Research Projects at the LTP

Quantum Field Theory
High Energy Physics
General Relativity
Astrophysics
Statistical and Plasma Physics

Quantum Field Theory

One of the jobs of physicists is to study the forces of nature. Electrical forces hold the atoms together to form crystals and other forms of matter, gravity guides the motion of the planets, while the weak and strong forces are responsible for nuclear power and hold the key to understand the origin of the sunlight and the evolution of stars. Quantum Field Theory is the framework for the study of the forces and fields of nature, from a quantum mechanical perspective, at the fundamental level. Its methods are the routine working tools of theoretical high energy physicists.

Quantum Field Theoretical methods have successfully found their way in applications to a variety of problems in such diverse areas as Statistical Mechanics, Condensed Matter Physics, Astrophysics and Cosmology. In these contexts, the theoretical framework has come to be known as Finite Temperature Field Theory or Quantum Statistical Field Theory. Along these lines, the research interests lie on the foundations and applications of what has is now known as the Covariant Formulation of Finite Temperature Field Theory.
While the general principles are well known, the application of Finite Temperature Field Theory methods to systems that exhibit gauge invariance is not free of ambiguities. Even in the simplest theory of this kind, Quantum Electrodynamics at finite temperature, the problems are already apparent. Most, if not, all of them are tied up to the issue of what is the proper way to deal, in the context of Statistical Mechanics, with the unphysical gauge degrees of freedom that must be present in the theory in order to formulate it in covariant way. Several alternatives have been proposed in the literature to deal with this issue. In our own publications we have advocated the use of the Coulomb gauge as the proper one to use in this context, and in our work we have examined some of the consequences and implications of this idea.
( J. F. Nieves )
One of the most successful developments in Theoretical Particle Physics has been the understanding of symmetries in Quantum Field Theory in terms of Lie algebras and groups . Since the formulation of Yang-Mills theories and the impressive agreement of the Standard model with experiment, continuous Lie groups and their algebras have been the guiding path in the study of physical models in grand unified theories, supersymmetry, supergravity and string theory.
In this context, one currrent research project focuses on studying the role that quantum group symmetries could play in quantum field theory. Quantum groups are algebraic structures which were discovered as a realization of symmetries in the theory of integrable models in Statistical Mechanics and Inverse Scattering theory. From the mathematical point of view these algebraic constructions are understood as deformations of Lie algebras with a non-commutative tensor product. One of the main results of this work show that introducing quantum groups in Quantum mechanics and Field Theory introduces a discretization of space according to a non-linear lattice (q-lattice) structure.
( M. R. Ubriaco )

High Energy Physics

High Energy Physics is concerned with the study of the fundamental constituents of matter (the so called elementary particles) and their fundamental interactions. There is a fundamental reason why high energies are needed for research in this area. First, the elementary particles are the smallest building blocks of matter and therefore, in order to study their properties and interactions, it is required to probe distances on the smallest possible scales. According to the principles of quantum mechanics, this in turn requires high energies.

The work in this area is concentrated in the study of the properties and interactions of neutrinos as they propagate through a background of matter under a variety of conditions. Neutrinos are the only particles, among the so called elementary particles, that have only weak interactions with the other ones, and do have neither strong nor electromagnetic interactions. It was thought originally that neutrinos were massless particles. Theoretically, this idea brings a compelling simplicity, which is embodied in the Standard Electroweak Theory. More recently, however, this notion has been challenged, because of the implications that a non-zero neutrino mass can have in the context of several astrophysical and cosmological problems, such as the Solar neutrino problem, the missing dark matter in the universe, the theory of the pripmordial abundance of the light elements (nucleosynthesis) and the dynamics of the supernova explossions. These developments, which are the result of research by hundreds of individuals, have given rise to a new field of physics research, both experimental and theoretical, which might be called Neutrino Astronomy and Neutrino Astrophysics, respectively.
The work carried out at the LTP is concerned with the application of the Quantum Field Theoretic methods to the study of the properties and interactions of neutrinos in general. Of particular interest is the study of their electromagnetic interactions, which is motivated on one hand by issues of principle related to the intrinsic properties of neutrinos with non-zero mass, and because of the potentially important implications and consequences they might have in the astrophysical amd cosmological settings mentioned above.
( J. F. Nieves )

General Relativity

Gravity is the main sculptor of the universe. General relativity, which modifies the classical concepts of space and time, is intended to explain gravitational phenomena. The properties of certain astronomical objects, such as quasars (structures that combine extreme luminosity, e.g. 100 times that of a bright galaxy, with great compactness), pulsars (extremely dense stars that emit electromagnetic pulses with great regularity), imply that there are processes involving gravitational fields so strong that general relativity is needed to interpret the observations. The astonishing dimensions of large-scale structure, structures that in some cases span hundreds of millions of light-years, indicate that the variable curvature employed in general relativity plays an important role in the dynamical evolution of the universe. Most cosmological theories imply that the universe is expanding, with the galaxies receding from one another (as is made plausible by observations of the red shifts of their spectra), and that the universe as it is known originated in a primeval explosion at a date of the order of 20 billions years ago.

According to our experience, that there is one time and three space dimensions, general relativity is formulated in a four dimensional space-time. However, there is nothing that restricts the theory to four dimensions. This explains the proliferation in recent years of higher dimensional theories. The main hypothesis in these theories is that underlying the four-dimensional space-time there is a manifold having a higher dimensionality, whose geometric structure can accommodate all known force fields. Work on this area focuses on a higher dimensional theory of the Kaluza-Klein type which intends the geometrization of the properties of matter. A fundamental task in this area is to isolate effects of higher dimensions that might be tested.

Our work is focused in the physical interpretation of the exact solutions to the combined Einstein-Maxwell equations. Also, we are interested in the study of Einstein's gravitational theory in strong gravitational fields, i.e. near pulsars and black holes.
(E. Esteban).

Astrophysics

The implications of general relativity in astrophysics and cosmology are enormous and far reaching. The research interests of the group in this areas include:

Studies in the formation and stability of ultra-compact objects, as well as the gravitational collapse. In cosmology, the main interest in the problem of inflation of the very early universe, inhomogeneous cosmologies, and the description of the present state of the universe.

The study of alternative gravitational theories. For instance, the so called conformal or Weyl gravity. Exact solutions to Weyl gravity are in agreement at small scales (i.e., our Solar system) with Einsteinian-Newtonian theories, although they differ at larger scales (i.e., at galactic distances). This is because Weyl gravity includes a linear potential which makes a dominant contribution at galactic distances. Preliminary studies of the galactic rotation curves in Weyl gravity fit well (without ad-hoc assumptions) the observed rotation curves. This could have an important implication in modern astronomy and astrophysics: there is no need to postulate the existence of dark matter.
( E. Esteban ).

Statistical and Plasma Physics

The liquid state of condensed matter has only begun to be understood within the last 3 to 4 decades upon the application of the techniques in Statistical Mechanics. Principal experimental support has come from diffraction and scattering probes in liquids, which are getting continually sophisticated with advances in technology. A third ingredient in our understanding of liquids has been the numerical simulations of systems on a computer once again using statistical mechanical principles. The last point is particularly significant from a theoretical perspective since through the simulations a mathematical model can be solved "exactly" on a machine thus providing "checks and balances" on theoretical approximations. The near revolutionary strides in computing technology over the past decade have greately increased our ability to delve into complex liquid systems. A general feature of liquid structure is that for most liquids a good part of structure is determined by geometric packing of hard cores mimicked often in the theoretical models by hard spheres. Scattering experiments show that liquids possess short range order in contrast to long range periodicity in crystal structure.
One interest of this laboratory is the structure and thermodynamics of complex systems such as liquid mixtures, electrolytes both in the bulk and near interfaces involving different geometries, and electrolyte-polyelectrolyte/colloid mixtures using theoretical and numerical methods. An interesting recent theoretical prediction that we have seen for multi-component electrolyte-polyelectrolyte systems is that due to collective effects of the various species an attractive interaction can exist between two similarly charged polyions. This has been confirmed by other research groups. We are presently trying to see if machine simulations lead to the same results. The behaviour of polyelectrolytes and of electrolytes near interfaces has practical implications for a wide variety of biological systems, e.g., DNA, many proteins, and industries, e.g., detergents and soaps, colloids. Classical ionic liquids display a gas-liquid phase transition at low concentration and low temperature. Monte Carlo simulations have now firmly established the phenomenon. We are looking to explore this ionic criticality in two component asymmetric electrolyte systems. When experience has been gained we hope to study the feature in 3 or 4 component electrolyte-macroion solutions.
( L. B. Bhuiyan )
The role of Quantum Groups in two-dimensional lattice models has been the subject of intense research since the early 1970's. These algebraic constructions are solutions of the Yang-Baxter equation for the corresponding lattice models. During the 1980's a better insight into the mathematical formalism of quantum groups was achieved through its understanding in terms of the theory of Hopf algebras. Starting in 1990 a new trend of research began, mostly in the physicist community, with the objective of inquiring about new roles that quantum group theory could play in physics. Since quantum groups have their origin in models relevant to physical phenomena, it is natural to investigate on the effect that quantum group symmetries could have on field of physics other than integrable models.
Along this line, the present project's interest resides in studying the effect of quantum group symmetries on the thermodynamics of quantum systems. For these purposes, the high and low temperature behavior of quantum group invariant hamiltonians are studied. The quantum fields involved are those whose algebra is covariant under quantum group transformations. One of the main conclusions of this work show that quantum group fields exhibit anyonic behavior in two and three spatial dimensions.
(M. R. Ubriaco)

webmaster@ltp.upr.clu.edu
Mon Sep 22 11:00:25 AST 2008