Instantons and Unitarily Inequivalent Quantum Vacua
| Název práce v češtině: | Instantóny a unitárni neekvivalentní kvantová vakua |
|---|---|
| Název v anglickém jazyce: | Instantons and Unitarily Inequivalent Quantum Vacua |
| Klíčová slova: | Instantony, unitárni neekvivalentní reprezentace, vakua, kanonické komutční relace. |
| Klíčová slova anglicky: | instantons, unitarily inequivalent representations, vacuum, canonical commutation relations. |
| Akademický rok vypsání: | 2009/2010 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Ústav částicové a jaderné fyziky (32-UCJF) |
| Vedoucí / školitel: | prof. Alfredo Iorio, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 17.09.2010 |
| Datum zadání: | 17.09.2010 |
| Datum a čas obhajoby: | 30.01.2012 00:00 |
| Datum odevzdání elektronické podoby: | 08.12.2011 |
| Datum odevzdání tištěné podoby: | 08.12.2011 |
| Datum proběhlé obhajoby: | 30.01.2012 |
| Oponenti: | RNDr. Jiří Novotný, CSc. |
| Zásady pro vypracování |
| 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. |
| Seznam odborné literatury |
| [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. |