24 research outputs found
Seiberg-Witten map with Lorentz-invariance and gauge-covariant star product
We develop the Seiberg-Witten map using the gauge-covariant star product with the noncommutativity tensor theta(mu v)(x). The latter guarantees the Lorentz invariance of the theory. The usual form of this map and its other recent generalizations do not consider such a covariant star product. We construct the Seiberg-Witten map for the gauge parameter, the gauge field and the strength tensor to the first order in the noncommutativity parameter theta(mu v)(x). Prescription for the generalization of the map to higher orders is also given. Interestingly, the associativity of the covariant star product both in the first and second orders requires the same constraints, namely, on the theta(mu v)(x) and on the space-time connection. This fact suggests that the same constraints could be enough to ensure the associativity in all orders. The resulting Seiberg-Witten map applies both to the internal and space-time gauge theories. Comparisons with the Seiberg-Witten map based on other (non-covariant) star products are given and some characteristic properties are also presented. As an application, we consider the GL(2, C) noncommutative gauge theory of gravitation, in which it is shown that the connection determines a space-time with symplectic structure (as proposed by Zumino et al [33]). This example shows that the constraints required for the associativity of the gauge-covariant star product can be satisfied. The presented GL(2, C) noncommutative gauge theory of gravitation is also compared to the one (given by Chamseddine [44]) with non-covariant star product. (C) 2022 The Author(s). Published by Elsevier B.V.Peer reviewe
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
Jost-Lehmann-Dyson Representation, Analyticity in Angle Variable and Upper Bounds in Noncommutative Quantum Field Theory
The existence of Jost-Lehmann-Dyson representation analogue has been proved
in framework of space-space noncommutative quantum field theory. On the basis
of this representation it has been found that some class of elastic amplitudes
admits an analytical continuation into complex \cos\vartheta plane and
corresponding domain of analyticity is Martin ellipse. This analyticity
combined with unitarity leads to Froissart-Martin upper bound on total cross
section.Comment: LaTeX, 15 pages, improved version, misprints corrected, the
references added, to appear in Theor. 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