SU(n) and Quantum SU(n) Symmetries in Physical Systems [Slides]
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Presence of SU(n) or other Lie group symmetry in a physical system is its powerful, usually underutilized property. In many cases it allows for finding analytical solutions to nonlinear differential equations describing this system. Power of the method is presented on diversified examples from mathematical physics: Lie-group symmetries in finding solutions of generalized, multidimensional theory of gravity; analytical Dirac–equation solutions for description of conducting polymers; stability of qubit states in quantum computers; spatial defects in condensed matter; reconstruction of 3D object from its 2D tomographic image; significant improvement of numerical solutions stability for Euler equations. The next question after obtaining such Lie group symmetric solution is: does a generalized solution with appropriate quantum group symmetry exists for the given physical system, and if yes what is the physical meaning of the deformation parameter q introduced by such solution. In many cases it can be identified. Any SU(n) solution is by its nature singular, assuming a perfect symmetry of the physical system discussed. Such solution gives a powerful insight to theoretical physics, yet the assumption may be too demanding for experimental applications. Deformation parameter q from a quantum group symmetry allows for a continuum of solutions, more applicable to experiments.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- DOE Contract Number:
- 89233218CNA000001
- OSTI ID:
- 1813827
- Report Number(s):
- LA-UR-21-28124
- Country of Publication:
- United States
- Language:
- English
Similar Records
q-quaternions and q-deformed su(2) instantons
Quantum-mechanical aspects of SU(3) Skyrme model in collective-coordinate quantization
Covariant q-differential operators and unitary highest weight representations for U{sub q}su{sub n,n}
Journal Article
·
Mon Oct 15 00:00:00 EDT 2007
· Journal of Mathematical Physics
·
OSTI ID:21013730
Quantum-mechanical aspects of SU(3) Skyrme model in collective-coordinate quantization
Journal Article
·
Wed Jun 15 00:00:00 EDT 1988
· Phys. Rev. D; (United States)
·
OSTI ID:6933369
Covariant q-differential operators and unitary highest weight representations for U{sub q}su{sub n,n}
Journal Article
·
Wed Jun 01 00:00:00 EDT 2005
· Journal of Mathematical Physics
·
OSTI ID:20699200