73 research outputs found
Noncommutative Quantization in 2D Conformal Field Theory
The simplest possible noncommutative harmonic oscillator in two dimensions is
used to quantize the free closed bosonic string in two flat dimensions. The
partition function is not deformed by the introduction of noncommutativity, if
we rescale the time and change the compactification radius appropriately. The
four point function is deformed, preserving, nevertheless, the sl(2,C)
invariance. Finally the first Ward identity of the deformed theory is derived.Comment: 5 pages, The solitonic contribution to the partition function has
been computed. The parameter has been analytically continued to
$-i\theta
The gravitational chiral anomaly of spin-1/2 field in the presence of twisted boundary conditions for ordinary field theory
We calculate the chiral anomaly in the neighbourhood of the fixed point space
M_h which is constructed by the group action of a discrete symmetry h on a
compact manifold M. The Feynman diagrams approach for the corresponding
supersymmetric quantum mechanical system with twisted boundary conditions is
used. The result we derive in this way agrees with the generalization of the
ordinary index theorem (the G-index theorem) on the spin complex.Comment: 8 page
Self-similar solutions of R\'enyi's entropy and the concavity of its entropy power
We study the class of self-similar probability density functions with finite
mean and variance which maximize R\'{e}nyi's entropy. The investigation is
restricted in the Schwartz space and in the space of
-differentiable compactly supported functions .
Interestingly the solutions of this optimization problem do not coincide with
the solutions of the usual porous medium equation with a Dirac point source, as
it occurs in the optimization of Shannon's entropy. We also study the concavity
of the entropy power in with respect to time using two different
methods. The first one takes advantage of the solutions determined earlier
while the second one is based on a setting that could be used for Riemannian
manifolds.Comment: 18 pages, 2 figure
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