Bulg. J. Phys. vol.33 no.s2 (2006), pp. 26-41


Local Current Algebras: Early Ideas and New Quantum-Theoretical Directions

G.A. Goldin
Departments of Mathematics and Physics, Rutgers University, SERC Bldg., Room 239, Busch Campus, 118 Frelinghuysen Road, Piscataway, NJ 08854, USA
Abstract. Local currents combine the ideas of space-time locality and symmetry by means of an infinite-dimensional Lie algebra of operators. We review some early ideas about relativistic and nonrelativistic local current algebras, and discuss their relation to quantum kinematics. We then summarize three directions of recent research: a model for quantized vortex filaments (with R. Owczarek and D. H. Sharp); a prescription for nonlinear modification of quantum mechanics (with H.-D. Doebner); and local currents for a deformed algebra of quantum mechanics (with S. Sarkar).

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