Klein factors and Fermi-Bose equivalence

• Published in: Journal of the Korean Physical Society Vol. 68; no. 11; pp. 1272 - 1286
• Main Author: Lee, Taejin
• Format: Journal Article
• Language: English
• Published: Seoul The Korean Physical Society 01-06-2016; 한국물리학회
• Subjects: Mathematical and Computational Physics; Particle and Nuclear Physics; Physics; Physics and Astronomy; Theoretical; 물리학; Klein factor; Gross-Neveu model; Thirring model; Fermi-Bose equivalence; Boundary state
• ISSN: 0374-4884; 1976-8524
• DOI: 10.3938/jkps.68.1272

Generalizing the kink operator of the Heisenberg spin 1/2 model, we construct a set of Klein factors explicitly such that (1+1)-dimensional fermion theories with an arbitrary number of species are mapped onto the corresponding boson theories with the same number of species and vice versa. The actions for the resultant theories do not possess a nontrivial Klein factor. With this set of Klein factors, we are also able to map the simple boundary states, such as the Neumann and the Dirichlet boundary states, of the fermion (boson) theory onto those of the boson (fermion) theory. Applications of the Fermi-Bose equivalence with the constructed Klein factors to well-known (1+1)-dimensional theories have been discussed.