287 research outputs found
Nonassociative Weyl star products
Deformation quantization is a formal deformation of the algebra of smooth
functions on some manifold. In the classical setting, the Poisson bracket
serves as an initial conditions, while the associativity allows to proceed to
higher orders. Some applications to string theory require deformation in the
direction of a quasi-Poisson bracket (that does not satisfy the Jacobi
identity). This initial condition is incompatible with associativity, it is
quite unclear which restrictions can be imposed on the deformation. We show
that for any quasi-Poisson bracket the deformation quantization exists and is
essentially unique if one requires (weak) hermiticity and the Weyl condition.
We also propose an iterative procedure that allows to compute the star product
up to any desired order.Comment: discussion extended, tipos corrected, published versio
Gauge invariance and classical dynamics of noncommutative particle theory
We consider a model of classical noncommutative particle in an external
electromagnetic field. For this model, we prove the existence of generalized
gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is
discussed, in particular, the motion in the constant magnetic field is studied
in detail.Comment: 10 page
Current fluctuations in composite conductors: Beyond the second cumulant
Employing the non-linear -model we analyze current fluctuations in
coherent composite conductors which contain a diffusive element in-between two
tunnel barriers. For such systems we explicitly evaluate the
frequency-dependent third current cumulant which also determines the leading
Coulomb interaction correction to shot noise. Our predictions can be directly
tested in future experiments.Comment: 6 pages, 1 figur
- …