Quantum field theories on noncommutative R^4 versus theta-expanded quantum field theories
arXiv:hep-th/0206018
Abstract
I recall the main motivation to study quantum field theories on noncommutative spaces and comment on the most-studied example, the noncommutative R^4. That algebra is given by the *-product which can be written in (at least) two ways: in an integral form or an exponential form. These two forms of the *-product are adapted to different classes of functions, which, when using them to formulate field theory, lead to two versions of quantum field theories on noncommutative R^4. The integral form requires functions of rapid decay and a (preferably smooth) cut-off in the path integral, which therefore should be evaluated by exact renormalisation group methods. The exponential form is adapted to analytic functions with arbitrary behaviour at infinity, so that Feynman graphs can be used to compute the path integral (without cut-off) perturbatively.
LaTeX, 27 pages, 3 figures, uses feynmf package. v2: references and some clarifications added. v3: view of *-products changed, additional references added. To appear in proceedings of Hesselberg 2002 workshop on "Theory of renormalisation and regularisation", eds. R. Nest, F. Scheck and E. Vogt
References in corpus (21)
- The quantum structure of spacetime at the Planck scale and quantum fields
- Noncommutative Perturbative Dynamics
- Gravity coupled with matter and foundation of non-commutative geometry
- The Spectral Action Principle
- The IR/UV Connection in the Non-Commutative Gauge Theories
- On the unitarity problem in space/time noncommutative theories
- Algebras of distributions suitable for phase-space quantum mechanics. I
- The One-loop UV Divergent Structure of U(1) Yang-Mills Theory on Noncommutative R^4
- Renormalization of Quantum Field Theories on Noncommutative R^d, I. Scalars
- Perturbative quantum gauge fields on the noncommutative torus
- Non-renormalizability of θ-expanded noncommutative QED
- On Noncommutative and semi-Riemannian Geometry
- Wilsonian Renormalization Group and the Non-Commutative IR/UV Connection
- Renormalization of noncommutative Yang-Mills theories: A simple example
- Noncommutative Lorentz Symmetry and the Origin of the Seiberg-Witten Map
- Quantisation of θ-expanded non-commutative QED
- Discrete Kaluza-Klein from scalar fluctuations in noncommutative geometry
- Interacting fermions on noncommutative spaces: Exactly solvable quantum field theories in 2n+1 dimensions
- Nonpertubative Effects of Extreme Localization in Noncommutative Geometry
- Noncommutative Yang-Mills and Noncommutative Relativity: A Bridge Over Trouble Water
- Noncommutative geometry and fundamental interactions