291 research outputs found
Duality and Braiding in Twisted Quantum Field Theory
We re-examine various issues surrounding the definition of twisted quantum
field theories on flat noncommutative spaces. We propose an interpretation
based on nonlocal commutative field redefinitions which clarifies previously
observed properties such as the formal equivalence of Green's functions in the
noncommutative and commutative theories, causality, and the absence of UV/IR
mixing. We use these fields to define the functional integral formulation of
twisted quantum field theory. We exploit techniques from braided tensor algebra
to argue that the twisted Fock space states of these free fields obey
conventional statistics. We support our claims with a detailed analysis of the
modifications induced in the presence of background magnetic fields, which
induces additional twists by magnetic translation operators and alters the
effective noncommutative geometry seen by the twisted quantum fields. When two
such field theories are dual to one another, we demonstrate that only our
braided physical states are covariant under the duality.Comment: 35 pages; v2: Typos correcte
Noncommutative Quantum Mechanics and Seiberg-Witten Map
In order to overcome ambiguity problem on identification of mathematical
objects in noncommutative theory with physical observables, quantum mechanical
system coupled to the NC U(1) gauge field in the noncommutative space is
reformulated by making use of the unitarized Seiberg-Witten map, and applied to
the Aharonov-Bohm and Hall effects of the NC U(1) gauge field. Retaining terms
only up to linear order in the NC parameter \theta, we find that the AB
topological phase and the Hall conductivity have both the same formulas as
those of the ordinary commutative space with no \theta-dependence.Comment: 7 pages, no figures, uses revtex4; 8 pages, conclusion changed,
Appendix adde
Theory of a Higher Order Phase Transition: Superconducting Transition in BKBO
We describe here the properties expected of a higher (with emphasis on the
order fourth) order phase transition. The order is identified in the sense
first noted by Ehrenfest, namely in terms of the temperature dependence of the
ordered state free energy near the phase boundary. We have derived an equation
for the phase boundary in terms of the discontinuities in thermodynamic
observables, developed a Ginzburg-Landau free energy and studied the
thermodynamic and magnetic properties. We also discuss the current status of
experiments on and other based superconductors,
the expectations for parameters and examine alternative explanations of the
experimental results.Comment: 18 pages, no figure
Noncommutativity and Lorentz Violation in Relativistic Heavy Ion Collisions
The experimental detection of the effects of noncommuting coordinates in
electrodynamic phenomena depends on the magnitude of |\theta B|, where \theta
is the noncommutativity parameter and B a background magnetic field. With the
present upper bound on \theta, given by \theta_{\rm bound} \simeq 1/(10 {\rm
TeV})^2, there was no large enough magnetic field in nature, including those
observed in magnetars, that could give visible effects or, conversely, that
could be used to further improve \theta_{\rm bound}. On the other hand,
recently it has been proposed that intense enough magnetic fields should be
produced at the beginning of relativistic heavy ion collisions. We discuss here
lepton pair production by free photons as one kind of signature of
noncommutativity and Lorentz violation that could occur at RHIC or LHC. This
allows us to obtain a more stringent bound on \theta, given by 10^{-3}
\theta_{\rm bound}, if such "exotic" events do not occur.Comment: Five pages, no figures
Noncommutativity, generalized uncertainty principle and FRW cosmology
We consider the effects of noncommutativity and the generalized uncertainty
principle on the FRW cosmology with a scalar field. We show that, the
cosmological constant problem and removability of initial curvature singularity
find natural solutions in this scenarios.Comment: 8 pages, to appear in IJT
Time-Space Noncommutativity in Gravitational Quantum Well scenario
A novel approach to the analysis of the gravitational well problem from a
second quantised description has been discussed. The second quantised formalism
enables us to study the effect of time space noncommutativity in the
gravitational well scenario which is hitherto unavailable in the literature.
The corresponding first quantized theory reveals a leading order perturbation
term of noncommutative origin. Latest experimental findings are used to
estimate an upper bound on the time--space noncommutative parameter. Our
results are found to be consistent with the order of magnitude estimations of
other NC parameters reported earlier.Comment: 7 pages, revTe
Noncommutative quantum mechanics and Bohm's ontological interpretation
We carry out an investigation into the possibility of developing a Bohmian
interpretation based on the continuous motion of point particles for
noncommutative quantum mechanics. The conditions for such an interpretation to
be consistent are determined, and the implications of its adoption for
noncommutativity are discussed. A Bohmian analysis of the noncommutative
harmonic oscillator is carried out in detail. By studying the particle motion
in the oscillator orbits, we show that small-scale physics can have influence
at large scales, something similar to the IR-UV mixing
A Non-Perturbative Study of Gauge Theory on a Non-Commutative Plane
We perform a non-perturbative study of pure gauge theory in a two dimensional
non-commutative (NC) space. On the lattice, it is equivalent to the twisted
Eguchi-Kawai model, which we simulated at N ranging from 25 to 515. We observe
a clear large-N scaling for the 1- and 2-point function of Wilson loops, as
well as the 2-point function of Polyakov lines. The 2-point functions agree
with a universal wave function renormalization. Based on a Morita equivalence,
the large-N double scaling limit corresponds to the continuum limit of NC gauge
theory, so the observed large-N scaling demonstrates the non-perturbative
renormalizability of this NC field theory. The area law for the Wilson loops
holds at small physical area as in commutative 2d planar gauge theory, but at
large areas we find an oscillating behavior instead. In that regime the phase
of the Wilson loop grows linearly with the area. This agrees with the
Aharonov-Bohm effect in the presence of a constant magnetic field, identified
with the inverse non-commutativity parameter.Comment: 18 pages, 6 figures, final version published in JHE
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