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Theoretical Physics & Cosmology
Group Members
·Emilio Elizalde
(CSIC)
*New!* DMC2009
·Sergei
D. Odintsov (ICREA)
·Pedro J. Silva (I3P,
CSIC)
·Sante Carloni (PostDoc
Beatriu de Pinós)
·Diego Sáez Gómez (PhD Student)
·Antonio Jesús López Revelles (PhD
Student)
·Gloria
Garcia Cuadrado (PhD Student)
·Roger Oliva
(PhD Student)
Research Topics
I. Quantum Gravity
& Fundamental Theories
· Quantum
fields in curved space-time
· Black
hole structure
· String,
brane, M-theory inspired models
· Uses
of the renormalization group
· AdS/CFT
correspondence and brane worlds
II. Vacuum Structure
& Casimir Effect
· Quantum
vacuum fluctuations, also dynamical effects
· External
fields, finite temperature QFT, chemical potentials
· Strong
magnetic field effects in cosmology
· Zeta
regularization and effective actions in QG
III. Cosmology & Dark Energy
· Early
time Universe, inflation
· Dark
energy models
· Phantom
cosmology, future singularities
· Braneworld
cosmology and modified gravity
IV. Zeta functions
& Applications
· Zeta
functions of yDOs
· Heat-kernel
techniques
· Zeta
function regularization, Hadamard regularization
· Determinants,
the multiplicative anomaly (or deffect)
Some
books & review papers
· Riemann
and Related Zeta Functions
· Zeta-Function
Regularization of Sums Over Known Spectrum
· Zeta
Function Regularization Generalized
· The
Casimir Effect in Flat Spacetime
· Heat-Kernel
and Zeta-Function Regularization Techniques in the Theory of Quantum Fields on
Hyperbolic Space
· Quantum
Properties of Extended Objects
· Finite-Temperature
Effects in Quantum Field Theory
· String
Theory at Non-Zero Temperature
· Covariant
Effective in 2D Gravity
· A: Calculation
of Heat-Kernel Coefficients
These lectures
were addressed to non-specialists willing to learn some basic facts,
approaches, tools and observational evidence which conform modern cosmology.
The aim is also to try to complement the many excellent treatises that exists
on the subject (an exhaustive treatment being in any case impossible for lack
of time, in the lectures, and of space here), instead of trying to cover
everything in a telegraphic way. We start by recalling in the introduction a
couple of philosophical questions that have always upset inquiring minds. We
then present some original mathematical approaches to investigate a number of
basic questions, as the comparison of two point distributions (each point
corresponding to a galaxy or galaxy cluster), the use of non-standard statistics
in the analysis of possible non-Gaussianities, and the use of zeta
regularization in the study of the contributions of vacuum energy effects at
the cosmological scale. And we also summarize a number of important issues
which are both undoubtedly beautiful (from the physical viewpoint) and useful
in present-day observational cosmology. To finish, the reader should be warned
that, for the reasons already given and lack of space, some fundamental issues,
as inflation, quantum gravity and string theoretical fundamental approaches to
cosmology will not be dealt with here. A minimal treatment of any of them would
consume more pages than the ones at disposal and, again, a number of excellent
treatments of these subjects are available.
Zeta-function regularization is a powerful method in perturbation theory.
This book is meant as a guide for the student of this subject. Everything is
explained in detail, in particular the mathematical difficulties and tricky
points, and several applications are given to show how the procedure works in
practice (e.g. Casimir effect, gravity
and string theory, high-temperature phase transition, topological symmetry
breaking). The formulas some of which
are new can be used for accurate numerical calculations. The book is to be
considered as a basic introduction and a collection of exercises for those who
want to apply this regularization procedure in practice.
One of the
aims of this book is to explain in a basic manner the seemingly difficult
issues of mathematical structure using
some specific examples as a guide. In each of the cases considered, a
comprehensible physical problem is approached, to which the corresponding
mathematical scheme is applied, its usefulness being duly demonstrated. The
authors try to fill the gap that always exists between the physics of quantum
field theories and the mathematical methods best suited for its formulation,
which are increasingly demanding on the mathematical ability of the physicist.
Papers,
Projects & Links
· CSIC
· IEEC
· MIT
· CERN
· DURSI
· Ministerio de Educación y Ciencia
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