Noncommutative deformations of quantum field theories, locality, and causality
arXiv:1012.3536 · doi:10.1007/s11232-010-0058-7
Abstract
We investigate noncommutative deformations of quantum field theories for different star products, particularly emphasizing the locality properties and the regularity of the deformed fields. Using functional analysis methods, we describe the basic structural features of the vacuum expectation values of star-modified products of fields and field commutators. As an alternative to microcausality, we introduce a notion of -locality, where is the noncommutativity parameter. We also analyze the conditions for the convergence and continuity of star products and define the function algebra that is most suitable for the Moyal and Wick-Voros products. This algebra corresponds to the concept of strict deformation quantization and is a useful tool for constructing quantum field theories on a noncommutative space-time.
LaTeX, 14 pages, no figures. Presented at the 2nd Intern. Conf. "String Field Theory and Related Aspects" (Steklov Math. Institute, Moscow, April 2009)
References in corpus (23)
- Quantum Field Theory on Noncommutative Spaces
- The quantum structure of spacetime at the Planck scale and quantum fields
- On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
- General Properties of Noncommutative Field Theories
- Statistics and UV-IR Mixing with Twisted Poincare Invariance
- On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
- Twisting all the way: from Classical Mechanics to Quantum Fields
- Wedge-Local Quantum Fields and Noncommutative Minkowski Space
- String-localized Quantum Fields and Modular Localization
- Twisted Noncommutative Field Theory with the Wick-Voros and Moyal Products
- Noncommutative field theory with the Wick-Voros product
- Noncommutative Deformations of Wightman Quantum Field Theories
- PCT, spin and statistics, and analytic wave front set
- Spectral Representation and Dispersion Relations in Field Theory on Noncommutative Space
- Star product algebras of test functions
- Noncommutativity and theta-locality
- Test Functions Space in Noncommutative Quantum Field Theory
- Failure of microcausality in quantum field theory on noncommutative spacetime
- Twisted Quantum Fields on Moyal and Wick-Voros Planes are Inequivalent
- Locality, Causality and Noncommutative Geometry
- Duality and Braiding in Twisted Quantum Field Theory
- On topological tensor products of functional Frechet and DF spaces
- On kernel theorems for Frechet and DF spaces
Cited by in corpus (5)
- Moyal multiplier algebras of the test function spaces of type S
- Algebras with convergent star products and their representations in Hilbert spaces
- Twisted convolution and Moyal star product of generalized functions
- Consistent Anomalies in Translation-Invariant Noncommutative Gauge Theories
- Wedge locality and asymptotic commutativity