2,194 research outputs found
Topological Order and the Quantum Spin Hall Effect
The quantum spin Hall (QSH) phase is a time reversal invariant electronic
state with a bulk electronic band gap that supports the transport of charge and
spin in gapless edge states. We show that this phase is associated with a novel
topological invariant, which distinguishes it from an ordinary insulator.
The classification, which is defined for time reversal invariant
Hamiltonians, is analogous to the Chern number classification of the quantum
Hall effect. We establish the order of the QSH phase in the two band
model of graphene and propose a generalization of the formalism applicable to
multi band and interacting systems.Comment: 4 pages RevTeX. Added reference, minor correction
A path integral derivation of -genus
The formula for the Hirzebruch -genus of complex manifolds is a
consequence of the Hirzebruch-Riemann-Roch formula. The classical index
formulae for Todd genus, Euler number, and Signature correspond to the case
when the complex variable 0, -1, and 1 respectively. Here we give a {\it
direct} derivation of this nice formula based on supersymmetric quantum
mechanics.Comment: 5 page
The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
We study various improved staggered quark Dirac operators on quenched gluon
backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We
find a clear separation of the spectrum into would-be zero modes and others.
The number of would-be zero modes depends on the topological charge as expected
from the Index Theorem, and their chirality expectation value is large
(approximately 0.7). The remaining modes have low chirality and show clear
signs of clustering into quartets and approaching the random matrix theory
predictions for all topological charge sectors. We conclude that improvement of
the fermionic and gauge actions moves the staggered quarks closer to the
continuum limit where they respond correctly to QCD topology.Comment: 4 pages, 3 figure
New Implications of Lorentz Violation
In this proceedings, I summarize two recently discovered theoretical
implications that Lorentz violation has on physical systems. First, I discuss
new models for neutrino oscillations in which relatively simple combinations of
Lorentz-violating parameters can mimic the major features of the current
neutrino oscillation data. Second, I will present results on Yang-Mills
instantons in Lorentz-violating background fields. An explicit solution is
presented for unit winding number in SU(2).Comment: 8 pages, proceedings for 2003 Coral Gables Conference, Ft.
Lauderdale, F
Multi-Periodic Coherent States and the WKB-Exactness
We construct the path integral formula in terms of ``multi-periodic''
coherent state as an extension of the Nielsen-Rohrlich formula for spin. We
make an exact calculation of the formula and show that, when a parameter
corresponding to the magnitude of spin becomes large, the leading order term of
the expansion coincides with the exact result. We also give an explicit
correspondence between the trace formula in the multi-periodic coherent state
and the one in the ``generalized'' coherent state.Comment: 28 pages, late
Multi-Periodic Coherent States and the WKB-Exactness II ``Non-compact Case and Classical theories Revisited''
We show that the WKB approximation gives the exact result in the trace
formula of ``'', which is the non-compact counterpart of , in terms
of the ``multi-periodic'' coherent state. We revisit the symplectic 2-forms on
and and, especially, construct that on with the unitary
form. We also revisit the exact calculation of the classical patition functions
of them.Comment: LaTeX, 29 page
Instanton Moduli and Topological Soliton Dynamics
It has been proposed by Atiyah and Manton that the dynamics of Skyrmions may
be approximated by motion on a finite dimensional manifold obtained from the
moduli space of SU(2) Yang-Mills instantons. Motivated by this work we describe
how similar results exist for other soliton and instanton systems. We describe
in detail two examples for the approximation of the infinite dimensional
dynamics of sine-Gordon solitons by finite dimensional dynamics on a manifold
obtained from instanton moduli. In the first example we use the moduli space of
CP1 instantons and in the second example we use the moduli space of SU(2)
Yang-Mills instantons. The metric and potential functions on these manifolds
are constructed and the resulting dynamics is compared with the explicit exact
soliton solutions of the sine-Gordon theory.Comment: uuencoded tex file, 27 pages including 4 figures, requires phyzzx
macro. DAMTP 94-5
A Newman-Penrose Calculator for Instanton Metrics
We present a Maple11+GRTensorII based symbolic calculator for instanton
metrics using Newman-Penrose formalism. Gravitational instantons are exact
solutions of Einstein's vacuum field equations with Euclidean signature. The
Newman-Penrose formalism, which supplies a toolbox for studying the exact
solutions of Einstein's field equations, was adopted to the instanton case and
our code translates it for the computational use.Comment: 13 pages. Matches the published version. The web page of the codes is
changed as https://github.com/tbirkandan/NPInstanto
Consistent 3D Quantum Gravity on Lens Spaces
We study non-perturbative quantization of 3d gravity with positive
cosmological constant (de Sitter space being the prototype vacuum solution,
whose Euclideanization of course gives the three sphere) on the background
topology of lens space, which is a three spheres modulo a discrete group.
Instead of the strategy followed by a recent work \cite{Castro:2011xb}, which
compares results in the second and first order formulations of gravity, we
concentrate on the later solely. We note, as a striking feature, that the
quantization, that relies heavily on the axiomatics of topological quantum
field theory (TQFT) can only be consistently carried by augmenting the
conventional theory by an additional topological term coupled through a
dimensionless parameter. More importantly the introduction of this additional
parameter renders the theory finite.Comment: New section and references added. Accepted in Phys. Rev. D for
publicatio
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