22 research outputs found
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.Comment: 24 page
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.Comment: 16 page
Newtonian gravity as an entropic force: Towards a derivation of G
It has been suggested that the Newtonian gravitational force may emerge as an
entropic force from a holographic microscopic theory. In this framework, the
possibility is reconsidered that Newton's gravitational coupling constant G can
be derived from the fundamental constants of the underlying microscopic theory.Comment: 10 pages. v6: published versio
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.Comment: 4+epsilon, 1 figur
Finite states in four dimensional quantized gravity
This is the first in a series of papers outlining an algorithm to explicitly
construct finite quantum states of the full theory of gravity in Ashtekar
variables. The algorithm is based upon extending some properties of a special
state, the Kodama state for pure gravity with cosmological term, to
matter-coupled models. We then illustrate a presciption for nonperturbatively
constructing the generalized Kodama states, in preparation for subsequent works
in this series. We also introduce the concept of the semiclassical-quantum
correspondence (SQC). We express the quantum constraints of the full theory as
a system of equations to be solved for the constituents of the `phase' of the
wavefunction. Additionally, we provide a variety of representations of the
generalized Kodama states including a generalization of the topological
instanton term to include matter fields, for which we present arguments for the
field-theoretical analogue of cohomology on infinite dimensional spaces. We
demonstrate that the Dirac, reduced phase space and geometric quantization
procedures are all equivalent for these generalized Kodama states as a natural
consequence of the SQC. We relegate the method of the solution to the
constraints and other associated ramifications of the generalized Kodama states
to separate works.Comment: 42 pages: Accepted for publication by Class. Quantum Grav. journa
The geometric role of symmetry breaking in gravity
In gravity, breaking symmetry from a group G to a group H plays the role of
describing geometry in relation to the geometry the homogeneous space G/H. The
deep reason for this is Cartan's "method of equivalence," giving, in
particular, an exact correspondence between metrics and Cartan connections. I
argue that broken symmetry is thus implicit in any gravity theory, for purely
geometric reasons. As an application, I explain how this kind of thinking gives
a new approach to Hamiltonian gravity in which an observer field spontaneously
breaks Lorentz symmetry and gives a Cartan connection on space.Comment: 4 pages. Contribution written for proceedings of the conference
"Loops 11" (Madrid, May 2011
Hamiltonian analysis of SO(4,1) constrained BF theory
In this paper we discuss canonical analysis of SO(4,1) constrained BF theory.
The action of this theory contains topological terms appended by a term that
breaks the gauge symmetry down to the Lorentz subgroup SO(3,1). The equations
of motion of this theory turn out to be the vacuum Einstein equations. By
solving the B field equations one finds that the action of this theory contains
not only the standard Einstein-Cartan term, but also the Holst term
proportional to the inverse of the Immirzi parameter, as well as a combination
of topological invariants. We show that the structure of the constraints of a
SO(4,1) constrained BF theory is exactly that of gravity in Holst formulation.
We also briefly discuss quantization of the theory.Comment: 9 page
Entropic corrections to Newton's law
In this short letter we calculate separately the generalized uncertainty
principle (GUP) and self gravitational corrections to the Newton's
gravitational formula. We show that for a complete description of the GUP and
self-gravity effects, both temperature and the entropy must be modified.Comment: 4 pages, Accepted for publication in "Physica Scripta",Title changed,
Major revisio
Surface terms, Asymptotics and Thermodynamics of the Holst Action
We consider a first order formalism for general relativity derived from the
Holst action. This action is obtained from the standard Palatini-Hilbert form
by adding a topological-like term and can be taken as the starting point for
loop quantum gravity and spin foam models. The equations of motion derived from
the Holst action are, nevertheless, the same as in the Palatini formulation.
Here we study the form of the surface terms of the action for general
boundaries as well as the symplectic current in the covariant formulation of
the theory. Furthermore, we analyze the behavior of the surface terms in
asymptotically flat space-times. We show that the contribution to the
symplectic structure from the Holst term vanishes and one obtains the same
asymptotic expressions as in the Palatini action. It then follows that the
asymptotic Poincare symmetries and conserved quantities such as energy, linear
momentum and relativistic angular momentum found here are equivalent to those
obtained from the standard Arnowitt, Deser and Misner formalism. Finally, we
consider the Euclidean approach to black hole thermodynamics and show that the
on-shell Holst action, when evaluated on some static solutions containing
horizons, yields the standard thermodynamical relations.Comment: 16 page
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.Comment: Version published in Classical and Quantum Gravity. Significant
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