Instantons and Unitarily Inequivalent Quantum Vacua
| Thesis title in Czech: | Instantóny a unitárni neekvivalentní kvantová vakua |
|---|---|
| Thesis title in English: | Instantons and Unitarily Inequivalent Quantum Vacua |
| Key words: | Instantony, unitárni neekvivalentní reprezentace, vakua, kanonické komutční relace. |
| English key words: | instantons, unitarily inequivalent representations, vacuum, canonical commutation relations. |
| Academic year of topic announcement: | 2009/2010 |
| Thesis type: | diploma thesis |
| Thesis language: | angličtina |
| Department: | Institute of Particle and Nuclear Physics (32-UCJF) |
| Supervisor: | prof. Alfredo Iorio, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 17.09.2010 |
| Date of assignment: | 17.09.2010 |
| Date and time of defence: | 30.01.2012 00:00 |
| Date of electronic submission: | 08.12.2011 |
| Date of submission of printed version: | 08.12.2011 |
| Date of proceeded defence: | 30.01.2012 |
| Opponents: | RNDr. Jiří Novotný, CSc. |
| Guidelines |
| It is well known that certain Yang-Mills gauge theories admit solutions of the equations of motion descending from the Bianchi identities. These solutions are called instantons for their property of being localized in time rather than space and are of clear topological nature, the instanton number being connected to the Pontryagin index. The importance of these structure in gauge theories is paramount, see, e.g., [1] and [2].
When instantons are present the vacua of the quantum field theory in point are topologically disconnected (they belong to different homotopy classes) and only a quantum tunneling process allows to move from one vacuum to an inequivalent one. On the other hand, on very general grounds any quantum field possesses an infinity of vacua which are not unitarily equivalent, see, e.g., [3], and it appears that this is an instance independent on the topological structure of the theory. The candidate will investigate the relationship among these two inequivalences, the topological one and the unitary one in the most suitable context for this link (if any) to be visible. |
| References |
| [1] R. Rajaraman, Solitons and Instantons, North Holland, 1989.
[2] A.Iorio, Advanced Concepts of Symmetry, Lecture Notes of the Course LS NJSF129 (Summer Term 2009), in preparation. [3] H.Umezawa, Advanced Field Theory, AIP Publish., 1993 and R.F.Streater, A.S.Weightman, PCT, Spin and Statistics, and All that, Benjamin, 1964. [4] A.Iorio, G.Vitiello, Quantum Groups and von Neumann Theorem,Mod. Phys. Lett. B 8 (1994) 269 and Quantum Dissipation and Quantum Groups, Ann. Phys. 241 (1995) 496. |