## Abstract

Certain commutation relations among the current density operators in quantum field theories define an infinite-dimensional Lie algebra. The original current algebra of Gell-Mann described weak and electromagnetic currents of the strongly interacting particles (hadrons), leading to the Adler-Weisberger formula and other important physical results. This helped inspire mathematical and quantum-theoretic developments such as the Sugawara model, light cone currents, Virasoro algebra, the mathematical theory of affine Kac-Moody algebras, and nonrelativistic current algebra in quantum and statistical physics. Lie algebras of local currents may be the infinitesimal representations of loop groups, local current groups or gauge groups, diffeomorphism groups, and their semidirect products or other extensions. Broadly construed, current algebra thus leads directly into the representation theory of infinite-dimensional groups and algebras. Applications have ranged across conformally invariant field theory, vertex operator algebras, exactly solvable lattice and continuum models in statistical physics, exotic particle statistics and q-commutation relations, hydrodynamics and quantized vortex motion. This brief survey describes but a few highlights.

Original language | English (US) |
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Title of host publication | Encyclopedia of Mathematical Physics |

Subtitle of host publication | Five-Volume Set |

Publisher | Elsevier Inc. |

Pages | 674-679 |

Number of pages | 6 |

ISBN (Electronic) | 9780125126601 |

ISBN (Print) | 9780125126663 |

DOIs | |

State | Published - Jan 1 2004 |

## All Science Journal Classification (ASJC) codes

- Medicine (miscellaneous)