Field Theory on Curved Noncommutative Spacetimes
arXiv:1003.3190 · doi:10.3842/SIGMA.2010.061
Abstract
We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by using (Abelian) Drinfel'd twists and the associated *-products and *-differential geometry. In particular, we allow for position dependent noncommutativity and do not restrict ourselves to the Moyal-Weyl deformation. We construct action functionals for real scalar fields on noncommutative curved spacetimes, and derive the corresponding deformed wave equations. We provide explicit examples of deformed Klein-Gordon operators for noncommutative Minkowski, de Sitter, Schwarzschild and Randall-Sundrum spacetimes, which solve the noncommutative Einstein equations. We study the construction of deformed Green's functions and provide a diagrammatic approach for their perturbative calculation. The leading noncommutative corrections to the Green's functions for our examples are derived.
SIGMA Special Issue on Noncommutative Spaces and Fields
References in corpus (36)
- Quantum Gravity at a Lifshitz Point
- A Gravity Theory on Noncommutative Spaces
- Symmetry, Gravity and Noncommutativity
- Corrections to Schwarzschild Solution in Noncommutative Gauge Theory of Gravity
- Emergent Gravity from Noncommutative Spacetime
- On "full" twisted Poincare' symmetry and QFT on Moyal-Weyl spaces
- Fock space, quantum fields and kappa-Poincaré symmetries
- kappa-Minkowski spacetime as the result of Jordanian twist deformation
- Field theory on --Minkowski space revisited: Noether charges and breaking of Lorentz symmetry
- Twisting all the way: from Classical Mechanics to Quantum Fields
- Towards Quantum Noncommutative -deformed Field Theory
- Wedge-Local Quantum Fields and Noncommutative Minkowski Space
- Lie algebraic Noncommutative Gravity
- Direction-Dependent CMB Power Spectrum and Statistical Anisotropy from Noncommutative Geometry
- Cosmological and Black Hole Spacetimes in Twisted Noncommutative Gravity
- Constraints from CMB on Spacetime Noncommutativity and Causality Violation
- Cosmological horizons and reconstruction of quantum field theories
- Deformed Reissner--Nordstrom solutions in noncommutative gravity
- Noncommutative BTZ Black Hole and Discrete Time
- Remarks on twisted noncommutative quantum field theory
- Noncommutative supergravity in D=3 and D=4
- Twisted Gauge and Gravity Theories on the Groenewold-Moyal Plane
- kappa-deformed Spacetime From Twist
- Twisted Poincaré Invariant Quantum Field Theories
- Noncommutative Field Theory from twisted Fock space
- Quantum fields, non-locality and quantum group symmetries
- Spherically Symmetric Noncommutative Space: d = 4
- Noncommutative Geometries and Gravity
- Drinfeld Twist and General Relativity with Fuzzy Spaces
- Exact Black Hole Solutions in Noncommutative Gravity
- Noncommutative Black-Body Radiation: Implications On Cosmic Microwave Background
- Algebraic approach to quantum gravity II: noncommutative spacetime
- Symmetry Reduction in Twisted Noncommutative Gravity with Applications to Cosmology and Black Holes
- Noncommutative Corrections to the Robertson-Walker metric
- Quantum deformations of Schwarzschild and Schwarzschild-de Sitter spacetimes
- High energy improved scalar quantum field theory from noncommutative geometry without UV/IR-mixing