Twisting all the way: From classical mechanics to quantum fields

Journal Article · Tue Jan 15 04:00:00 EST 2008 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.77.025037· OSTI ID:21038976

Aschieri, Paolo ^[1]; Lizzi, Fedele; Vitale, Patrizia ^[2]

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1. Centro Studi e Ricerche 'Enrico Fermi' Compendio Viminale, 00184 Rome (Italy)
2. Dipartimento di Scienze Fisiche, Universita di Napoli Federico II and INFN, Sezione di Napoli Monte S. Angelo, Via Cintia, 80126 Naples (Italy)

We discuss the effects that a noncommutative geometry induced by a Drinfeld twist has on physical theories. We systematically deform all products and symmetries of the theory. We discuss noncommutative classical mechanics, in particular its deformed Poisson bracket and hence time evolution and symmetries. The twisting is then extended to classical fields, and then to the main interest of this work: quantum fields. This leads to a geometric formulation of quantization on noncommutative space-time, i.e., we establish a noncommutative correspondence principle from *-Poisson brackets to * commutators. In particular commutation relations among creation and annihilation operators are deduced.

• OSTI ID: 21038976
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 2 Vol. 77; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANNIHILATION OPERATORS
CLASSICAL MECHANICS
COMMUTATION RELATIONS
GEOMETRY
HAMILTONIANS
QUANTIZATION
QUANTUM FIELD THEORY
SPACE-TIME
SYMMETRY