13,996 research outputs found
Alternative Canonical Formalism for the Wess-Zumino-Witten Model
We study a canonical quantization of the Wess--Zumino--Witten (WZW) model
which depends on two integer parameters rather than one. The usual theory can
be obtained as a contraction, in which our two parameters go to infinity
keeping the difference fixed. The quantum theory is equivalent to a generalized
Thirring model, with left and right handed fermions transforming under
different representations of the symmetry group. We also point out that the
classical WZW model with a compact target space has a canonical formalism in
which the current algebra is an affine Lie algebra of non--compact type.
Also, there are some non--unitary quantizations of the WZW model in which
there is invariance only under half the conformal algebra (one copy of the
Virasoro algebra).Comment: 22 pages; UR-133
Dynamical Aspects of Lie--Poisson Structures
Quantum Groups can be constructed by applying the quantization by deformation
procedure to Lie groups endowed with a suitable Poisson bracket. Here we try to
develop an understanding of these structures by investigating dynamical systems
which are associated with this bracket. We look at and , as
submanifolds of a 4--dimensional phase space with constraints, and deal with
two classes of problems. In the first set of examples we consider some
hamiltonian systems associated with Lie-Poisson structures and we investigate
the equations of the motion. In the second set of examples we consider systems
which preserve the chosen bracket, but are dissipative. However in this
approach, they survive the quantization procedure.Comment: 17 pages, figures not include
A novel approach to non-commutative gauge theory
We propose a field theoretical model defined on non-commutative space-time
with non-constant non-commutativity parameter , which satisfies two
main requirements: it is gauge invariant and reproduces in the commutative
limit, , the standard gauge theory. We work in the slowly
varying field approximation where higher derivatives terms in the star
commutator are neglected and the latter is approximated by the Poisson bracket,
. We derive an explicit expression for both the NC
deformation of Abelian gauge transformations which close the algebra
, and the NC field strength ,
covariant under these transformations, . NC
Chern-Simons equations are equivalent to the requirement that the NC field
strength, , should vanish identically. Such equations are
non-Lagrangian. The NC deformation of Yang-Mills theory is obtained from the
gauge invariant action, . As guiding example, the case of
-like non-commutativity, corresponding to rotationally invariant NC
space, is worked out in detail.Comment: 16 pages, no figures. Minor correction
Noncommutative via closed star product
We consider linear star products on of Lie algebra type. First we
derive the closed formula for the polydifferential representation of the
corresponding Lie algebra generators. Using this representation we define the
Weyl star product on the dual of the Lie algebra. Then we construct a gauge
operator relating the Weyl star product with the one which is closed with
respect to some trace functional, . We introduce
the derivative operator on the algebra of the closed star product and show that
the corresponding Leibnitz rule holds true up to a total derivative. As a
particular example we study the space with type
noncommutativity and show that in this case the closed star product is the one
obtained from the Duflo quantization map. As a result a Laplacian can be
defined such that its commutative limit reproduces the ordinary commutative
one. The deformed Leibnitz rule is applied to scalar field theory to derive
conservation laws and the corresponding noncommutative currents.Comment: published versio
Transplantable zebrafish models of neuroendocrine tumors
Neuroendocrine tumors (NETs)are rare neoplasms whose incidence is increasing. NETs constitute a heterogeneous group of tumors. Their clinical features, functional properties, and clinical course are different on the basis of their site of origin. Due to the heterogeneity of these tumors, a coordinated multidisciplinary approach is required in these patients. However, medical doctor encounters many difficulties when providing care for patients with NETs. This review provides an overview of the state of the art of zebrafish model in the cancer research with a main focus on NETs
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