29 research outputs found
Background Independence and Asymptotic Safety in Conformally Reduced Gravity
We analyze the conceptual role of background independence in the application
of the effective average action to quantum gravity. Insisting on a background
independent renormalization group (RG) flow the coarse graining operation must
be defined in terms of an unspecified variable metric since no rigid metric of
a fixed background spacetime is available. This leads to an extra field
dependence in the functional RG equation and a significantly different RG flow
in comparison to the standard flow equation with a rigid metric in the mode
cutoff. The background independent RG flow can possess a non-Gaussian fixed
point, for instance, even though the corresponding standard one does not. We
demonstrate the importance of this universal, essentially kinematical effect by
computing the RG flow of Quantum Einstein Gravity in the ``conformally
reduced'' Einstein--Hilbert approximation which discards all degrees of freedom
contained in the metric except the conformal one. Without the extra field
dependence the resulting RG flow is that of a simple -theory. Including
it one obtains a flow with exactly the same qualitative properties as in the
full Einstein--Hilbert truncation. In particular it possesses the non-Gaussian
fixed point which is necessary for asymptotic safety.Comment: 4 figures
Conformal sector of Quantum Einstein Gravity in the local potential approximation: non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance
We explore the nonperturbative renormalization group flow of Quantum Einstein
Gravity (QEG) on an infinite dimensional theory space. We consider "conformally
reduced" gravity where only fluctuations of the conformal factor are quantized
and employ the Local Potential Approximation for its effective average action.
The requirement of "background independence" in quantum gravity entails a
partial differential equation governing the scale dependence of the potential
for the conformal factor which differs significantly from that of a scalar
matter field. In the infinite dimensional space of potential functions we find
a Gaussian as well as a non-Gaussian fixed point which provides further
evidence for the viability of the asymptotic safety scenario. The analog of the
invariant cubic in the curvature which spoils perturbative renormalizability is
seen to be unproblematic for the asymptotic safety of the conformally reduced
theory. The scaling fields and dimensions of both fixed points are obtained
explicitly and possible implications for the predictivity of the theory are
discussed. Spacetime manifolds with as well as topology are
considered. Solving the flow equation for the potential numerically we obtain
examples of renormalization group trajectories inside the ultraviolet critical
surface of the non-Gaussian fixed point. The quantum theories based upon some
of them show a phase transition from the familiar (low energy) phase of gravity
with spontaneously broken diffeomorphism invariance to a new phase of unbroken
diffeomorphism invariance; the latter phase is characterized by a vanishing
expectation value of the metric
Towards Canonical Quantum Gravity for Geometries Admitting Maximally Symmetric Two-dimensional Surfaces
The 3+1 (canonical) decomposition of all geometries admitting two-dimensional
space-like surfaces is exhibited. A proposal consisting of a specific
re-normalization {\bf Assumption} and an accompanying {\bf Requirement} is put
forward, which enables the canonical quantization of these geometries. The
resulting Wheeler-deWitt equation is based on a re-normalized manifold
parameterized by three smooth scalar functionals. The entire space of solutions
to this equation is analytically given, exploiting the freedom left by the
imposition of the {\bf Requirement} and contained in the third functional.Comment: 27 pages, no figures, LaTex2e source fil
The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
We discuss various basic conceptual issues related to coarse graining flows
in quantum gravity. In particular the requirement of background independence is
shown to lead to renormalization group (RG) flows which are significantly
different from their analogs on a rigid background spacetime. The importance of
these findings for the asymptotic safety approach to Quantum Einstein Gravity
(QEG) is demonstrated in a simplified setting where only the conformal factor
is quantized. We identify background independence as a (the ?) key prerequisite
for the existence of a non-Gaussian RG fixed point and the renormalizability of
QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum
Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to
appear in General Relativity and Gravitatio
The Flux-Line Lattice in Superconductors
Magnetic flux can penetrate a type-II superconductor in form of Abrikosov
vortices. These tend to arrange in a triangular flux-line lattice (FLL) which
is more or less perturbed by material inhomogeneities that pin the flux lines,
and in high- supercon- ductors (HTSC's) also by thermal fluctuations. Many
properties of the FLL are well described by the phenomenological
Ginzburg-Landau theory or by the electromagnetic London theory, which treats
the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft
mainly because of the large magnetic penetration depth: The shear modulus of
the FLL is thus small and the tilt modulus is dispersive and becomes very small
for short distortion wavelength. This softness of the FLL is enhanced further
by the pronounced anisotropy and layered structure of HTSC's, which strongly
increases the penetration depth for currents along the c-axis of these uniaxial
crystals and may even cause a decoupling of two-dimensional vortex lattices in
the Cu-O layers. Thermal fluctuations and softening may melt the FLL and cause
thermally activated depinning of the flux lines or of the 2D pancake vortices
in the layers. Various phase transitions are predicted for the FLL in layered
HTSC's. The linear and nonlinear magnetic response of HTSC's gives rise to
interesting effects which strongly depend on the geometry of the experiment.Comment: Review paper for Rep.Prog.Phys., 124 narrow pages. The 30 figures do
not exist as postscript file
Effects of lead and selected pyrethroids/piperonyl butoxide alone and in combination on Na, K‐ATPase
Canonical quantization of some midi-superspace models in 2+1 and 3+1 dimensions
A proposal is put forward which enables the canonical quantization of a family of axially symmetric geometries in 2+1 dimensions and a corresponding spherically symmetric family in 3+1 dimensions. The proposal consists of a particular renormalization assumption and an accompanying requirement and results in a Wheeler-DeWitt equation which is based on a renormalized manifold parametrized by three smooth scalar functionals. The aforementioned equation is analytically solved for both the 2+1 and 3+1 case. © 2009 IOP Publishing Ltd