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Henrique de A. Gomes

Publications and source records attributed to Henrique de A. Gomes.

6 recordsLinked to original sources
arXiv2018

Local(ish) gravity theories in conformal superspace

Motivated by well-known obstacles to quantum gravity, I look for the most general geometrodynamical symmetries compatible with a reduced physical configuration space for metric gravity. I argue that they lead either to a completely static Universe, or one embodying spatial conformal diffeomorphisms. Demanding locality for an action compatible with these principles determines the sort of terms one can add, both for the purely gravitational part as well as matter couplings. The symmetries guarantee that there are two gravitational propagating physical degrees of freedom (and no explicit refoliation-invariance). The simplest such system has a geometric interpretation as a geodesic model in infinite dimensional conformal superspace. An approximate solution to the equations of motion corresponds to a static Bianchi IX spatial ansatz. The unique coupling to electromagnetism forces its propagation equations to be hyperbolic, enabling us to build" a standard space-time causal structure. There are, however, deviations from the standard Maxwell equations when space-time anisotropies become too large. Regarding quantization, with the geometric interpretation and the lack of refoliation invariance, the path integral treatment of the symmetries becomes much less involved than the similar approaches to GR. The symmetries form an (infinite-dimensional) Lie algebra, and no BFV treatment is necessary. We find that the propagator around the flat solution has up to 6-th order spatial derivatives, giving it plausible regularization properties as in Horava-Lifschitz.

gr-qc↗
arXiv2018

Back to Parmenides

After a brief introduction to issues that plague the realization of a theory of quantum gravity, I suggest that the main one concerns a quantization of the principle of relative simultaneity. This leads me to a distinction between time and space, to a further degree than that present in the canonical approach to general relativity. With this distinction, one can make sense of superpositions as interference between alternative paths in the relational configuration space of the entire Universe. But the full use of relationalism brings us to a timeless picture of Nature, as it does in the canonical approach (which culminates in the Wheeler-DeWitt equation). After a discussion of Parmenides and the Eleatics' rejection of time, I show that there is middle ground between their view of absolute timelessness and a view of physics taking place in timeless configuration space. In this middle ground, even though change does not fundamentally exist, the illusion of change can be recovered in a way not permitted by Parmenides. It is recovered through a particular density distribution over configuration space which gives rise to 'records'. Incidentally, this distribution seems to have the potential to dissolve further aspects of the measurement problem that can still be argued to haunt the application of decoherence to Many-Worlds quantum mechanics. I end with a discussion indicating that the conflict between the conclusions of this paper and our view of the continuity of the self may still intuitively bother us. Nonetheless, those conclusions should be no more challenging to our intuition than Derek Parfit's thought experiments on the subject.

quant-ph↗
arXiv2009

A Note on the Topology of a Generic Subspace of Riem

For Riem(M) the space of Riemannian metrics over a compact 3-manifold without boundary $M$, we study topological properties of the dense open subspace Riem'(M) of metrics which possess no Killing vectors. Given the stratification of Riem(M), we work under the condition that, in a sense defined in the text, the connected components of each stratum do not accumulate. Given this condition we find that one of the most fundamental results regarding the topology of Riem(M), namely that it has trivial homotopy groups, would still be true for Riem'(M). This would make the topology of Riem'(M) completely understood. Coupled with the fact that for Riem'(M), we have a proper principal fibration with the group of diffeomorphisms, which makes Riem'(M)/Diff(M) a proper manifold (as opposed to Riem(M)/Diff(M)), we would have that the homotopy groups of the quotient are given by the homotopy groups of Diff(M), which reflects the topology of $M$. These results would render the space of metrics with no symmetries subject to the above condition, as an ideal setting for geometrodynamical analysis.

math-ph↗
arXiv2007

Huygens-Fresnel Principle in Superspace

We first roughly present a summary of the optico-mechanical analogy, which has always been so profitable in physics. Then we put forward a geometrodynamical formulation of gravity suitable to our intentions, both formally and conceptually. We present difficulties in some approaches to canonically quantize gravity which can be amended by the idea put forward in this paper, which we introduce in the last section. It consists basically in trying to find an intermediary between the quantization step going from the classical superhamiltonian constraint to the Wheeler-DeWitt equation. This is accomplished by inputting interference beyond the WKB approximation, through a type of Huygens-Fresnel Principle (HFP) in superspace.

gr-qc↗
arXiv2006

Geometrical Methods in Gauge Theory

In this work we explore the geometrical interpretation of gauge theories through the formalism of fiber bundles. Moreover, we conduct an investigation in the topology of fiber bundles, providing a proof of the Classification Theorem. In the last chapter we present some applications, such as electromagnetism and generalized Kaluza-Klein Theory.

math-ph↗