Contact person: Gyula Fodor,
Quantum symmetries
Gabriella Böhm, Kornél Szlachányi, Péter Vecsernyés
Our research subject lies in the intersection point of mathematics and physics. We investigate questions motivated by algebraic quantum field theory – like reconstruction of symmetries and of the field algebra, classification of phases -with mathematical methods and rigor. In the forefront of our interest are algebraic structures that are capable to describe superselection symmetries, like e.g. (weak) Hopf algebras and Hopf algebroids. We apply category theoretic methods at the first place to study their properties and realization in low dimensional quantum field theories.
Integrable systems
László Fehér
Exactly solvable (“integrable”) models play important role in almost all branches of physics. Behind solvability there usually lurks a corresponding symmetry, which also underlies the singular mathematical beauty of the integrable systems. László Fehér has been working on this area for a long time: after studies of Kepler-like systems his research focused on models of conformal field theory and their symmetry algebras, then on soliton equations and dynamical Yang-Baxter structures. In the last few years one-dimensional many-body systems of Calogero-Moser-Sutherland and Ruijsenaars-Schneider type occupied his attention. These models appear in several fields of physics and possess close ties to interesting areas of mathematics. The main goal of on-going research is to develop a unified group-theoretic understanding of these models and their duality relations, principally by applying methods of Hamiltonian reduction.
Strong gravitational fields
László Szabados
The most accurate theory of gravitational phenomena is Einstein's general relativity. Its field equations are strongly non-linear partial differential equations, which, for weak gravitational fields, can be approximated by the well known linear wave equations. However, for strong gravitational fields the non-linearities play important role, which yield unexpected, even qualitatively new phenomena. Therefore, the use of non-perturbative, exact mathematical methods (rather than the perturbative, approximate methods) is inevitable. Thus our investigations are concentrated on the conceptual issues and the internal, mathematical structure of the theory (such as the structure of the phase space, the canonical and Hamiltonian structure, the conserved quantities, boundary conditions etc); as well as on the properties of the special spacetime configurations describing strong gravitational fields (e.g. the global and asymptotic properties of the spacetime, its causal structure, the singularities, the horizons and their geometric and thermal properties, radiative modes, the energy-momentum and angular momentum carried away by strong gravitational waves, etc).
Gravitational radiation from compact binaries
Balázs Mikóczi
Our research objectives are aimed at the description of the spinning sources (spin-orbit and spin-spin contributions) and the gravitational waves from eccentric inspiraling compact binaries using the post-Newtonian formalism. We have accomplished a parameter estimation for the eccentric GW (including pericenter precession) signals in frequency domain. Our main result is that the source localization precision improves significantly for supermassive black hole binaries due to eccentricity.
Localized solutions in field theories
Gyula Fodor and Péter Forgács
Gravitational attraction forms a spherically symmetric star-like object from a scalar field, which is called oscillaton in the literature. Oscillatons are extremely long living and stable, but their mass decreases very slowly because of scalar field radiation. We have shown that the oscillaton radiation rate is exponentially small in terms of their mass. Consequently, oscillatons do not fade away, and they are possible dark matter candidates. Scalar fields such as axions, or the inflaton field may form localized structures and enhance structure formation.
