On second quantization on noncommutative spaces with twisted symmetries

Abstract

By application of the general twist-induced star-deformation procedure we translate second quantization of a system of bosons/fermions on a symmetric spacetime in a non-commutative language. The procedure deforms in a coordinated way the spacetime algebra and its symmetries, the wave-mechanical description of a system of n bosons/fermions, the algebra of creation and annihilation operators and also the commutation relations of the latter with functions of spacetime; our key requirement is the mode-decomposition independence of the quantum field. In a conservative view, the use of noncommutative coordinates can be seen just as a way to better express non-local interactions of a special kind. In a non-conservative one, we obtain a covariant framework for QFT on the corresponding noncommutative spacetime consistent with quantum mechanical axioms and Bose-Fermi statistics. One distinguishing feature is that the field commutation relations remain of the type "field (anti)commutator=a distribution". We illustrate the results by choosing as examples interacting non-relativistic and free relativistic QFT on Moyal space(time)s.

Latex file, 45 pages. I have corrected a small typo present in 3 points of the previous version and in the version published also in JPA (which had occurred via late careless serial replacements, with no consequences on the results of the calculations): ${\beta }^{\ast }={\beta }^{-1}$ has been corrected into ${\beta }^{\ast }=S({\beta }^{-1})$

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Cited by in corpus (21)

• Braided Cartan Calculi and Submanifold Algebras
• Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field
• Field Theory on Curved Noncommutative Spacetimes
• Twisted bialgebroids versus bialgebroids from a Drinfeld twist
• Interpolations between Jordanian Twists Induced by Coboundary Twists
• Effects of Twisted Noncommutativity in Multi-particle Hamiltonians
• On the consequences of twisted Poincare' symmetry upon QFT on Moyal noncommutative spaces
• Twisted submanifolds of R^n
• Twist star products and Morita equivalence
• Multiparticle states in braided lightlike $\kappa$-Minkowski noncommutative QFT
• Noncommutative connections on bimodules and Drinfeld twist deformation
• Braided Field Quantization from Quantum Poincare Covariance
• Twisted Quadrics and Algebraic Submanifolds in ${\mathbb{R}}^n$
• Learning from Julius' star, *, $\star$
• Braided Tensor Products and the Covariance of Quantum Noncommutative Free Fields
• Thermal effective potential in two- and three- dimensional non-commutative spaces
• Braided Commutative Geometry and Drinfel'd Twist Deformations
• Twisted geometry for submanifolds of ${\mathbb{R}}^n$
• Energy Spectrum and Phase Transition of Superfluid Fermi Gas of Atoms on Noncommutative Space
• Noncommutative spaces with twisted symmetries and second quantization
• Remarks on SU_q(2) fermions