Algebraic and Topological Approaches for Atomic Nuclei and Related Systems

The primary goal of the current proposal is to understand the structure of atomic nuclei and its evolution by means of algebraic and topological approaches, and to employ the algebraic approach to Quark Gluon Plasma.

The algebraic approach can offer considerable insight into complex dynamics by classifying underlying symmetries, derive selection rules, calculate many observables and predict many properties in nuclei in a tractable manner.

The topological approach can offer new insight into the phases of matter of the nucleus.The different objectives of the proposal are ""Monte-Carlo code for interacting fermions and bosons"": we will develop a new open-access code for numerical calculations of fermions and bosons using the Monte-Carlo method. ""Mapping the Shell Model (SM) onto the Interacting Boson Model (IBM)"": we suggest a novel mapping approach based on effective field theory (EFT) in which we write the SM and IBM in EFT and investigate the structure of Lie algebras of the Feynman integrals, a method used for calculating multiloop radiative corrections, and use them to map the SM onto the IBM. ""Topological phases of atomic nuclei"": we will investigate the occurrence of Berry phases in semi-magic mid shell nuclei and find classes of topological orders in atomic nuclei by examining known and new analogies with condensed matter physics. ""Algebraic approach to QGP"": we will introduce a new algebraic model for QGP based on boson-fermion effective degrees of freedom with similar principles as the interacting boson-fermion model for atomic nuclei, in order to calculate the phase diagram in a tractable framework with insight to the symmetries of the diagram.

The above objectives can spur more studies by the researcher, the supervisor and other experimental and theoretical research groups in different fields of physics and thus the researcher asks for their funding.