938 research outputs found
Groupoid Quantization of Loop Spaces
We review the various contexts in which quantized 2-plectic manifolds are
expected to appear within closed string theory and M-theory. We then discuss
how the quantization of a 2-plectic manifold can be reduced to ordinary
quantization of its loop space, which is a symplectic manifold. We demonstrate
how the latter can be quantized using groupoids. After reviewing the necessary
background, we present the groupoid quantization of the loop space of R^3 in
some detail.Comment: 19 pages, Proceedings of the Corfu Summer Institute 2011 - School and
Workshops on Elementary Particle Physics and Gravity, September 4-18, 2011,
Corfu, Greec
Branes, Quantization and Fuzzy Spheres
We propose generalized quantization axioms for Nambu-Poisson manifolds, which
allow for a geometric interpretation of n-Lie algebras and their enveloping
algebras. We illustrate these axioms by describing extensions of
Berezin-Toeplitz quantization to produce various examples of quantum spaces of
relevance to the dynamics of M-branes, such as fuzzy spheres in diverse
dimensions. We briefly describe preliminary steps towards making the notion of
quantized 2-plectic manifolds rigorous by extending the groupoid approach to
quantization of symplectic manifolds.Comment: 18 pages; Based on Review Talk at the Workshop on "Noncommutative
Field Theory and Gravity", Corfu Summer Institute on Elementary Particles and
Physics, September 8-12, 2010, Corfu, Greece; to be published in Proceedings
of Scienc
Groupoids, Loop Spaces and Quantization of 2-Plectic Manifolds
We describe the quantization of 2-plectic manifolds as they arise in the
context of the quantum geometry of M-branes and non-geometric flux
compactifications of closed string theory. We review the groupoid approach to
quantizing Poisson manifolds in detail, and then extend it to the loop spaces
of 2-plectic manifolds, which are naturally symplectic manifolds. In
particular, we discuss the groupoid quantization of the loop spaces of R^3, T^3
and S^3, and derive some interesting implications which match physical
expectations from string theory and M-theory.Comment: 71 pages, v2: references adde
The 2-Hilbert Space of a Prequantum Bundle Gerbe
We construct a prequantum 2-Hilbert space for any line bundle gerbe whose
Dixmier-Douady class is torsion. Analogously to usual prequantisation, this
2-Hilbert space has the category of sections of the line bundle gerbe as its
underlying 2-vector space. These sections are obtained as certain morphism
categories in Waldorf's version of the 2-category of line bundle gerbes. We
show that these morphism categories carry a monoidal structure under which they
are semisimple and abelian. We introduce a dual functor on the sections, which
yields a closed structure on the morphisms between bundle gerbes and turns the
category of sections into a 2-Hilbert space. We discuss how these 2-Hilbert
spaces fit various expectations from higher prequantisation. We then extend the
transgression functor to the full 2-category of bundle gerbes and demonstrate
its compatibility with the additional structures introduced. We discuss various
aspects of Kostant-Souriau prequantisation in this setting, including its
dimensional reduction to ordinary prequantisation.Comment: 97 pages; v2: minor changes; Final version to be published in Reviews
in Mathematical Physic
Ab-initio quantum transport simulation of self-heating in single-layer 2-D materials
Through advanced quantum mechanical simulations combining electron and phonon
transport from first-principles self-heating effects are investigated in n-type
transistors with a single-layer MoS2, WS2, and black phosphorus as channel
materials. The selected 2-D crystals all exhibit different phonon-limited
mobility values, as well as electron and phonon properties, which has a direct
influence on the increase of their lattice temperature and on the power
dissipated inside their channel as a function of the applied gate voltage and
electrical current magnitude. This computational study reveals (i) that
self-heating plays a much more important role in 2-D materials than in Si
nanowires, (ii) that it could severely limit the performance of 2-D devices at
high current densities, and (iii) that black phosphorus appears less sensitive
to this phenomenon than transition metal dichalcogenides
Cheeger-Simons differential characters with compact support and Pontryagin duality
By adapting the Cheeger-Simons approach to differential cohomology, we
establish a notion of differential cohomology with compact support. We show
that it is functorial with respect to open embeddings and that it fits into a
natural diagram of exact sequences which compare it to compactly supported
singular cohomology and differential forms with compact support, in full
analogy to ordinary differential cohomology. We prove an excision theorem for
differential cohomology using a suitable relative version. Furthermore, we use
our model to give an independent proof of Pontryagin duality for differential
cohomology recovering a result of [Harvey, Lawson, Zweck - Amer. J. Math. 125
(2003) 791]: On any oriented manifold, ordinary differential cohomology is
isomorphic to the smooth Pontryagin dual of compactly supported differential
cohomology. For manifolds of finite-type, a similar result is obtained
interchanging ordinary with compactly supported differential cohomology.Comment: 33 pages, no figures - v3: Final version to be published in
Communications in Analysis and Geometr
Finite-volume corrections to the leading-order hadronic contribution to
We present preliminary results of a 2+1-flavor study of finite-volume effects
in the lattice QCD computation of the leading-order hadronic contribution to
the muon anomalous magnetic moment. We also present methods for obtaining
directly the invariant hadronic polarization function, , and the
Adler function at all discrete lattice values of , including .
Results are obtained with HEX-smeared clover fermions.Comment: 7 pages, 2 figures, Contribution to the Proceedings of the 32nd
International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June
2014, Columbia University, New York, NY, US
Continuum EoS for QCD with Nf=2+1 flavors
We report on a continuum extrapolated result [arXiv:1309.5258] for the
equation of state (EoS) of QCD with dynamical quark flavors. In this
study, all systematics are controlled, quark masses are set to their physical
values, and the continuum limit is taken using at least three lattice spacings
corresponding to temporal extents up to . A Symanzik improved gauge and
stout-link improved staggered fermion action is used. Our results are available
online [ancillary file to arXiv:1309.5258].Comment: Conference proceedings, 7 pages, 4 figures. Talk presented at 31st
International Symposium on Lattice Field Theory (LATTICE 2013), July 29 -
August 3, 2013, Mainz, German
Differential cohomology and locally covariant quantum field theory
We study differential cohomology on categories of globally hyperbolic Lorentzian manifolds. The Lorentzian metric allows us to define a natural transformation whose kernel generalizes Maxwell's equations and fits into a restriction of the fundamental exact sequences of differential cohomology. We consider smooth Pontryagin duals of differential cohomology groups, which are subgroups of the character groups. We prove that these groups fit into smooth duals of the fundamental exact sequences of differential cohomology and equip them with a natural presymplectic structure derived from a generalized Maxwell Lagrangian. The resulting presymplectic Abelian groups are quantized using the CCR-functor, which yields a covariant functor from our categories of globally hyperbolic Lorentzian manifolds to the category of C*-algebras. We prove that this functor satisfies the causality and time-slice axioms of locally covariant quantum field theory, but that it violates the locality axiom. We show that this violation is precisely due to the fact that our functor has topological subfunctors describing the Pontryagin duals of certain singular cohomology groups. As a byproduct, we develop a Fr\'echet-Lie group structure on differential cohomology groups
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