Date of Award
Physics, Particles (Nuclear physics), Field theory (Physics), Phase transformations (Statistical physics), Quantum theory
In this paper, recent developments leading to a new formulation of the Nambu Jona-Lasinio (NJL) model for vacuum phase transitions (VPTs) which accounts for the divergence present in the original model, as well as generalizing it to multiple flavors of leptons, will be discussed. Originally the NJL model was conceived from a comparison between particle physics and the Bardeen Cooper Schrieffer (BCS) Theory of Superconductivity. Nambu and Jona-Lasinio used the component of Cooper pairs to model the behavior of a pair of massless fermions which condense in a vacuum via a VPT to form a massive fermion. However, Nambu and Jona-Lasinio found that their theory contained a divergent integral in the expression for the vacuum energy. They resolved this by introducing an ambiguous cutoff which prevented the acquisition of quantitative results. Using a new regularization renormalization method proposed by Ni's colleague and former student, Yang, Ni disposed of this cutoff and allowed for the NJL model to produce quantitative results. However, discrepancies in the final vacuum energy density, as well as the lack of generalization from this theory to multiple flavors of leptons indicated that more research was necessary to propose a complete NJL theory. New research conducted by Ni and his collaborators (including this author) generalizes the NJL model by taking the vacuum energy as a sum over all of the multiple flavors of leptons. This same approach of using the vacuum energy has been taken to applying the NJL model to quarks. Computational solutions to the mass ratio equations proposed by the NJL model have not yet been obtained. These computational results shall be used to confirm the validity of the proposed theoretical framework.
Harter, Grant A., "Implications of the Nambu Jona Lasinio Model with a New Regularization Renormalization Method" (2017). University Honors Theses. Paper 402.