Noncommutative Quantum Field Theories

Abstract

We start by reviewing the formulation of noncommutative quantum mechanics as a constrained system. Then, we address to the problem of field theories defined on a noncommutative space-time manifold. The Moyal product is introduced and the appearance of the UV/IR mechanism is exemplified. The emphasis is on finding and analyzing noncommutative quantum field theories which are renormalizable and free of nonintegrable infrared singularities. In this last connection we give a detailed discussion of the quantization of the noncommutative Wess-Zumino model as well as of its low energy behavior.

45 pages, 11 figures, lectures delivered at the XII Jorge Andre Swieca Summar School, Section Particles and Fields, Campos de Jordao, Brazil, 2003. Three references added, typos corrected

References in corpus (4)

• Spin-Statistics and CPT Theorems in Noncommutative Field Theory
• Spontaneous Symmetry Breaking in Noncommutative Field Theory
• Noncommutative version of an arbitrary nondegenerated mechanics
• Higher loop corrections in noncommutative supersymmetric QED

Cited by in corpus (28)

• Superfield covariant analysis of the divergence structure of noncommutative supersymmetric QED${}_4$
• Energy nonconservation as a link between $f(R,T)$ gravity and noncommutative quantum theory
• The noncommutative degenerate electron gas
• Emergence of Geometric phase shift in Planar Non-commutative Quantum Mechanics
• A squeezed review on coherent states and nonclassicality for non-Hermitian systems with minimal length
• Scattering of spin 1/2 particles by the 2+1 dimensional noncommutative Aharonov-Bohm potential
• Non-commutative space engine: a boost to thermodynamic processes
• Noncommutative Geometry and Fluid Dynamics
• Properties of an axisymmetric Lorentzian non-commutative black hole
• Free-fall in a uniform gravitational field in non-commutative quantum mechanics
• On the duality of three-dimensional superfield theories
• The coupling of fermions to the three-dimensional noncommutative $C{P}^{N-1}$ model: minimal and supersymmetric extensions
• Lorentz symmetry breaking in the noncommutative Wess-Zumino model: One loop corrections
• Noncommutative quantum mechanics as a gauge theory
• The three-dimensional noncommutative Gross-Neveu model
• Born series and unitarity in noncommutative quantum mechanics
• On the quantum dynamics of non-commutative systems
• Canonical Structure of Noncommutative Quantum Mechanics as Constraint System
• Noncommutative quantum mechanics: uniqueness of the functional description
• Noncommutativity and relativity
• From Noncommutative Sphere to Nonrelativistic Spin
• Galilei Group with multiple central extension, vorticity and entropy generation: "Exotic" fluid in 3+1-dimensions
• Thermostatistical analysis and negative heat capacities of Yukawa and Lee-Wick potentials in noncommutative phase spaces
• The 1/N Expansion in Noncommutative Quantum Mechanics
• Alternative Approach to Noncommutative Quantum Mechanics on a Curved Space
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms
• Noncommutative Cubic Scalar Field Theory and Tree Level Processes
• Noncommutativity in Configuration Space Induced by A Conjugate Magnetic Field in Phase Space