[Show abstract][Hide abstract] ABSTRACT: Deformation quantization is a formal deformation of the algebra of smooth
functions on some manifold. In the classical setting, the Poisson bracket
serves as an initial conditions, while the associativity allows to proceed to
higher orders. Some applications to string theory require deformation in the
direction of a quasi-Poisson bracket (that does not satisfy the Jacobi
identity). This initial conditions is incompatible with associativity, it is
quite unclear which restrictions can be imposed on the deformation. We show
that for any quasi-Poisson bracket the deformation quantization exists and is
essentially unique if one requires (weak) hermiticity and the Weyl condition.
We also propose an iterative procedure that allows to compute the star product
up to any desired order.
Journal of High Energy Physics 06/2015; 2015(9). DOI:10.1007/JHEP09(2015)103 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We investigate whether inclusion of dimension six terms in the Standard Model
lagrangean may cause the unification of the coupling constants at a scale
comprised between 10^14 and 10^17 GeV. Particular choice of the dimension 6
couplings is motivated by the spectral action. Given the theoretical and
phenomenological constraints, as well as recent data on the Higgs mass, we find
that the unification is indeed possible, with a lower unification scale
slightly favoured.
International Journal of Modern Physics A 10/2014; 30(07). DOI:10.1142/S0217751X15500335 · 1.70 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We discuss the propagation of bosons (scalars, gauge fields and gravitons) at high energy in the context of the spectral action. Using heat kernel techniques, we find that in the high-momentum limit the quadratic part of the action does not contain positive powers of the derivatives. We interpret this as the fact that the two-point Green functions vanish for nearby points, where the proximity scale is given by the inverse of the cutoff. (C) 2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
Physics Letters B 12/2013; 731. DOI:10.1016/j.physletb.2014.02.053 · 6.13 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We provide a holographic description of two-dimensional dilaton gravity with
Anti-de Sitter boundary conditions. We find that the asymptotic symmetry
algebra consists of a single copy of the Virasoro algebra with non-vanishing
central charge and point out difficulties with the standard canonical
treatment. We generalize our results to higher spin theories and thus provide
the first examples of two-dimensional higher spin gravity with holographic
description. For spin-3 gravity we find that the asymptotic symmetry algebra is
a single copy of the W_3-algebra.
Physical Review D 11/2013; 89(4). DOI:10.1103/PhysRevD.89.044001 · 4.64 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We consider gated graphene nanoribbons subject to Berry-Mondragon boundary
conditions in the presence of weak impurities. Using field--theoretical
methods, we calculate the density of charge carriers (and, thus, the quantum
capacitance) as well as the optical and DC conductivities at zero temperature.
We discuss in detail their dependence on the gate (chemical) potential, and
reveal a non-linear behaviour induced by the quantization of the transversal
momentum.
[Show abstract][Hide abstract] ABSTRACT: Poisson sigma models are a very rich class of two-dimensional theories that
includes, in particular, all 2D dilaton gravities. By using the Hamiltonian
reduction method, we show that a Poisson sigma model (with a sufficiently
well-behaving Poisson tensor) on a finite cylinder is equivalent to a
noncommutative quantum mechanics for the boundary data.
[Show abstract][Hide abstract] ABSTRACT: We propose Lobachevsky boundary conditions that lead to asymptotically H^2xR
solutions. As an example we check their consistency in conformal Chern-Simons
gravity. The canonical charges are quadratic in the fields, but nonetheless
integrable, conserved and finite. The asymptotic symmetry algebra consists of
one copy of the Virasoro algebra with central charge c=24k, where k is the
Chern-Simons level, and an affine u(1). We find also regular non-perturbative
states and show that none of them corresponds to black hole solutions. We
attempt to calculate the one-loop partition function, find a remarkable
separation between bulk and boundary modes, but conclude that the one-loop
partition function is ill-defined due to an infinite degeneracy. We comment on
the most likely resolution of this degeneracy.
Journal of High Energy Physics 12/2012; 2013(6). DOI:10.1007/JHEP06(2013)015 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute the Casimir energy for a free scalar field on the spaces where is two-dimensional deformed two-sphere.
Modern Physics Letters A 05/2012; 10(09). DOI:10.1142/S0217732395000806 · 1.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study magneto--optical properties of monolayer graphene by means of
quantum field theory methods in the framework of the Dirac model. We reveal a
good agreement between the Dirac model and a recent experiment on giant Faraday
rotation in cyclotron resonance. We also predict other regimes when the effects
are well pronounced. The general dependence of the Faraday rotation and
absorption on various parameters of samples is revealed both for suspended and
epitaxial graphene.
[Show abstract][Hide abstract] ABSTRACT: The principal object in noncommutatve geometry is the spectral triple
consisting of an algebra A, a Hilbert space H, and a Dirac operator D. Field
theories are incorporated in this approach by the spectral action principle,
that sets the field theory action to Tr f(D^2/\Lambda^2), where f is a real
function such that the trace exists, and \Lambda is a cutoff scale. In the
low-energy (weak-field) limit the spectral action reproduces reasonably well
the known physics including the standard model. However, not much is known
about the spectral action beyond the low-energy approximation. In this paper,
after an extensive introduction to spectral triples and spectral actions, we
study various expansions of the spectral actions (exemplified by the heat
kernel). We derive the convergence criteria. For a commutative spectral triple,
we compute the heat kernel on the torus up the second order in gauge connection
and consider limiting cases.
Journal of Physics A Mathematical and Theoretical 01/2012; 45(37). DOI:10.1088/1751-8113/45/37/374020 · 1.58 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: It has been proposed that the Poincaré and some other symmetries of noncommutative field theories should be twisted. Here we extend this idea to gauge transformations and find that twisted gauge symmetries close for arbitrary gauge group. We also analyse twisted-invariant actions in noncommutative theories.
Modern Physics Letters A 11/2011; 21(16). DOI:10.1142/S0217732306020755 · 1.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We compute a Chern–Simons term induced by the fermions on noncommutative torus interacting with two U(1) gauge fields. For rational noncommutativity θ∝P/Q we find a new mixed term in the action which involves only those fields which are (2π)/Q periodic, like the fields in a crystal with Q2 nodes.
Modern Physics Letters A 11/2011; 22(17). DOI:10.1142/S0217732307023596 · 1.20 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: This is a short non-technical introduction to applications of the Quantum
Field Theory methods to graphene. We derive the Dirac model from the tight
binding model and describe calculations of the polarization operator
(conductivity). Later on, we use this quantity to describe the Quantum Hall
Effect, light absorption by graphene, the Faraday effect, and the Casimir
interaction.
International Journal of Modern Physics A 11/2011; 27(15). DOI:10.1142/S0217751X1260007X · 1.70 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The spectral action for a non-compact commutative spectral triple is computed
covariantly in a gauge perturbation up to order 2 in full generality. In the
ultraviolet regime, $p\to\infty$, the action decays as $1/p^4$ in any even
dimension.
[Show abstract][Hide abstract] ABSTRACT: In a $U(1)_{\star}$-noncommutative (NC) gauge field theory we extend the
Seiberg-Witten (SW) map to include the (gauge-invariance-violating) external
current and formulate - to the first order in the NC parameter -
gauge-covariant classical field equations. We find solutions to these equations
in the vacuum and in an external magnetic field, when the 4-current is a static
electric charge of a finite size $a$, restricted from below by the elementary
length. We impose extra boundary conditions, which we use to rule out all
singularities, $1/r$ included, from the solutions. The static charge proves to
be a magnetic dipole, with its magnetic moment being inversely proportional to
its size $a$. The external magnetic field modifies the long-range Coulomb field
and some electromagnetic form-factors. We also analyze the ambiguity in the SW
map and show that at least to the order studied here it is equivalent to the
ambiguity of adding a homogeneous solution to the current-conservation
equation.
[Show abstract][Hide abstract] ABSTRACT: It has been argued, that in noncommutative field theories sizes of physical
objects cannot be taken smaller than an elementary length related to
noncommutativity parameters. By gauge-covariantly extending field equations of
noncommutative U(1)_*-theory to the presence of external sources, we find
electric and magnetic fields produces by an extended charge. We find that such
a charge, apart from being an ordinary electric monopole, is also a magnetic
dipole. By writing off the existing experimental clearance in the value of the
lepton magnetic moments for the present effect, we get the bound on
noncommutativity at the level of 10^4 TeV.
[Show abstract][Hide abstract] ABSTRACT: The graviton 1-loop partition function is calculated for Euclidean
generalised massive gravity (GMG) using AdS heat kernel techniques. We find
that the results fit perfectly into the AdS/(L)CFT picture. Conformal
Chern-Simons gravity, a singular limit of GMG, leads to an additional
contribution in the 1-loop determinant from the conformal ghost. We show that
this contribution has a nice interpretation on the conformal field theory side
in terms of a semi-classical null vector at level two descending from a primary
with conformal weights (3/2,-1/2).
Journal of High Energy Physics 03/2011; 2011(6). DOI:10.1007/JHEP06(2011)111 · 6.11 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We adopt the Dirac model for quasiparticles in graphene and calculate the
finite temperature Casimir interaction between a suspended graphene layer and a
parallel conducting surface. We find that at high temperature the Casimir
interaction in such system is just one half of that for two ideal conductors
separated by the same distance. In this limit single graphene layer behaves
exactly as a Drude metal. In particular, the contribution of the TE mode is
suppressed, while one of the TM mode saturates the ideal metal value. Behaviour
of the Casimir interaction for intermediate temperatures and separations
accessible for an experiment is studied in some detail. We also find an
interesting interplay between two fundamental constants of graphene physics:
the fine structure constant and the Fermi velocity.
[Show abstract][Hide abstract] ABSTRACT: We give a nontechnical introduction to the problem of non-uniqueness of star
products and describe a covariant resolution of this problem. Some implications
(e.g., for noncommutative gravity) and further prospects are discussed.
[Show abstract][Hide abstract] ABSTRACT: This Chapter contains definitions of main spectral functions, lists their properties, and methods of computation. The material
includes the Riemann zeta-function, the zeta-function of selfadjoint elliptic second order differential operators (both positive
and semidefinite), relations between the zeta-function residues and the heat kernel coefficients. Among less standard issues,
a brief description of the spectral density of operators, relation between its large eigenvalue behavior and heat kernel asymptotic
expansions is included to fill in existing gaps in textbooks. Determinants of differential operators are introduced by using
the Ray-Singer formula followed by other regularization schemes. Then the zeta-function and the determinant of a Dirac operator
are introduced. Much space is devoted to variations of determinants generated by transformations of the operators and to spectral
functions associated to transformations of so called chiral operators. This material later serves as a basis for calculations
of quantum anomalies. The index theorem, which is elaborated in many monographs, here is explained rather briefly to express
a merit of the Atiyah-Singer theory and set some definitions.