27,028 research outputs found
Neutron electric polarizability from unquenched lattice QCD using the background field approach
A calculational scheme for obtaining the electric polarizability of the
neutron in lattice QCD with dynamical quarks is developed, using the background
field approach. The scheme differs substantially from methods previously used
in the quenched approximation, the physical reason being that the QCD ensemble
is no longer independent of the external electromagnetic field in the dynamical
quark case. One is led to compute (certain integrals over) four-point
functions. Particular emphasis is also placed on the physical role of constant
external gauge fields on a finite lattice; the presence of these fields
complicates the extraction of polarizabilities, since it gives rise to an
additional shift of the neutron mass unrelated to polarizability effects. The
method is tested on a SU(3) flavor-symmetric ensemble furnished by the MILC
Collaboration, corresponding to a pion mass of m_pi = 759 MeV. Disconnected
diagrams are evaluated using stochastic estimation. A small negative electric
polarizability of alpha =(-2.0 +/- 0.9) 10^(-4) fm^3 is found for the neutron
at this rather large pion mass; this result does not seem implausible in view
of the qualitative behavior of alpha as a function of m_pi suggested by Chiral
Effective Theory.Comment: 36 pages, 11 figures. Note added concerning analytic continuation in
the external electric field; some notation made more precis
Time-Sliced Perturbation Theory for Large Scale Structure I: General Formalism
We present a new analytic approach to describe large scale structure
formation in the mildly non-linear regime. The central object of the method is
the time-dependent probability distribution function generating correlators of
the cosmological observables at a given moment of time. Expanding the
distribution function around the Gaussian weight we formulate a perturbative
technique to calculate non-linear corrections to cosmological correlators,
similar to the diagrammatic expansion in a three-dimensional Euclidean quantum
field theory, with time playing the role of an external parameter. For the
physically relevant case of cold dark matter in an Einstein--de Sitter
universe, the time evolution of the distribution function can be found exactly
and is encapsulated by a time-dependent coupling constant controlling the
perturbative expansion. We show that all building blocks of the expansion are
free from spurious infrared enhanced contributions that plague the standard
cosmological perturbation theory. This paves the way towards the systematic
resummation of infrared effects in large scale structure formation. We also
argue that the approach proposed here provides a natural framework to account
for the influence of short-scale dynamics on larger scales along the lines of
effective field theory.Comment: 29 pages, 2 figures, discussion on IR safety expanded, appendix C
added; version published in JCA
Worm Algorithm for Problems of Quantum and Classical Statistics
This is a chapter of the multi-author book "Understanding Quantum Phase
Transitions," edited by Lincoln Carr and published by Taylor and Francis. In
this chapter, we give a general introduction to the worm algorithm and present
important results highlighting the power of the approachComment: 27 pages, 15 figures, chapter in a boo
Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane
We present an overview of pattern formation analysis for an analogue of the
Swift-Hohenberg equation posed on the real hyperbolic space of dimension two,
which we identify with the Poincar\'e disc D. Different types of patterns are
considered: spatially periodic stationary solutions, radial solutions and
traveling waves, however there are significant differences in the results with
the Euclidean case. We apply equivariant bifurcation theory to the study of
spatially periodic solutions on a given lattice of D also called H-planforms in
reference with the "planforms" introduced for pattern formation in Euclidean
space. We consider in details the case of the regular octagonal lattice and
give a complete descriptions of all H-planforms bifurcating in this case. For
radial solutions (in geodesic polar coordinates), we present a result of
existence for stationary localized radial solutions, which we have adapted from
techniques on the Euclidean plane. Finally, we show that unlike the Euclidean
case, the Swift-Hohenberg equation in the hyperbolic plane undergoes a Hopf
bifurcation to traveling waves which are invariant along horocycles of D and
periodic in the "transverse" direction. We highlight our theoretical results
with a selection of numerical simulations.Comment: Dedicated to Klaus Kirchg\"assne
Renormalizing a BRST-invariant composite operator of mass dimension 2 in Yang-Mills theory
We discuss the renormalization of a BRST and anti-BRST invariant composite
operator of mass dimension 2 in Yang-Mills theory with the general BRST and
anti-BRST invariant gauge fixing term of the Lorentz type. The interest of this
study stems from a recent claim that the non-vanishing vacuum condensate of the
composite operator in question can be an origin of mass gap and quark
confinement in any manifestly covariant gauge, as proposed by one of the
authors. First, we obtain the renormalization group flow of the Yang-Mills
theory. Next, we show the multiplicative renormalizability of the composite
operator and that the BRST and anti-BRST invariance of the bare composite
operator is preserved under the renormalization. Third, we perform the operator
product expansion of the gluon and ghost propagators and obtain the Wilson
coefficient corresponding to the vacuum condensate of mass dimension 2.
Finally, we discuss the connection of this work with the previous works and
argue the physical implications of the obtained results.Comment: 49 pages, 35 eps-files, A number of typographic errors are corrected.
A paragraph is added in the beginning of section 5.3. Two equations (7.1) and
(7.2) are added. A version to be published in Phys. Rev.
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