21 research outputs found
On the pathwidth of almost semicomplete digraphs
We call a digraph {\em -semicomplete} if each vertex of the digraph has at
most non-neighbors, where a non-neighbor of a vertex is a vertex such that there is no edge between and in either direction.
This notion generalizes that of semicomplete digraphs which are
-semicomplete and tournaments which are semicomplete and have no
anti-parallel pairs of edges. Our results in this paper are as follows. (1) We
give an algorithm which, given an -semicomplete digraph on vertices
and a positive integer , in time either
constructs a path-decomposition of of width at most or concludes
correctly that the pathwidth of is larger than . (2) We show that there
is a function such that every -semicomplete digraph of pathwidth
at least has a semicomplete subgraph of pathwidth at least .
One consequence of these results is that the problem of deciding if a fixed
digraph is topologically contained in a given -semicomplete digraph
admits a polynomial-time algorithm for fixed .Comment: 33pages, a shorter version to appear in ESA 201
Nonperturbative late time asymptotics for heat kernel in gravity theory
Recently proposed nonlocal and nonperturbative late time behavior of the heat
kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is
dominated by two terms one of which represents a trivial covariantization of
the flat-space result and another one is given by the Gibbons-Hawking integral
over asymptotically-flat infinity. Nonlocal terms of the effective action
generated by this asymptotics might underly long- distance modifications of the
Einstein theory motivated by the cosmological constant problem. New mechanisms
of the cosmological constant induced by infrared effects of matter and graviton
loops are briefly discussed.Comment: 22 pages, LaTeX, final version, to be published in Phys. Rev.
Quantum Dirac constraints, Ward identities and path integral in relativistic gauge
Quantum Dirac constraints in generic constrained system are solved by
directly calculating in the one-loop approximation the path integral with
relativistic gauge fixing procedure. The calculations are based on the
reduction algorithms for functional determinants extended to gauge theories.
Explicit mechanism of transition from relativistic gauge conditions to unitary
gauges, participating in the construction of this solution, is revealed by the
method of Ward identities.Comment: 12 pages, LaTe
Nonlocal action for long-distance modifications of gravity theory
We construct the covariant nonlocal action for recently suggested
long-distance modifications of gravity theory motivated by the cosmological
constant and cosmological acceleration problems. This construction is based on
the special nonlocal form of the Einstein-Hilbert action explicitly revealing
the fact that this action within the covariant curvature expansion begins with
curvature-squared terms. Nonlocal form factors in the action of both quantum
and brane-induced nature are briefly discussed. In particular, it is emphasized
that for certain class of quantum initial value problems nonlocal nature of the
Euclidean action does not contradict the causality of effective equations of
motion.Comment: 13 pages, LaTeX, final version to appear in Phys. Lett.
Effective equations of motion and initial conditions for inflation in quantum cosmology
We obtain effective equations of inflationary dynamics for the mean inflaton
and metric fields in the no-boundary and tunneling quantum states of the
Universe. In the slow roll approximation (taking the form of the local
Schwiger-DeWitt expansion) effective equations follow from the Euclidean
effective action on the DeSitter gravitational instanton. Effective equations
are applied in the model of the inflaton scalar field coupled to the GUT sector
of matter fields and also having a strong nonminimal coupling to the curvature.
The inverse of its big negative nonminimal coupling constant, serves as a small
parameter of the slow roll expansion and semiclassical expansion of quantum
gravitational effects. As a source of initial conditions we use a sharp
probability peak recently obtained in the one-loop approximation for the
no-boundary and tunneling quantum states and belonging (in virtue of a strong
nonminimal coupling) to the GUT energy scale much below the Planck scale. The
obtained equations in the tunneling quantum state predict a finite duration of
inflationary stage compatible with the observational status of inflation
theory, whereas for the no-boundary state they lead to the infinite
inflationary epoch with a constant inflaton field.Comment: 23 pages, LaTe
Open inflation from quantum cosmology with a strong nonminimal coupling
We propose the mechanism of quantum creation of the open Universe in the
observable range of values of . This mechanism is based on the
no-boundary quantum state with the Hawking-Turok instanton applied to the model
with a strong nonminimal coupling of the inflaton field. We develop the slow
roll perturbation expansion for the instanton solution and obtain a nontrivial
contribution to the classical instanton action. The interplay of this classical
contribution with the loop effects due to quantum effective action generates
the probability distribution peak with necessary parameters of the inflation
stage without invoking any anthropic considerations. In contrast with a similar
mechanism for closed models, existing only for the tunneling quantum state of
the Universe, the observationally justified open inflation originates from the
no-boundary cosmological wavefunction.Comment: 28 pages, LaTe
Relativistic Gauge Conditions in Quantum Cosmology
This paper studies the quantization of the electromagnetic field on a flat
Euclidean background with boundaries. One-loop scaling factors are evaluated
for the one-boundary and two-boundary backgrounds. The mode-by-mode analysis of
Faddeev-Popov quantum amplitudes is performed by using zeta-function
regularization, and is compared with the space-time covariant evaluation of the
same amplitudes. It is shown that a particular gauge condition exists for which
the corresponding operator matrix acting on gauge modes is in diagonal form
from the beginning. Moreover, various relativistic gauge conditions are studied
in detail, to investigate the gauge invariance of the perturbative quantum
theory.Comment: 26 pages, plain TeX, no figure
Quantum origin of the early inflationary Universe
We give a detailed presentation of a recently proposed mechanism of
generating the energy scale of inflation by loop effects in quantum cosmology.
We discuss the quantum origin of the early inflationary Universe from the
no-boundary and tunneling quantum states and present a universal effective
action algorithm for the distribution function of chaotic inflationary
cosmologies in both of these states. The energy scale of inflation is
calculated by finding a sharp probability peak in this distribution function
for a tunneling model driven by the inflaton field with large negative constant
of non-minimal interaction. The sub-Planckian parameters of this peak
(the mean value of the corresponding Hubble constant , its
quantum width and the number of inflationary
e-foldings ) are found to be in good correspondence with the
observational status of inflation theory, provided the coupling constants of
the theory are constrained by a condition which is likely to be enforced by the
(quasi) supersymmetric nature of the sub-Planckian particle physics model.Comment: 43 pages, LaTeX, figures not include
On the 3-particle scattering continuum in quasi one dimensional integer spin Heisenberg magnets
We analyse the three-particle scattering continuum in quasi one dimensional
integer spin Heisenberg antiferromagnets within a low-energy effective field
theory framework. We exactly determine the zero temperature dynamical structure
factor in the O(3) nonlinear sigma model and in Tsvelik's Majorana fermion
theory. We study the effects of interchain coupling in a Random Phase
Approximation. We discuss the application of our results to recent
neutron-scattering experiments on the Haldane-gap material .Comment: 8 pages of revtex, 5 figures, small changes, to appear in PR
One loop renormalization of the four-dimensional theory for quantum dilaton gravity.
We study the one loop renormalization in the most general metric-dilaton
theory with the second derivative terms only. The general theory can be divided
into two classes, models of one are equivalent to conformally coupled with
gravity scalar field and also to general relativity with cosmological term. The
models of second class have one extra degree of freedom which corresponds to
dilaton. We calculate the one loop divergences for the models of second class
and find that the arbitrary functions of dilaton in the starting action can be
fine-tuned in such a manner that all the higher derivative counterterms
disappear on shell. The only structures in both classical action and
counterterms, which survive on shell, are the potential (cosmological) ones.
They can be removed by renormalization of the dilaton field which acquire the
nontrivial anomalous dimension, that leads to the effective running of the
cosmological constant. For some of the renormalizable solutions of the theory
the observable low energy value of the cosmological constant is small as
compared with the Newtonian constant. We also discuss another application of
our result.Comment: 21 pages, latex, no figures