Quantum field theory in generalised Snyder spaces

Abstract

We discuss the generalisation of the Snyder model that includes all possible deformations of the Heisenberg algebra compatible with Lorentz invariance and investigate its properties. We calculate peturbatively the law of addition of momenta and the star product in the general case. We also undertake the construction of a scalar field theory on these noncommutative spaces showing that the free theory is equivalent to the commutative one, like in other models of noncommutative QFT.

arXiv comment12 pages. arXiv admin note: substantial text overlap with arXiv:1608.06207

References in corpus (22)

• Quantum Field Theory on Noncommutative Spaces
• The algebraic structure of the generalized uncertainty principle
• Quantum mechanics on the noncommutative plane and sphere
• Exact Solution of the Harmonic Oscillator in Arbitrary Dimensions with Minimal Length Uncertainty Relations
• Short Distance vs. Long Distance Physics: The Classical Limit of the Minimal Length Uncertainty Relation
• Classical and quantum mechanics of the nonrelativistic Snyder model
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Modification of Heisenberg uncertainty relations in non-commutative Snyder space-time geometry
• Scalar field theory on kappa-Minkowski spacetime and translation and Lorentz invariance
• Noncommutative Spaces and Poincaré Symmetry
• Snyder space revisited
• Kappa-deformed Snyder spacetime
• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Particle Dynamics on Snyder space
• Kappa-Minkowski spacetime, Kappa-Poincaré Hopf algebra and realizations
• Snyder dynamics in a Schwarzschild spacetime
• Massless Scalar Field Theory in a Quantised Space-Time
• Algebraic approach to quantum gravity II: noncommutative spacetime
• Realizations of $\kappa$-Minkowski space, Drinfeld twists and related symmetry algebras
• Spectrum of the hydrogen atom in Snyder space in a semiclassical approximation
• Hermitian realizations of kappa-Minkowski spacetime
• Generalized relativistic kinematics in Poincaré-invariant models

Cited by in corpus (20)

• Bumblebee gravity and particle motion in Snyder noncommutative spacetime structures
• Worldline Formalism in Snyder Spaces
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Nonassociative Snyder phi4 Quantum Field Theory
• Associative realizations of the extended Snyder model
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Generalizations of Snyder model to curved spaces
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Snyder-type spaces, twisted Poincaré algebra and addition of momenta
• Unification of $\kappa$-Minkowski and extended Snyder spaces
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Noncommutative Yang model and its generalizations
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• Twist for Snyder space
• Physical velocity of particles in relativistic curved momentum space
• Doubly special relativity as a non-local quantum field theory
• Relative-locality geometry for the Snyder model
• Thermal and spectral dimension of (generalized) Snyder noncommutative spacetimes
• Covariant dynamics on the energy-momentum space: scalar field theory
• Three dimensional DKP oscillator in a curved Snyder space