Path Integral Approach to Noncommutative Space-Times

Abstract

We propose a path integral formulation of noncommutative generalizations of spacetime manifold in even dimensions, characterized by a length scale ${\lambda }_P$. The commutative case is obtained in the limit ${\lambda }_P=0$.

Latex, 12 pages, updated version published in Journal of Mathematical Physics, 39, 2584-2591, 1998

References in corpus (2)

• The quantum structure of spacetime at the Planck scale and quantum fields
• On Finite 4D Quantum Field Theory in Non-Commutative Geometry

Cited by in corpus (15)

• Path Integral Formulation of Noncommutative Quantum Mechanics
• A comparative review of four formulations of noncommutative quantum mechanics
• Noncommutative Geometry for Pedestrians
• Unsharp Degrees of Freedom and the Generating of Symmetries
• Path integral representations in noncommutative quantum mechanics and noncommutative version of Berezin-Marinov action
• Noncommutative Field Theory from Quantum Mechanical Space-Space Noncommutativity
• Coulomb potential in one dimension with minimal length: A path integral approach
• Worldline approach to noncommutative field theory
• Path Integral Quantisation of Finite Noncommutative Geometries
• Self-quartic interaction for a scalar field in an extended DFR noncommutative spacetime
• Path Integrals in Noncommutative Quantum Mechanics
• Some aspects of quantum mechanics and field theory in a Lorentz invariant noncommutative space
• Path integrals in Snyder space
• The standard electroweak model in the noncommutative $DFR$ space-time
• Lagrangian Aspects of Quantum Dynamics on a Noncommutative Space