My Journey Into the Physics of David Finkelstein

Abstract

David Finkelstein was a co-pioneer of the use of topology and solitons in theoretical physics. The author reflects on the great impact Finkelstein had on his research throughout his career. The author provides an application of one of Finkelsteins idea pertaining to the fusion of quantum theory with relativity by utilizing techniques from Loop Quantum Gravity.My first encounter with the ideas of David Finkelstein was as a graduate student at Brown. It was the mid 90s and the role of topological defects, such as magnetic monopoles and cosmic strings, in cosmology were quite topical. Even after the measurement of the first doppler peak by the COBE/DMR experiment ruled out cosmic strings as a candidate for seeding the large scale structure in the universe, topological defects had other important roles to play in the early universe. But from a pedagogical point of view the study of topological defects was a great subject for a Ph.D student. Topological defects provided an arena that integrates the role topology in quantum field theory, the relation between symmetry breaking patterns and the vacuum manifold as well as the connection between topological charge and homotopy groups.One day I was walking down the hall when one of my professors Antal Jevicki asked me what I was working on. I proudly told him that I was working on the interaction between monopoles and domain walls. It was a new way of solving the monopole problem in cosmology. As the early universe expanded an cooled to temperatures below the GUT phase transition, monopoles are predicted to form as a result of breaking the GUT group G, G = SU (5) to the standard model subgroup H, H = SU (3) × SU (2) × U(1). In some GUT theories domain walls will be produced. It was postulated by Dvali and Vaschapati that the domain walls could sweep up the monopoles. Monopoles are classified by a non-trivial homotopy group, which determines the topological charge of the monopole π 2 (G/H ) = Z.