arXiv subjects
Publications and source records attributed to J. A. Nieto.
We propose a possible relation between complex networks and gravity. Our guide in our proposal is the power-law distribution of the node degree in network theory and the information approach to gravity. The established bridge may allow us to carry geometric mathematical structures, which are considered in gravitational theories, to probabilistic aspects studied in the framework of complex networks and vice versa.
We describe a program for developing a canonical gravity in 2+2 dimensions (two time and two space dimensions). Our procedure is similar to the usual canonical gravity but with two times rather than just one time. Our work may be of particular interest as an alternative approach to loop quantum gravity in 2+2 dimensions.
We review remarkable results in several mathematical scenarios, including graph theory, division algebras, cross product formalism and matroid theory. Specifically, we mention the following subjects: (1) the Euler relation in graph theory, and its higher-dimensional generalization, (2) the dimensional theorem for division algebras and in particular the Hurwitz theorem for normed division algebras, (3) the vector cross product dimensional possibilities, (4) some theorems for graphs and matroids. Our main goal is to motivate a possible research work in these four topics, putting special interest in their possible links.
We consider a variational formalism to describe black holes solution in higher dimensions. Our procedure clarifies the arbitrariness of the radius parameter and, in particular, the meaning of the event horizon of a black hole. Moreover, our formalism enables us to find a surprising link between black holes and the golden ratio.
We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.
We study a cosmological model in 1+D+d dimensions where D dimensions are associated with the usual Friedman-Robertson-Walker type metric with radio a(t) and d dimensions corresponds to an additional homogeneous space with radio b(t). We make a general analysis of the field equations and then we obtain solutions involving the two cosmological radii, a(t) and b(t). The particular case D=3, d=1 is studied in some detail.
We develop the classical and quantum theory of a spinning particle moving in a Mobius strip. We first propose a Lagrangian for such a system and then we proceed to quantize the system via the constraint Hamiltonian system formalism. Our results may be of particular interest in several physical scenarios, including solid state physics and optics. In fact, the present work may shed some new light on the recent discoveries on condensed matter concerning topological insulators.
We show that qubit and chirotope concepts are closely related. In fact, we prove that the qubit concept leads to a generalization of the chirotope concept, which we call qubitope. Moreover, we argue that a possible qubitope theory may suggest interesting applications of oriented matroid theory in at least three physical contexts, in which qubits make their appearance, namely string theory, black holes and quantum information.
We establish a connection between oriented matroid theory and loop quantum gravity in (2+2) (two time and two space dimensions) and 8-dimensions. We start by observing that supersymmetry implies that the structure constants of the real numbers, complex numbers, quaternions and octonions can be identified with the chirotope concept. This means, among other things, that normed divisions algebras, which are only possible in 1,2, 4 or 8-dimensions, are linked to oriented matroid theory. Therefore, we argue that the possibility for developing loop quantum gravity in 8-dimensions must be taken as important alternative. Moreover, we show that in 4-dimensions, loop quantum gravity theories in the (1+3) or (0+4) signatures are not the only possibilities. In fact, we show that loop quantum gravity associated with the (2+2)-signature may also be an interesting physical structure.
We assume gravity in a $d$-dimensional manifold $M$ and consider a splitting of the form $M=M_{p}\times M_{q}$, with $d=p+q$. The most general two-block metric associated with $M_{p}$ and $M_{q}$ is used to derive the corresponding Einstein-Hilbert action $\mathcal{S}$. We focus on the special case of two distinct conformal factors $ψ$ and $ϕ$ ($ψ$ for the metric in $M_{p}$ and $ϕ$ for the metric in $M_{q}$), and we write the action $\mathcal{S}$ in the form $\mathcal{S=S}_{p}\mathcal{+S}%_{q} $, where $\mathcal{S}_{p}$ and $\mathcal{S}_{q}$ are actions associated with $M_{p}$ and $M_{q}$, respectively. We show that a simplified action is obtained precisely when $ψ=ϕ^{-1}$. In this case, we find that under the duality transformation $ϕ\leftrightarrow ϕ^{-1}$, the action $\mathcal{S}_{p}$ for the $M_{p}$-space or the action $\mathcal{S}%_{q}$ for the $M_{q}$-space remain invariant, but not both. This result establishes an analogy between Farkas property in oriented matroid theory and duality in general relativity. Furthermore, we argue that our approach can be used in several physical scenarios such as 2t physics and cosmology.
We find a link between oriented matroid theory and 2d gravity with torsion. Our considerations may be useful in the context of noncommutative phase space in a target spacetime of signature (2+2) and in a possible theory of gravity ramification.
We start by describing two of the main proposals for duality in Abelian gauge theories, namely $F$(ield strength)-duality approach and the $S$% -duality formalism. We then discuss how $F$-duality and $S$-duality can be applied to the case of linearized gravity. By emphasizing the similarities and differences between these two type of dualities we explore the possibility of combining them in just one duality formalism.
We generalize the connection between 2t physics and noncommutative geometry. In particular, we apply our formalism to a target spacetime of signature (2+2). Specifically, we compute an algebra of a generalized SL(2, R)-Hamiltonian constraint, showing that it satisfies a kind of algebra associated with the noncommutative group $U_{\star}(1,1)$. We also comment about a possible connection between our formalism and nonsymmetric gravitational theory.
We start a program of background independent quantum gravity in eight dimensions. We begin by considering canonical gravity \textit{a la} "Kaluza-Klein" in $D=d+1$ dimensions. We show that our canonical gravity approach can be applied to the case of self-dual gravity in four dimensions. Further, by using our previously proposed classical action of Ashtekar self-dual gravity formalism in eight dimensions, we proceed to develop the canonical approach in eight dimensions. Our construction considers different SO(8) symmetry breakings. In particular, the breaking $SO(8)=S_{R}^{7}% \times S_{L}^{7}\times G_{2}$ plays an important role in our discussion.
We consider some fundamental constants from the point of view of the duality symmetry. Our analysis of duality is focused on three issues: the maximum radiated power of gravitational waves, the cosmological constant, and the magnetic monopole mass. We show that the maximum radiated power of gravitational waves implies that the Planck time is a minimal time. Furthermore, we prove that duality implies a quantization of the cosmological constant. Finally, by using one of the Euler series for the number $π$, we show that the Dirac electric-magnetic charge quantization implies a mass for the magnetic monopole (or neutrino) of the order of $10^{-5}$ the mass of the electron.
We discuss different aspects of the 2+2-signature from the point of view of the quatl theory. In particular, we compare two alternative approaches to such a spacetime signature, namely the 1+1-matrix-brane and the 2+2-target spacetime of a string. This analysis also reveals hidden discrete symmetries of the 2+2-brane action associated with the 2+2-dimensional sector of a 2+10-dimensional target background.
We discuss the Ashtekar formalism from the point of view of twelve dimensions. We first focus on the 2+10 spacetime signature and then we consider the transition $2+10\to (2+2)+(0+8)$. We argue that both sectors 2+2 and 0+8, which are exceptional signatures, can be analyzed from the point of view of a self-dual action associated with the Ashtekar formalism.
We develop a linearized five dimensional Kaluza-Klein theory as a gauge theory. By perturbing the metric around flat and the De Sitter backgrounds, we first discuss linearized gravity as a gauge theory in any dimension. In the particular case of five dimensions, we show that using the Kaluza-Klein mechanism, the field equations of our approach implies both linearized gauge gravity and Maxwell theory in flat and the De Sitter scenarios. As a possible further development of our formalism, we also discuss an application in the context of a gravitational polarization scattering by means of the analogue of the Mueller matrix in optical polarization algebra. We argue that this application can be of particular interest in gravitational waves experiments.