arXiv subjects

Andrew Randono

Publications and source records attributed to Andrew Randono.

At least 19 recordsLinked to original sources

arXiv2025

Cloud Diffusion Part 1: Theory and Motivation

Diffusion models for image generation function by progressively adding noise to an image set and training a model to separate out the signal from the noise. The noise profile used by these models is white noise -- that is, noise based on independent normal distributions at each point whose mean and variance is independent of the scale. By contrast, most natural image sets exhibit a type of scale invariance in their low-order statistical properties characterized by a power-law scaling. Consequently, natural images are closer (in a quantifiable sense) to a different probability distribution that emphasizes large scale correlations and de-emphasizes small scale correlations. These scale invariant noise profiles can be incorporated into diffusion models in place of white noise to form what we will call a ``Cloud Diffusion Model". We argue that these models can lead to faster inference, improved high-frequency details, and greater controllability. In a follow-up paper, we will build and train a Cloud Diffusion Model that uses scale invariance at a fundamental level and compare it to classic, white noise diffusion models.

cs.CV↗

arXiv2014

Is de Sitter space a fermion?

Following up on a recent model yielding fermionic geometries, I turn to more familiar territory to address the question of statistics in purely geometric theories. Working in the gauge formulation of gravity, where geometry is characterized by a symmetry broken Cartan connection, I give strong evidence to suggest that de Sitter space itself, and a class of de Sitter-like geometries, can be consistently quantized fermionically. By this I mean that de Sitter space can be quantized such that the wavefunctional picks up an overall minus sign under a $2π$ rotational diffeomorphism. Surprisingly, the underlying mathematics is the same as that of the Skyrme model for strongly interacting baryons. This promotes the question {\it "Is geometry bosonic or fermionic?"} beyond the realm of the rhetorical and places it on uncomfortably familiar ground.

gr-qc↗

arXiv2011

Is geometry bosonic or fermionic?

It is generally assumed that the gravitational field is bosonic. Here we show that a simple propagating torsional theory can give rise to localized geometric structures that can consistently be quantized as fermions under exchange. To demonstrate this, we show that the model can be formally mapped onto the Skyrme model of baryons, and we use well-known results from Skyrme theory. This begs the question: {\it Is geometry bosonic or fermionic (or both)?}

gr-qc↗

arXiv2010

Gauge Gravity: a forward-looking introduction

This article is a review of modern approaches to gravity that treat the gravitational interaction as a type of gauge theory. The purpose of the article is twofold. First, it is written in a colloquial style and is intended to be a pedagogical introduction to the gauge approach to gravity. I begin with a review of the Einstein-Cartan formulation of gravity, move on to the Macdowell-Mansouri approach, then show how gravity can be viewed as the symmetry broken phase of an (A)dS-gauge theory. This covers roughly the first half of the article. Armed with these tools, the remainder of the article is geared toward new insights and new lines of research that can be gained by viewing gravity from this perspective. Drawing from familiar concepts from the symmetry broken gauge theories of the standard model, we show how the topological structure of the gauge group allows for an infinite class of new solutions to the Einstein-Cartan field equations that can be thought of as degenerate ground states of the theory. We argue that quantum mechanical tunneling allows for transitions between the degenerate vacua. Generalizing the tunneling process from a topological phase of the gauge theory to an arbitrary geometry leads to a modern reformulation of the Hartle-Hawking "no boundary" proposal.

gr-qc↗

arXiv2010

Torsional Monopoles and Torqued Geometries in Gravity and Condensed Matter

Torsional degrees of freedom play an important role in modern gravity theories as well as in condensed matter systems where they can be modeled by defects in solids. Here we isolate a class of torsion models that support torsion configurations with a localized, conserved charge that adopts integer values. The charge is topological in nature and the torsional configurations can be thought of as torsional `monopole' solutions. We explore some of the properties of these configurations in gravity models with non-vanishing curvature, and discuss the possible existence of such monopoles in condensed matter systems. To conclude, we show how the monopoles can be thought of as a natural generalization of the Cartan spiral staircase.

gr-qc↗

arXiv2010

Gravity from a fermionic condensate of a gauge theory

The most prominent realization of gravity as a gauge theory similar to the gauge theories of the standard model comes from enlarging the gauge group from the Lorentz group to the de Sitter group. To regain ordinary Einstein-Cartan gravity the symmetry must be broken, which can be accomplished by known quasi-dynamic mechanisms. Motivated by symmetry breaking models in particle physics and condensed matter systems, we propose that the symmetry can naturally be broken by a homogenous and isotropic fermionic condensate of ordinary spinors. We demonstrate that the condensate is compatible with the Einstein-Cartan equations and can be imposed in a fully de Sitter invariant manner. This lends support, and provides a physically realistic mechanism for understanding gravity as a gauge theory with a spontaneously broken local de Sitter symmetry.

hep-th↗

arXiv2010

The Immirzi Parameter as an Instanton Angle

The Barbero-Immirzi parameter is a one parameter quantization ambiguity underpinning the loop approach to quantum gravity that bears tantalizing similarities to the theta parameter of gauge theories such as Yang-Mills and QCD. Despite the apparent semblance, the Barbero-Immirzi field has resisted a direct topological interpretation along the same lines as the theta-parameter. Here we offer such an interpretation. Our approach begins from the perspective of Einstein-Cartan gravity as the symmetry broken phase of a de Sitter gauge theory. From this angle, just as in ordinary gauge theories, a theta-term emerges from the requirement that the vacuum is stable against quantum mechanical tunneling. The Immirzi parameter is then identified as a combination of Newton's constant, the cosmological constant, and the theta-parameter.

hep-th↗

arXiv2010

Entropic corrections to Newton's law

It has been known for some time that there is a deep connection between thermodynamics and gravity, with perhaps the most dramatic implication that the Einstein equations can be viewed as a thermodynamic equation of state. Recently Verlinde has proposed a model for gravity with a simple statistical mechanical interpretation that is applicable in the non-relatvistic regime. After critically analyzing the construction, we present a strong consistency check of the model. Specifically, we consider two well-motivated corrections to the area-entropy relation, the log correction and the volume correction, and follow Verlinde's construction to derive corrections to Newton's law of gravitation. We show that the deviations from Newton's law stemming from the log correction have the same form as the lowest order quantum effects of perturbative quantum gravity, and the deviations stemming from the volume correction have the same form as some modified Newtonian gravity models designed to explain the anomalous galactic rotation curves.

hep-th↗

arXiv2010

de Sitter Spaces

We exploit an interpretation of gravity as the symmetry broken phase of a de Sitter gauge theory to construct new solutions to the first order field equations. The new solutions are constructed by performing large $Spin(4,1)$ gauge transformations on the ordinary de Sitter solution and extracting first the tetrad, then the induced metric. The class of metrics so obtained is an infinite class labelled by an integer, $q$. Each solution satisfies the local field equations defining constant positive curvature, and is therefore locally isometric to de Sitter space wherever the metric is non-degenerate. The degeneracy structure of the tetrad and metric reflects the topological differences among the solutions with different $q$. By topological arguments we show that the solutions are physically distinct with respect to the symmetries of Einstein-Cartan theory. Ultimately, the existence of solutions of this type may be a distinguishing characteristic of gravity as a metric theory versus gravity as a gauge theory.

gr-qc↗

arXiv2010

Do Spinors Frame-Drag?

We investigate the effect of the intrinsic spin of a fundamental spinor field on the surrounding spacetime geometry. We show that despite the lack of a rotating stress-energy source (and despite claims to the contrary) the intrinsic spin of a spin-half fermion gives rise to a frame-dragging effect analogous to that of orbital angular momentum, even in Einstein-Hilbert gravity where torsion is constrained to be zero. This resolves a paradox regarding the counter-force needed to restore Newton's third law in the well known spin-orbit interaction. In addition, the frame-dragging effect gives rise to a {\it long-range} gravitationally mediated spin-spin dipole interaction coupling the {\it internal} spins of two sources. We argue that despite the weakness of the interaction, the spin-spin interaction will dominate over the ordinary inverse square Newtonian interaction in any process of sufficiently high-energy for quantum field theoretical effects to be non-negligible.

gr-qc↗

arXiv2009

The Internal Spin Angular Momentum of an Asymptotically Flat Spacetime

In this paper we investigate the manner in which the internal spin angular momentum of a spinor field is encoded in the gravitational field at asymptotic infinity. The inclusion of internal spin requires us to re-analyze our notion of asymptotic flatness. In particular, the Poincaré symmetry at asymptotic infinity must replaced by a spin-enlarged Poincaré symmetry. Likewise, the generators of the asymptotic symmetry group must be supplemented to account for the internal spin. In the Hamiltonian framework of first order Einstein-Cartan gravity, the extra generator comes from the boundary term of the Gauss constraint in the asymptotically flat context. With the additional term, we establish the relations among the Noether charges of a Dirac field, the Komar integral, and the asymptotic ADM-like geometric integral. We show that by imposing mild restraints on the generating functionals of gauge transformations at asymptotic infinity, the phase space is rendered explicitly finite. We construct the energy-momentum and the new total (spin+orbital) angular momentum boundary integrals that satisfy the appropriate algebra to be the generators of the spin-enlarged Poincaré symmetry. This demonstrates that the internal spin is encoded in the tetrad at asymptotic infinity. In addition, we find that a new conserved and (spin-enlarged) Poincaré invariant charge emerges that is associated with the global structure of a gauge transformation.

gr-qc↗

arXiv2008

A New Perspective on Covariant Canonical Gravity

We present a new approach to the covariant canonical formulation of Einstein-Cartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the relation between gravity and a general gauge theory. The dynamical variables are simply the frame field and the spin-connection pulled-back to the hypersurface, thereby eliminating the need for simplicity constraints on the momenta. A consequence of this is a degenerate (pre)symplectic form, which appears to be a necessary feature of the Einstein-Cartan formulation. A new feature unique to this approach arises when the constraint algebra is computed: the algebra is a deformation of the de Sitter, anti-de Sitter, or Poincaré algebra (depending on the value of the cosmological constant) with the deformation parameter being the conformal Weyl tensor.

gr-qc↗

arXiv2008

Canonical Lagrangian Dynamics and General Relativity

Building towards a more covariant approach to canonical classical and quantum gravity we outline an approach to constrained dynamics that de-emphasizes the role of the Hamiltonian phase space and highlights the role of the Lagrangian phase space. We identify a "Lagrangian one-form" to replace the standard symplectic one-form, which we use to construct the canonical constraints and an associated constraint algebra. The method is particularly useful for generally covariant systems and systems with a degenerate canonical symplectic form, such as Einstein Cartan gravity, to which we apply the method explicitly. We find that one can demonstrate the closure of the constraints without gauge fixing the Lorentz group or introducing primary constraints on the phase space variables. Finally, using geometric quantization techniques, we briefly discuss implications of the formalism for the quantum theory.

gr-qc↗

arXiv2008

A Mesoscopic Quantum Gravity Effect

We explore the symmetry reduced form of a non-perturbative solution to the constraints of quantum gravity corresponding to quantum de Sitter space. The system has a remarkably precise analogy with the non-relativistic formulation of a particle falling in a constant gravitational field that we exploit in our anaylsis. We find that the solution reduces to de Sitter space in the semi-classical limit, but the uniquely quantum features of the solution have peculiar property. Namely, the unambiguous quantum structures are neither of Planck scale nor of cosmological scale. Instead, we find a periodicity in the volume of the universe whose period, using the observed value of the cosmological constant, is on the order of the volume of the proton.

gr-qc↗

arXiv2007

In Search of Quantum de Sitter Space: Generalizing the Kodama State

The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter space. Despite this, the state fails to pass some of the key tests of a physically realistic quantum state. In an attempt to resolve this problem, we track down the root of the problem to a choice for a particular parameter: the Immirzi parameter. The Kodama state takes this parameter to be complex, whereas modern formulations of canonical quantum gravity require that the parameter is real. We generalize the Kodama state to real values of the Immirzi parameter, and find that the generalization opens up a large Hilbert space of states, one of which can be directly interpreted as particular slicing of de Sitter space. We then show that these states resolve, or are expected to resolve many of the problems associated with the original version of the Kodama state. In order to resolve the interpretation of the multitude of states, we develop a new model of covariant classical and quantum gravity where the full Lorentz group is retained as a local symmetry group, and the canonical evolution generated by the constraints has a close relation to a larger group: the de Sitter group. This formalism gives strong evidence that the multitude of generalized Kodama states can be unified into a single quantum state that is quantum de Sitter space.

gr-qc↗

arXiv2006

Generalizing the Kodama State I: Construction

The Kodama State is unique in being an exact solution to all the ordinary constraints of canonical quantum gravity that also has a well defined semi-classical interpretation as a quantum version of a classical spacetime, namely (anti)de Sitter space. However, the state is riddled with difficulties which can be tracked down to the complexification of the phase space necessary in its construction. This suggests a generalization of the state to real values of the Immirzi parameter. In this first part of a two paper series we show that one can generalize the state to real variables and the result is surprising in that it appears to open up an infinite class of physical states. We show that these states closely parallel the ordinary momentum eigenstates of non-relativistic quantum mechanics with the Levi-Civita curvature playing the role of the momentum. With this identification, the states inherit many of the familiar properties of the momentum eigenstates including delta-function normalizability. In the companion paper we will discuss the physical interpretation, CPT properties, and an interesting connection between the inner product and the Macdowell-Mansouri formulation of general relativity.

gr-qc↗

arXiv2006

Generalizing the Kodama State II: Properties and Physical Interpretation

In this second part of a two paper series we discuss the properties and physical interpretation of the generalized Kodama states. We first show that the states are the three dimensional boundary degrees of freedom of two familiar 4-dimensional topological invariants: the second Chern class and the Euler class. Using this, we show that the states have the familiar interpretation as WKB states, in this case corresponding not only to de Sitter space, but also to first order perturbations therein. In an appropriate spatial topology, the de Sitter solution has pure Chern-Simons functional form, and is the unique state in the class that is identically diffeomorphism and SU(2) gauge invariant. The q-deformed loop transform of this state yields evidence of a cosmological horizon when the deformation parameter is a root of untiy. We then discuss the behavior of the states under discrete symmetries, showing that the states violate $P$ and $T$ due to the presence of the Immirzi parameter, but they are $CPT$ invariant. We conclude with an interesting connection between the physical inner product and the Macdowell Mansouri formulation of gravity.

gr-qc↗

arXiv2005

A Note on Parity Violation and the Immirzi Parameter

There has been considerable recent interest in the Immirzi parameter as a measure of parity violating effects in the classical theory of gravitation with fermion coupling. Most recently it was shown that the Immirzi parameter together with the non-minimal coupling constant of Dirac spinors provides the measure for parity violating spin-spin interaction terms in the effective field theory. For complex values of the Immirzi parameter, the resulting effective field theory yields complex values for the torsion, and a non-unitary effective field theory that blows up for the special cases $γ=\pm i$ where the gravitational kinetic term is the Ashtekar action. We show that by restricting ourselves to real values for the torsion, there is a natural set of choice for the non-minimal coupling constant that yields real and unitary effective field theory that does not blow up for the special cases $γ=\pm i$. We then show that these particular values for the non-minimal coupling coefficients most naturally follow from a non-minimal pseudo-kinetic term in the fermion Lagrangian.

hep-th↗