4 research outputs found
Noncommutativity and theta-locality
In this paper, we introduce the condition of theta-locality which can be used
as a substitute for microcausality in quantum field theory on noncommutative
spacetime. This condition is closely related to the asymptotic commutativity
which was previously used in nonlocal QFT. Heuristically, it means that the
commutator of observables behaves at large spacelike separation like
, where is the noncommutativity parameter. The
rigorous formulation given in the paper implies averaging fields with suitable
test functions. We define a test function space which most closely corresponds
to the Moyal star product and prove that this space is a topological algebra
under the star product. As an example, we consider the simplest normal ordered
monomial and show that it obeys the theta-locality condition.Comment: LaTeX, 17 pages, no figures; minor changes to agree with published
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Towards an Axiomatic Formulation of Noncommutative Quantum Field Theory
We propose new Wightman functions as vacuum expectation values of products of
field operators in the noncommutative space-time. These Wightman functions
involve the -product among the fields, compatible with the twisted
Poincar\'e symmetry of the noncommutative quantum field theory (NC QFT). In the
case of only space-space noncommutativity (), we prove the CPT
theorem using the noncommutative form of the Wightman functions. We also show
that the spin-statistics theorem, demonstrated for the simplest case of a
scalar field, holds in NC QFT within this formalism.Comment: 16 pages, version to appear in J. Math. Phy
Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
We characterize the worldvolume theories on symmetric D-branes in a
six-dimensional Cahen-Wallach pp-wave supported by a constant Neveu-Schwarz
three-form flux. We find a class of flat noncommutative euclidean D3-branes
analogous to branes in a constant magnetic field, as well as curved
noncommutative lorentzian D3-branes analogous to branes in an electric
background. In the former case the noncommutative field theory on the branes is
constructed from first principles, related to dynamics of fuzzy spheres in the
worldvolumes, and used to analyse the flat space limits of the string theory.
The worldvolume theories on all other symmetric branes in the background are
local field theories. The physical origins of all these theories are described
through the interplay between isometric embeddings of branes in the spacetime
and the Penrose-Gueven limit of AdS3 x S3 with Neveu-Schwarz three-form flux.
The noncommutative field theory of a non-symmetric spacetime-filling D-brane is
also constructed, giving a spatially varying but time-independent
noncommutativity analogous to that of the Dolan-Nappi model.Comment: 52 pages; v2: References adde