Twisting all the way: from Classical Mechanics to Quantum Fields

Abstract

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 spacetime, i.e. we establish a noncommutative correspondence principle from *-Poisson brackets to *-commutators. In particular commutation relations among creation and annihilation operators are deduced.

32 pages. Added references and details in the introduction and in Section 5

References in corpus (4)

• A Gravity Theory on Noncommutative Spaces
• On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
• Ultraviolet Finiteness of the averaged Hamiltonian on the noncommutative Minkowski space
• Noncommutative Gravity and the *-Lie algebra of diffeomorphisms

Cited by in corpus (8)

• Twisted Statistics in kappa-Minkowski Spacetime
• Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
• Covariant particle statistics and intertwiners of the kappa-deformed Poincare algebra
• Dynamical symmetries in noncommutative theories
• Duality and Braiding in Twisted Quantum Field Theory
• Hopf Algebra Symmetry and String Theory
• f-oscillators deformation for Moyal algebras
• The Structure of Spacetime and Noncommutative Geometry