharp…
We look at gravitational attraction in simplicial gravity using the dynamical triangulation method. On the dynamical triangulation configurations we measure quenched propagators of a free massive scalar field. The masses measured from these…
A supersymmetric analysis is presented for the d-dimensional Dirac equation with central potentials under spin-symmetric (S(r) = V(r)) and pseudo-spin-symmetric (S(r) = - V(r)) regimes. We construct the explicit shift operators that are…
Euclidean random matrices arise in a wide range of physical systems where interactions are determined by spatial configurations, including disordered media and cooperative phenomena in atomic ensembles. Unlike classical random matrix…
We summarise the results of our recent paper (arXiv:1511.08737) highlighting what might be considered to be a Lie-algebraic derivation of eleven-dimensional supergravity.
The text is an essentially self-contained introduction to four-dimensional N=1 supergravity, including its couplings to super Yang-Mills and chiral matter multiplets, for readers with basic knowledge of standard gauge theories and general…
The explicit coordinate transformations which show the equivalence between the FRW metrics of four-dimensional open and closed universes and the metrics induced on appropriate submanifolds in a five-dimensional pseudo-Euclidean space-time…
The Dirac theory in the Euclidean Taub-NUT space gives rise to a large collection of conserved operators associated to genuine or hidden symmetries. They are involved in interesting algebraic structures as dynamical algebras or even…
We consider arbitrary open sets $\Omega$ in Euclidean space with finite Lebesgue measure, and obtain upper bounds for (i) the largest Courant-sharp Dirichlet eigenvalue of $\Omega$, (ii) the number of Courant-sharp Dirichlet eigenvalues of…