Hidden symmetries and nonlinear (super)algebras

Abstract

Hidden symmetries, described by higher order in momenta integrals of motion that generate nonlinear algebras, are explored at the level of classical and quantum mechanics in a variety of physical systems related to conformal and superconformal invariance.

PhD thesis, Univ. de Santiago de Chile, 2020 (supervisor: Mikhail Plyushchay); 161 pages; Based on arXiv:1707.07357, arXiv:1711.00616, arXiv:1809.08527, arXiv:1902.00538, arXiv:1912.11752 and arXiv:2002.04341

References in corpus (18)

• Toward an AdS/cold atoms correspondence: a geometric realization of the Schroedinger symmetry
• Gravity duals for non-relativistic CFTs
• Self-isospectrality, special supersymmetry, and their effect on the band structure
• On the spectrum of nonrelativistic AdS/CFT
• Hidden Symmetries of Dynamics in Classical and Quantum Physics
• Hidden supersymmetry in quantum bosonic systems
• The H=xp model revisited and the Riemann zeros
• Analogue Cosmological Particle Creation: Quantum Correlations in Expanding Bose Einstein Condensates
• Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
• Effect of scalings and translations on the supersymmetric quantum mechanical structure of soliton systems
• Isoperiodic classical systems and their quantum counterparts
• On integral and differential representations of Jordan chains and the confluent supersymmetry algorithm
• Soliton defects in one-gap periodic system and exotic supersymmetry
• Hamiltonian reduction and supersymmetric mechanics with Dirac monopole
• Klein four-group and Darboux duality in conformal mechanics
• Curved Witten-Dijkgraaf-Verlinde-Verlinde equation and $\mathcal{N}=4$ mechanics
• Quantum Mechanics and Hidden Superconformal Symmetry
• Lectures on exceptional orthogonal polynomials and rational solutions to Painlevé equations