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Seminars:
Group and Algebraic
Methods and Hamiltonian Systems
(Monday,
04/24)
Ademir Eugênio de Santana (Instituto de Física, Universidade de Brasília,
Brazil), in collaboration
with J. A. Cardeal (1), M. de Montigny
(2), F. C. Khanna (2,3), T. M. Rocha Filho (4) and A. E. Santana (4) ((1) UEFS, (2) Univ. Alberta,
Canada, (3) TRIUMF, Canada, (4) UnB)
Gauge
Symmetries in Fokker-Planck Dynamics
Abstract: We use a covariant Galilean formalism,
based in the light-cone of the (4+1) Minkowski
space, to introduce a U(1)-gauge invariant Lagrangian
written in Riemannian manifold, say R, such that, with a proper choice for
the gauge condition, the Fokker-Planck equation is derived. The metric (and
so the connection) in R is defined with the diffusion tensor, which is in
turn investigated with Lie group methods applied to differential equations.
Our main results include the extension of the formalism for non-abelian gauge groups, in particular considering the su(2)
symmetry, and some analytical expressions derived for the drift and
diffusion terms.
Anatol Odzijewicz (University in Bialystok, Poland)
Banach
Lie-Poisson Spaces and Quantization
Abstract: The predual Banach space $\g_*$ of Banach
Lie algebra $\g$ fulfilling the condition $\ad^*_x\g_*\subset\g_*$, for
$x\in\g$, has canonically defined Poisson bracket, i.e. it is Banach Lie-Poisson space. In particular the predual of $W^*$-algebra form the subcategory in the
category of Banach Lie-Poisson spaces. We will
present a method of quantization related to the above structures. Examples
illustrating this method will be also presented. References 1.
A
. Odzijewicz, T. Ratiu,
Banach Lie-Poisson spaces and reduction, Comm.
Math. Ph. 243(1) 1-54 2003, http://arxiv.org/abs/math.SG/0210207 2.
A
. Odzijewicz, Coherent States and
Geometric Quantization, Commun. Math. Phys. 150
385-413 1992.
Ricardo Antonio
Mosna (IMECC -
UNICAMP, Brazil),
in collaboration with Marcos B. Jardim
Nonsingular
Solutions of Hitchin's Equations for Noncompact Gauge Groups
Abstract: Let G be a real form of the complex Lie
group SL(
2,C
). We consider a general ansatz for solving the
2-dimensional Hitchin's equations associated to
G, which arise as dimensional reduction of the 4-dimensional anti-self-dual
Yang-Mills equation, with remarkable integrability
properties. For G=SO(2,1), the resulting field
equations are shown to reduce to either the Liouville,
elliptic sinh-Gordon or elliptic sine-Gordon
equations. As opposed to the compact case, given by G=SU(2),
the field equations associated with the group SO(2,1) are shown to have
nonsingular solutions with nondiverging actions.
We conclude by discussing some particular solutions, defined on R^2, S^2
and T^2, that come out of this ansatz.
Integrable Systems and Gauge Theories
(Tuesday, 04/25)
Andre Fonseca (Departamento de Matemática,
Faculdade de Engenharia Industrial - São Bernardo do Campo, Brazil)
Solitons
Bifurcations in Presence of Surface Tension
Abstract: In this work we apply a non pertubative approach to analyse
solitons bifurcation in presence of surface
tension, which is a reformulation of standard methods based on the
reversibility proprieties of the system. The hypothesis are non restrictive
and the results can be extended to a much wider variety of systems. The
usual idea of tracking intersections of unstable manifolds with some
invariant set is again used, but reversibility plays important role
establishing in a geometrical point of view some kind of symmetry which, in
a classical way, is unknown or non existent. Using a computer program we
determine soliton solutions and also their
bifurcations in the space of parameters giving a picture of the structural
distribution to phase and amplitude shifts phenomena.
Dmitri
Gitman (Departamento de Física
Nuclear - Universidade de São Paulo, Brazil), in
collaboration with Igor Tyutin
Symmetries
and Constraint Structure of General Gauge Theory
Abstract: The aim of the present work is to relate
symmetries and constraint structure of a general gauge theory. To this end,
we analyze a symmetry equation in a special orthogonal constraint basis and
derive, thus, a general structure of symmetries of a general gauge theory.
We construct a general expression for the gauge charge as a decomposition in the orthogonal constraint basis.
These results allow us to identify physical functions defined as commuting
with first-class constraints in the Hamiltonian formulation and defined as
gauge invariant functions in the Lagrangian
formulation. In particular, we prove the famous Dirac conjecture.
J.P.
(Hans) Goedbloed (FOM - Institute for Plasma
Physics `Rijnhuizen', Netherlands)
Magnetohydrodynamic Spectral
Theory of Laboratory and Astrophysical Plasmas
Abstract: Spectral theory of linear waves and
instabilities of magnetohydrodynamics (MHD)
describes an enormous variety of plasma dynamics in the laboratory and in
the Universe. The reason is the abundance of plasmas: more than 90% of
visible matter in the Universe is plasma, whereas dark matter may have a
substantial plasma component as well. The theoretical basis comes from the
fact that MHD spectral theory can be cast in a completely analogous form to
that of quantum mechanics: the MHD force operator is self-adjoint in the Hilbert space of plasma displacement
vectors [1]. Nevertheless, MHD spectral theory is still very incomplete at
present. In particular, group theoretical investigation of symmetry
properties has hardly been undertaken. Considering the central role plasmas
are to play in a future model of the Universe, this calls
for a major mathematical effort.
Probably,
the complicating factor is the omni-presence of
large background flows, which are often super‘sonic’
(surpass one the three criticalMHDspeeds),
implying that the standard picture developed for static plasmas breaks
down: Plasma dynamics is to be described by non-selfadjoint
operators and the necessary background states are frequently transonic. The
mathematical problems associated with these two features are enormous, but
recently found monotonicity properties of the
complex spectrum and singularities in the equilibrium flows provide
confidence that a meaningful structure will eventually emerge.
This
will be illustrated with recent results on the spectrum of accretion disks
[2] and new instabilities driven by transonic transitions of the flow that
involve singular trans-slow Alfv´en modes with a
continuous spectrum [3]. Except that these instabilities appear to have
exciting physical properties (facilitating accretion flows and jet
formation), they have quite interesting geometrical properties as well
since they ‘live’ on the curved two-dimensional surfaces spanned by the
plasma velocity and magnetic fields.
[1]
J.P. Goedbloed and S. Poedts,
Principles of Magnetohydrodynamics ( Cambridge
University
Press, 2004); ISBN 0521626072.
[2]
R. Keppens, F. Casse,
and J.P. Goedbloed, ‘Waves and instabilities in
accretion disks: Magnetohydrodynamic spectroscopic
analysis’, Astrophys. J. 569, L121–L126 (2002).
[3]
J.P. Goedbloed, A.J.C. Beli¨en,
B. van der Holst, and
R. Keppens, ‘Unstable continuous spectra of
transonic axisymmetric plasmas’, Phys. Plasmas
11, 28–54 (2004).
Quantum Field Theory
(Tuesday, 04/25, and Wednesday, 04/26)
Antonio
José Accioly (LAFEX-CBPF
and Instituto
de Física Teórica -
UNESP, Brazil),
in collaboration with Marco Dias (IFT-UNESP)
Boson-Boson
Bound States in Higher-Derivative Electromagnetism Augmented by a Chern-Simons Term
Abstract: A rough comparison between the number of
boson-boson bound states in the electromagnetic theories of Podolsky-Chern-Simons and Maxwell-Chern-Simons, is drawn appealling to
Bargmann's condition. This approximate
calculation shows that the higher-derivative terms are responsible for a
remarkable increase in the number of bound states.
Aram
Saharian (Department
of Physics, Yerevan State
University , Armenia
and Depto. de Física, Universidade Federal da Paraíba, Brazil)
Generalized
Abel-Plana Formula as a Renormalization Tool in Quantum Field Theory with
Boundaries
Abstract: Applications of the generalized
Abel-Plana formula are described for the evaluation of the vacuum
expectation values of the energy-momentum tensor in quantum field theory
with boundaries. Various boundary geometries are considered.
Eugênio R. Bezerra de Mello (Departamento
de Física, Universidade
Federal da Paraíba, Brazil)
Vacuum
Polarization Effects in Higher Dimensional Global Monopole Spacetime
Abstract: We analyse the
vacuum polarization effects associated with a massless
scalar field in a higher dimensional global monopole spacetime,
admitting a non-vanishing curvature coupling between the field and the
geometry. Specifically we calculate the renormalized vacuum expectation
value of the square of the field. In order to develop this analysis we
construct the general Euclidean Green function. We also investigate the
general structure of the renormalized vacuum expectation value of the
energy-momentum tensor.
Fabio Braghin
(Instituto de Física - Universidade de São Paulo,
Brazil)
Free
Parameters in Quantum Theories: an Analysis with the Variational
Approximation
Abstract: The usual renormalization procedure for
the gaussian variational
appoach for the $lambda phi^4$ model is reanalysed. Privileged values of the free parameters
(mass and coupling constant) and the stability of the approximation is also
investigated differently from done before. The minimization of the renormalized
energy density with respect to the free parameters (bare or renormalized
ones) is done and several results can be different from the same procedure
for the regularized theory. Some parameters are placed in the complex
plane, in particular the physical mass. The behavior of the expected value
of the field as an order parameter is investigated all along the work.
Jorge
Gamboa (Universidad de Santiago de Chile, Chile)
Lorentz
Invariance Violation and Neutrino Physics
Abstract: We propose that a tiny violation of
Lorentz and $CPT$ symmetry may be enough to explain the solar and
atmospheric neutrino puzzle as well as the LSND anomaly. We present a toy
model to support such an assertion. In this scenario neutrino oscillation
can arise even for massless neutrinos (or
neutrinos degenerate in mass).
Jorge
M. C. Malbouisson (Instituto de Física, Universidade Federal da
Bahia, Brazil),
in collaboration with F.C. Khanna, A.P.C. Malbouisson and A.E. Santana
Compactified Large-$N$
Gross-Neveu Model at Finite Temperature
Abstract: We consider the $N$-components
$D$-dimensional Euclidean massive Gross-Neveu
model, confined in a ($D-1$)-dimensional cubic box (edge $L$), at finite
temperature ($T$). Using $\zeta$-function analytical regularization, we
determine the large-$N$ effective coupling constant ($g$) as a function of
$L$, $T$ and the fixed coupling constant ($\lambda$), for the cases $D=2,3,4$. In all cases, we find that $g$ tends to 0 when
$L$ goes to 0 or $T$ goes to infinity, corresponding to an "asymptotic
freedom" type of behavior. For finite $L$ and $T$, distinct behaviors
appear depending on the value of $\lambda$. For small $\lambda$ only
``asymptotic freedom" occurs. However, for $\lambda$ greater than a
``critical" value ($\lambda_c$), starting
from small values of $L$ (and low enough temperatures), a divergence of $g$
appears as $L$ approaches a value $L_{c}(\lambda)$
which lies in a finite interval for $\lambda\geq
\lambda_c$. Such behavior suggests that the
system becomes spatially confined in a box of size $L_{c}(\lambda)$
if $\lambda$ is large enough. If the temperature is raised, the divergence desappears at a temperature $T_d$
which can be seen as a deconfining temperature.
Taking the fermionic mass as the constituent
quark mass, the confining length and the deconfining
temperature obtained are comparable with the estimated values for hadrons.
Márcio José Martins (Universidade
Federal de São Carlos, Brazil)
Integrable Lattice
Models based on Superalgebras
Abstract: In this talk we will discuss
trigonometric vertex models associated with solutions of the Yang-Baxter
equation which are invariant relative to q-deformed superalgebras.
The associated R-matrices are presented in terms of the standard Weyl basis and novel solvable lattice models not
predicted before are pointed out. This approach allowed us to formulate the
quantum inverse scattering method for a large class of integrable
models invariant by superalgebras from a unified
point of view.
Rubens
Luis Pinto Gurgel do Amaral
(Instituto de Física, Universidade Federal Fluminense,
Brazil),
in collaboration with L. V. Belvedere and K. D. Rothe
Bosonization within Thermofield Dynamics Approach
Abstract: We consider the two-dimensional free massless scalar field within the thermofield
dynamics approach. The corresponding two-point function exhibits two
infrared singularities, one similar to the zero temperature case and a new
temperature dependent one, implying an indefinite-metric Hilbert space on
which the massless scalar thermofield
acts. We show that one can nevertheless define positive definite Wick
ordered exponentials of a massless scalar thermofield, provided we ssociate
with them a conserved charge (superselection
rule). We also consider the two-dimensional Fermi thermofield
and compute the corresponding two-point function. We use the Wick-ordered
exponentials of the free massless scalar thermofield as building blocks for the operator thermofield bosonization of
the free massless Fermi field and show that the
Fermi thermofield satisfies the correct
statistics. We further compute the fermion thermofield current by a point-splitting limit and
verify that the current satisfies the usual bosonization
correspondence. We further illustrate the use of thermofield
bosonization by solving the massless
Thirring model at finite temperature.
Silvio Paolo Sorella (Universidade Estadual do Rio de
Janeiro, Brazil),
in collaboration with
D. Dudal, M. Capri, J. Gracey, V. Lemes, R, Sobreiro, and
H. Verschelde
Infrared
behavior of the gluon and ghost propagators in Yang-Mills theories
Abstract: Dimension two gauge condensates and their
role for the infrared behavior of the gluon and ghost propagators in nonabelian gauge theories are reviewed. A few remarks
on the issue of the gauge invariance of these condensates are presented.
Principles of
Quantum Theory
(Thursday, 04/27)
Bert
Schroer (TEO-CBPF,
Brazil)
Holography,
its Bondy-Metzner-Sachs Symmetry Group and
Localization-Entropy
Abstract:
After briefly illustrating the holography (for a wedge region and a double
cone) in case of a free field, I will explain how modular localization
theory generalizes this in the presence of interactions. Here I will freely
use the modular concepts which Jens Mund
introduced in his prior talk on "Modular localization and string-localized
quantum fields". The holographic projections have an easily
recognizable infinite dimensional BMS-like symmetry group which in the case
of double cone holography is actually identical to the classical Bondi-Metzner-Sachs group in the Penrose setting.
Holography is extremely useful to define and calculate localization entropy
which turns out to have a surprising connection to the global heat bath
entropy density of thermal QFT on the lightfront.
Jens
Mund (Departamento
de Física, Universidade
Federal de Juiz de Fora, Brazil),
in collaboration with B. Schroer and J. Yngvason
String-Localized
Quantum Fields and Modular Localization
Abstract: The concept of modular localization
introduced by Brunetti, Guido and Longo, and Schroer, can be used to construct quantum fields. I
shall report on the construction of free fields which are localized in
semi-infinite strings extending to spacelike
infinity. Particular applications are - massless
`infinite spin' particles - Anyons in 2+1
dimensions - string-localized vector potential for photons.
Classical and
Quantum Gravity and Cosmology
(Thursday,
04/27)
Henrique Pereira de Oliveira
(Instituto de Física, Universidade Estadual do Rio de Janeiro, Brazil)
Spectral
Methods in Gravitation and Cosmology
Abstract: General Relativity is a nonlinear field
theory, and for this reason there are few relevant exact solutions of the
field equations. Numerical techniques are possibly the only way of dealing
with the intrinsic nonlinearities of the field equations. Therefore, we intend
to present some interesting applications of the Galerkin
and pseudospectral methods in problems of
Gravitation and Cosmology, where minimum computational effort is usually
sufficient for the knowledge of the basic physical aspects of the system
under consideration.
Ilya Shapiro
(Departamento de Física, Univeridade Federal de
Juiz de Fora, Brazil)
Local
Conformal Symmetry and its Fate at Quantum Level
Abstract: The purpose of this talk is to present a
short review of local conformal symmetry in curved $4d$ space-time.
Furthermore we discuss the conformal anomaly and anomaly-induced effective
actions. Despite the conformal symmetry is always broken at quantum level,
it may be a basis of useful and interesting approximations for
investigating quantum corrections.
Victor de Oliveira Rivelles
(Instituto de Física, Universidade de São Paulo, Brazil)
Noncommutative Gravity
Abstract: We consider a gravity theory where the noncommutative parameter is a covariantly
constant tensor so that it can be coupled to the geometric tensors in a
natural way. We find that the theory is invariant under a restricted class
of volume preserving transformations thus leading to unimodular
gravity. The correction to the Newtonian potential is found. The Moyal product in curved spacetime
is defined by replacing ordinary derivatives by covariant ones and becomes
non-associative.
Strings, Branes and Supersymmetric
Theories
(Friday, 04/28)
Edmundo
Marinho do Monte (Departamento de Física, Universidade Federal da Paraíba, Brazil)
Change of the Bulk's Signature with
Change of the Brane-World's Topology
Abstract: In the present paper we make a brief
review about the immersion problem in physics and prove that if we have
$Y:(M^{n},g)\longrightarrow
(\bar{M}^{D},\bar{g})$, a local isometric embedding, a topology $\tau'_{\eta}$ of $Y(W^{n})$
different of the induced topology $\tau_{\eta}$ of the $Y(W^{n})$, ($W^{n}$ a neighborhood of $p
\in M^{n}$) and the determinants of the metric tensor $g_{ij}$ and $g'_{\mu \nu}$ are
not equal in sign at a point, then there is a change of signature of the
bulk, $(\bar{M}^{D},\bar{g})$.We use the Schwarzschild space-time as a brane-world embedded in the six-dimensional bulk and a
change of topology via Kruskal metric obtaining
in this form a signature change that bulk.
Francesco Toppan (TEO-CBPF, Brazil)
New Results in Supersymmetric
Quantum Mechanics
Abstract: Supersymmetric
quantum mechanics was invented 25 years ago. We present now for the first
time the classification of its irreducible representations. As a byproduct,
new invariant off-shell actions and new non-linear on-shell actions are
presented.
Gerardo Aldazabal
(Instituto Balseiro-C, Bariloche,
Argentina)
Particle Physics from D-Branes at Gepner Points
Abstract: The fact that gauge
interactions are localized on D-branes world
volumes opened new roads to establish a link between Particle Physics and String
theory. Many interesting studies have been performed in this D-brane world scenario, mainly, in the framework of toroidal like compactifications. For instance, we know that D-branes
intersecting at angles or D-branes stuck at orbifold singularities are needed in order to obtain chiral spectra. Also, consistent D-brane
configurations, leading to "closed to Standard Model" models have been found.
We will discuss a generalization of
these toroidal like scenarios to include internal manifolds
described by rational conformal
field theories, in particular by Gepner models.
We will illustrate how these constructions can lead to appealing models,
closed to the Standard Model or some of its extensions.
Henrique
Boschi Filho (Instituto de Física, Universidade Federal do Rio de Janeiro, Brazil), in collaboration with N. R. F. Braga (IF-UFRJ, Brazil)
AdS/CFT
Correspondence and Strong Interactions
Abstract: Inspired in the exact AdS/CFT
duality we consider phenomenological models to describe strong interactions
in terms of strings in a slice of an anti-de Sitter space. The size of the
slice is related to an infrared cutoff of the boundary gauge theory. With
this model we obtain masses of light hadrons and the static quark
anti-quark phenomenological potential.
Ion Vasile Vancea (Departamento
de Física, Universidade Federal Rural do Rio de Janeiro, Brazil)
Thermal D-branes
States from Superstrings in Light-Cone Gauge
Abstract: We present the construction of the
thermal D-brane states in TFD approach in the GS
formulation of the superstring.
Jorge Stephany
(Universidad Simón Bolívar, Venezuela), in collaboration
with N. Hatcher and A. Restuccia
On the Quantization of Massive Superparticles
Abstract: We consider the action of the $D=11$ supermembrane wrapping a compactified
sector of the target space in such a way that a non trivial central charge
in the SUSY algebra is induced. This corresponds to a superparticle
in $D=9$ with additional fermionic terms
associated to the central charges. We perform the covariant quantization of
this system. The resulting multiplet contains
$2^8$ states corresponding to a $KKB$ ultrashort multiplet.
Ricardo Medina (Universidade Federal de Itajubá,
Brazil),
in collaboration with L. A. Barreiro
Higher N-Point Amplitudes in Open
Superstring Theory
Abstract: Massless string
scattering amplitudes are important as a tool to find the low energy
effective lagrangian of the theory. For a long
time it has been believed that these amplitudes can be used to find only
the first (alpha') terms of it, since only 3 and 4-point amplitudes were
possible to be computed in a closed form. We report on the progress done in
recent years, where methods have been found to compute 5 and higher point
amplitudes, for bosons, in a closed form.
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