Ray extensions of the regular representation of noncompact non-Abelian Lie groups are examined as generalizations of the Cartesian coordinate representation of ordinary quantum mechanics to the case of generalized non-Cartesian coordinates and generalized noncommuting momenta. (The momenta are in fact the generators of the representation, and so they satisfy the Lie algebra of the group.) The concept of configuration ray representation is introduced within this new kinematic formalism as subrepresentations of the regular representation which are embossed with the “relativity theory” of a given system. The main features of the mathematical formalism leading to these representations in configuration spacetime are discussed, and their importance for non-Abelian quantum kinematics and dynamics is emphasized. Two miscellaneous examples on the calculus of phase functions for configuration ray representations are given.
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Krause, J. Configuration ray representations in non-Abelian quantum kinematics and dynamics. Int J Theor Phys 33, 1617–1637 (1994). https://doi.org/10.1007/BF00672687
- Field Theory
- Elementary Particle
- Quantum Field Theory
- Quantum Mechanic
- Mathematical Formalism