120 research outputs found
Anomalies and Schwinger terms in NCG field theory models
We study the quantization of chiral fermions coupled to generalized Dirac
operators arising in NCG Yang-Mills theory. The cocycles describing chiral
symmetry breaking are calculated. In particular, we introduce a generalized
locality principle for the cocycles. Local cocycles are by definition
expressions which can be written as generalized traces of operator commutators.
In the case of pseudodifferential operators, these traces lead in fact to
integrals of ordinary local de Rham forms. As an application of the general
ideas we discuss the case of noncommutative tori. We also develop a gerbe
theoretic approach to the chiral anomaly in hamiltonian quantization of NCG
field theory.Comment: 30 page
Non-commutative geometry and the standard model vacuum
The space of Dirac operators for the Connes-Chamseddine spectral action for
the standard model of particle physics coupled to gravity is studied. The model
is extended by including right-handed neutrino states, and the S0-reality axiom
is not assumed. The possibility of allowing more general fluctuations than the
inner fluctuations of the vacuum is proposed. The maximal case of all possible
fluctuations is studied by considering the equations of motion for the vacuum.
Whilst there are interesting non-trivial vacua with Majorana-like mass terms
for the leptons, the conclusion is that the equations are too restrictive to
allow solutions with the standard model mass matrix.Comment: 21 pages. v2: some comments improve
Quantum line bundles on noncommutative sphere
Noncommutative (NC) sphere is introduced as a quotient of the enveloping
algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we
introduce projective modules which are analogues of line bundles on the usual
sphere (we call them quantum line bundles) and define a multiplicative
structure in their family. Also, we compute a pairing between certain quantum
line bundles and finite dimensional representations of the NC sphere in the
spirit of the NC index theorem. A new approach to constructing the differential
calculus on a NC sphere is suggested. The approach makes use of the projective
modules in question and gives rise to a NC de Rham complex being a deformation
of the classical one.Comment: LaTeX file, 15 pp, no figures. Some clarifying remarks are added at
the beginning of section 2 and into section
Star Product and Invariant Integration for Lie type Noncommutative Spacetimes
We present a star product for noncommutative spaces of Lie type, including
the so called ``canonical'' case by introducing a central generator, which is
compatible with translations and admits a simple, manageable definition of an
invariant integral. A quasi-cyclicity property for the latter is shown to hold,
which reduces to exact cyclicity when the adjoint representation of the
underlying Lie algebra is traceless. Several explicit examples illuminate the
formalism, dealing with kappa-Minkowski spacetime and the Heisenberg algebra
(``canonical'' noncommutative 2-plane).Comment: 21 page
Twisting all the way: from Classical Mechanics to Quantum Fields
We discuss the effects that a noncommutative geometry induced by a Drinfeld
twist has on physical theories. We systematically deform all products and
symmetries of the theory. We discuss noncommutative classical mechanics, in
particular its deformed Poisson bracket and hence time evolution and
symmetries. The twisting is then extended to classical fields, and then to the
main interest of this work: quantum fields. This leads to a geometric
formulation of quantization on noncommutative spacetime, i.e. we establish a
noncommutative correspondence principle from *-Poisson brackets to
*-commutators. In particular commutation relations among creation and
annihilation operators are deduced.Comment: 32 pages. Added references and details in the introduction and in
Section
Anomalies in noncommutative gauge theories, Seiberg-Witten transformation and Ramond-Ramond couplings
We propose an exact expression for the unintegrated form of the star gauge
invariant axial anomaly in an arbitrary even dimensional gauge theory. The
proposal is based on the inverse Seiberg-Witten map and identities related to
it, obtained earlier by comparing Ramond-Ramond couplings in different
decsriptions. The integrated anomalies are expressed in terms of a simplified
version of the Elliott formula involving the noncommutative Chern character.
These anomalies, under the Seiberg-Witten transformation, reduce to the
ordinary axial anomalies. Compatibility with existing results of anomalies in
noncommutative theories is established.Comment: 16 pages. LaTe
Voros product and the Pauli principle at low energies
Using the Voros star product, we investigate the status of the two particle
correlation function to study the possible extent to which the previously
proposed violation of the Pauli principle may impact at low energies. The
results show interesting features which are not present in the computations
made using the Moyal star product.Comment: 5 pages LateX, minor correction
Entropy of the Randall-Sundrum black brane world to all orders in the Planck length
We study the effects, to all orders in the Planck length from a generalized
uncertainty principle (GUP), on the statistical entropy of massive scalar bulk
fields in the Randall-Sundrum black brane world. We show that the
Bekenstein-Hawking area law is not preserved, and contains small corrections
terms proportional to the black hole inverse area.Comment: 19 pages, 1 figure. (v2): section 4 improve
Star Product Geometries
We consider noncommutative geometries obtained from a triangular Drinfeld
twist. This allows to construct and study a wide class of noncommutative
manifolds and their deformed Lie algebras of infinitesimal diffeomorphisms.
This way symmetry principles can be implemented. We review two main examples
[15]-[18]: a) general covariance in noncommutative spacetime. This leads to a
noncommutative gravity theory. b) Symplectomorphims of the algebra of
observables associated to a noncommutative configuration space. This leads to a
geometric formulation of quantization on noncommutative spacetime, i.e., we
establish a noncommutative correspondence principle from *-Poisson brackets to
*-commutators.
New results concerning noncommutative gravity include the Cartan structural
equations for the torsion and curvature tensors, and the associated Bianchi
identities. Concerning scalar field theories the deformed algebra of classical
and quantum observables has been understood in terms of a twist within the
algebra.Comment: 27 pages. Based on the talk presented at the conference "Geometry and
Operators Theory," Ancona (Italy), September 200
Conformal Anomalies in Noncommutative Gauge Theories
We calculate conformal anomalies in noncommutative gauge theories by using
the path integral method (Fujikawa's method). Along with the axial anomalies
and chiral gauge anomalies, conformal anomalies take the form of the
straightforward Moyal deformation in the corresponding conformal anomalies in
ordinary gauge theories. However, the Moyal star product leads to the
difference in the coefficient of the conformal anomalies between noncommutative
gauge theories and ordinary gauge theories. The (Callan-Symanzik)
functions which are evaluated from the coefficient of the conformal anomalies
coincide with the result of perturbative analysis.Comment: 17 pages, Latex, no figures, minor corrections and references added;
to appear in Phys. Rev.
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