41 research outputs found
Comment on `Hawking radiation from fluctuating black holes'
Takahashi & Soda (2010 Class. Quantum Grav. v27 p175008, arXiv:1005.0286)
have recently considered the effect (at lowest non-trivial order) of dynamical,
quantized gravitational fluctuations on the spectrum of scalar Hawking
radiation from a collapsing Schwarzschild black hole. However, due to an
unfortunate choice of gauge, the dominant (even divergent) contribution to the
coefficient of the spectrum correction that they identify is a pure gauge
artifact. I summarize the logic of their calculation, comment on the
divergences encountered in its course and comment on how they could be
eliminated, and thus the calculation be completed.Comment: 12 pages, 1 fig; feynmp, amsref
Presymplectic current and the inverse problem of the calculus of variations
The inverse problem of the calculus of variations asks whether a given system
of partial differential equations (PDEs) admits a variational formulation. We
show that the existence of a presymplectic form in the variational bicomplex,
when horizontally closed on solutions, allows us to construct a variational
formulation for a subsystem of the given PDE. No constraints on the
differential order or number of dependent or independent variables are assumed.
The proof follows a recent observation of Bridges, Hydon and Lawson and
generalizes an older result of Henneaux from ordinary differential equations
(ODEs) to PDEs. Uniqueness of the variational formulation is also discussed.Comment: v2: 17 pages, no figures, BibTeX; minor corrections, close to
published versio
Formation of Electronic Nematic Phase in Interacting Systems
We study the formation of an electronic nematic phase characterized by a
broken point-group symmetry in interacting fermion systems within the weak
coupling theory. As a function of interaction strength and chemical potential,
the phase transition between the isotropic Fermi liquid and nematic phase is
first order at zero temperature and becomes second order at a finite
temperature. The transition is present for all typical, including quasi-2D,
electronic dispersions on the square lattice and takes place for arbitrarily
small interaction when at van Hove filling, thus suppressing the Lifshitz
transition. In connection with the formation of the nematic phase, we discuss
the origin of the first order transition and competition with other broken
symmetry states.Comment: revtex4, 6 pages, 6 figures; revised introduction, updated reference
Comments on Microcausality, Chaos, and Gravitational Observables
Observables in gravitational systems must be non-local so as to be invariant
under diffeomorphism gauge transformations. But at the classical level some
such observables can nevertheless satisfy an exact form of microcausality. This
property is conjectured to remain true at all orders in the semiclassical
expansion, though with limitations at finite or . We
also discuss related issues concerning observables in black hole spacetimes and
comment on the senses in which they do and do not experience the form of chaos
identified by Shenker and Stanford. In particular, in contrast to the situation
in a reflecting cavity, this chaos does not afflict observables naturally
associated with Hawking radiation for evaporating black holes.Comment: 16 pages, 1 figure; references adde
Coupling a Point-Like Mass to Quantum Gravity with Causal Dynamical Triangulations
We present a possibility of coupling a point-like, non-singular, mass
distribution to four-dimensional quantum gravity in the nonperturbative setting
of causal dynamical triangulations (CDT). In order to provide a point of
comparison for the classical limit of the matter-coupled CDT model, we derive
the spatial volume profile of the Euclidean Schwarzschild-de Sitter space glued
to an interior matter solution. The volume profile is calculated with respect
to a specific proper-time foliation matching the global time slicing present in
CDT. It deviates in a characteristic manner from that of the pure-gravity
model. The appearance of coordinate caustics and the compactness of the mass
distribution in lattice units put an upper bound on the total mass for which
these calculations are expected to be valid. We also discuss some of the
implementation details for numerically measuring the expectation value of the
volume profiles in the framework of CDT when coupled appropriately to the
matter source.Comment: 26 pages, 9 figures, updated published versio
Spontaneous breaking of four-fold rotational symmetry in two-dimensional electronic systems explained as a continuous topological transition
The Fermi liquid approach is applied to the problem of spontaneous violation
of the four-fold rotational point-group symmetry () in strongly correlated
two-dimensional electronic systems on a square lattice. The symmetry breaking
is traced to the existence of a topological phase transition. This continuous
transition is triggered when the Fermi line, driven by the quasiparticle
interactions, reaches the van Hove saddle points, where the group velocity
vanishes and the density of states becomes singular. An unconventional Fermi
liquid emerges beyond the implicated quantum critical point.Comment: 6 pages, 4 figure
Cosmological perturbation theory and quantum gravity
It is shown how cosmological perturbation theory arises from a fully quantized perturbative theory of quantum gravity. Central for the derivation is a non-perturbative concept of gauge-invariant local observables by means of which perturbative invariant expressions of arbitrary order are generated. In particular, in the linearised theory, first order gauge-invariant observables familiar from cosmological perturbation theory are recovered. Explicit expressions of second order quantities are presented as well
Fermi surface instabilities at finite Temperature
We present a new method to detect Fermi surface instabilities for interacting
systems at finite temperature. We first apply it to a list of cases studied
previously, recovering already known results in a very economic way, and
obtaining most of the information on the phase diagram analytically. As an
example, in the continuum limit we obtain the critical temperature as an
implicit function of the magnetic field and the chemical potential
. By applying the method to a model proposed to describe reentrant
behavior in , we reproduce the phase diagram obtained
experimentally and show the presence of a non-Fermi Liquid region at
temperatures above the nematic phase.Comment: 10 pages, 10 figure
Generally covariant dynamical reduction models and the Hadamard condition
We recall and review earlier work on dynamical reduction models, both non-relativistic and relativistic, and discuss how they may relate to suggestions which have been made (including the matter-gravity entanglement hypothesis of one of us) for how quantum gravity could be connected to the resolution of the quantum-mechanical measurement problem. We then provide general guidelines for generalizing dynamical reduction models to curved spacetimes and propose a class of generally covariant relativistic versions of the GRW model. We anticipate that the collapse operators of our class of models may play a r\^ole in a yet-to-be-formulated theory of semiclassical gravity with collapses. We show explicitly that the collapse operators map a dense domain of states that are initially Hadamard to final Hadamard states -- a property that we expect will be needed for the construction of such a semiclassical theory. Finally, we provide a simple example in which we explicitly compute the violations in energy-momentum due to the state reduction process and conclude that this violation is of the order of a parameter of the model -- supposed to be small. We briefly discuss how this work may, upon further development of a suitable semiclassical gravity theory with collapses, enable further progress to be made on earlier work one of us and collaborators on the explanation of structure-formation in a homogeneous and isotropic quantum universe and on a possible resolution of the black hole information loss puzzle
Quantum gravity from the point of view of locally covariant quantum field theory
We construct perturbative quantum gravity in a generally covariant way. In particular our construction is background independent. It is based on the locally covariant approach to quantum field theory and the renormalized Batalin-Vilkovisky formalism. We do not touch the problem of nonrenormalizability and interpret the theory as an effective theory at large length scales