760 research outputs found
On a Lorentz-Invariant Interpretation of Noncommutative Space-Time and Its Implications on Noncommutative QFT
By invoking the concept of twisted Poincar\' e symmetry of the algebra of
functions on a Minkowski space-time, we demonstrate that the noncommutative
space-time with the commutation relations ,
where is a {\it constant} real antisymmetric matrix, can be
interpreted in a Lorentz-invariant way. The implications of the twisted
Poincar\'e symmetry on QFT on such a space-time is briefly discussed. The
presence of the twisted symmetry gives justification to all the previous
treatments within NC QFT using Lorentz invariant quantities and the
representations of the usual Poincar\'e symmetry.Comment: 12 pages, one reference adde
Quasiclassical Limit in q-Deformed Systems, Noncommutativity and the q-Path Integral
Different analogs of quasiclassical limit for a q-oscillator which result in
different (commutative and non-commutative) algebras of ``classical''
observables are derived. In particular, this gives the q-deformed Poisson
brackets in terms of variables on the quantum planes. We consider the
Hamiltonian made of special combination of operators (the analog of even
operators in Grassmann algebra) and discuss q-path integrals constructed with
the help of contracted ``classical'' algebras.Comment: 19 pages, Late
Twist as a Symmetry Principle and the Noncommutative Gauge Theory Formulation
Based on the analysis of the most natural and general ansatz, we conclude
that the concept of twist symmetry, originally obtained for the noncommutative
space-time, cannot be extended to include internal gauge symmetry. The case is
reminiscent of the Coleman-Mandula theorem. Invoking the supersymmetry may
reverse the situation.Comment: 13 pages, more accurate motivation adde
Covariant star product on symplectic and Poisson spacetime manifolds
A covariant Poisson bracket and an associated covariant star product in the
sense of deformation quantization are defined on the algebra of tensor-valued
differential forms on a symplectic manifold, as a generalization of similar
structures that were recently defined on the algebra of (scalar-valued)
differential forms. A covariant star product of arbitrary smooth tensor fields
is obtained as a special case. Finally, we study covariant star products on a
more general Poisson manifold with a linear connection, first for smooth
functions and then for smooth tensor fields of any type. Some observations on
possible applications of the covariant star products to gravity and gauge
theory are made.Comment: AMS-LaTeX, 27 pages. v2: minor corrections in presentation and
language, added one referenc
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