Noncommutative Geometry and Symplectic Field Theory
arXiv:hep-th/0611081 · doi:10.1016/j.physleta.2006.09.074
Abstract
In this work we study representations of the Poincare group defined over symplectic manifolds, deriving the Klein-Gordon and the Dirac equation in phase space. The formalism is associated with relativistic Wigner functions; the Noether theorem is derived in phase space and an interacting field, including a gauge field, approach is discussed.
To appear in Physics Letters A
References in corpus (5)
- String Theory and Noncommutative Geometry
- Quantum Field Theory on Noncommutative Spaces
- Features of Time-independent Wigner Functions
- Wigner Trajectory Characteristics in Phase Space and Field Theory
- The Hamiltonian BRST quantization of a noncommutative nonabelian gauge theory and its Seiberg-Witten map
Cited by in corpus (10)
- Quantum field theory on toroidal topology: algebraic structure and applications
- Realization of the Noncommutative Seiberg-Witten Gauge Theory by Fields in Phase Space
- The Noncommutative Harmonic Oscillator based in Simplectic Representation of Galilei Group
- Non-linear Liouville and Shrödinger equations in phase space
- Hénon-Heiles Interaction for Hydrogen Atom in Phase Space
- Symplectic Dirac Equation
- Size-effect at finite temperature in a quark-antiquark effective model in phase space
- The Landau Problem and non-Classicality
- On Scalar Electromagnetism in Phase Space
- Non-abelian gauge symmetry for fields in phase space: a realization of the Seiberg-Witten non-abelian gauge theory