Weyl and Conformal Symmetries
| Thesis title in Czech: | Weylova a konformní symetrie |
|---|---|
| Thesis title in English: | Weyl and Conformal Symmetries |
| Key words: | Klasická Weylova symetrie Liouvillova teorie |
| English key words: | Classical Weyl Symmetry Liouville theory |
| Academic year of topic announcement: | 2015/2016 |
| Thesis type: | Bachelor's 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: | 02.05.2019 |
| Date of assignment: | 02.05.2019 |
| Confirmed by Study dept. on: | 14.05.2019 |
| Date and time of defence: | 25.06.2019 09:00 |
| Date of electronic submission: | 16.05.2019 |
| Date of submission of printed version: | 16.05.2019 |
| Date of proceeded defence: | 25.06.2019 |
| Opponents: | Mgr. Martin Scholtz, Ph.D. |
| Guidelines |
| The relationship among conformal invariance in flat spacetimes and Weyl and diffeomorphic invariance in curved spacetimes has been established in [1] for classical field theories with arbitrary spin and dimension. Among other results (such as the identification of when and why in flat space scale invariance implies conformal invariance) the procedure invented in that work systematically produces the improvement terms of the energy-momentum tensor necessary for conformal symmetry and it is based on the conversion of a spatiotemporal symmetry (scale invariance) to an internal symmetry (Weyl invariance). The difference and similarities between spatiotemporal and inner symmetries is an old and fascinating problem, e.g., it is at the core of the discovery of supersymmetry in the early 1970s and of the on-going vigorous research activity on the gravity-gauge theory formulations of fundamental as well as applied aspects of particle physics.
The case of two dimensions, one space-one time, has been seen there to be special already in [1] and more recently in [2]. In particular in [2] it is shown that for the important case of the Liouville scalar theory Weyl and diffeomorphic invariance (on the ``curved side'') and scale invariance (on the ``flat side'') may not be equivalent. The candidate will clarify the latter point for the Liouville theory and, possibly, will consider other two dimensional theories. |
| References |
| [1] A.Iorio, L.O'Raifeartaigh, I.Sachs, C.Wiesendanger, Weyl-Gauging and Conformal Invariance, Nucl. Phys. B 495 (1997) 433.
[2] R.Jackiw, Theor. Math. Phys. 148 (2006) 941. [3] A.Iorio, Advanced Concepts of Symmetry, Lecture Notes of the Course LS NJSF129 (Summer Term 2009), in preparation (see also at http://www-ucjf.troja.mff.cuni.cz/~iorio the drafts A. Iorio, From the Coleman-Mandula Theorem to Supersymmetric Yang-Mills Theories, Lecture Notes (2001-2003), and A. Iorio, Relaxing Symmetries in Field Theory: from Noether theorem to noncommutativity and the challenges to Lorentz invariance, Lecture Notes (2005-2008)) |