2,105 research outputs found
Stokeling v. United States: Blurring The Line Of What Constitutes Physical Force Under The Elements Clause Of The Armed Career Criminal Act
The Symmetric Tensor Lichnerowicz Algebra and a Novel Associative Fourier-Jacobi Algebra
Lichnerowicz's algebra of differential geometric operators acting on
symmetric tensors can be obtained from generalized geodesic motion of an
observer carrying a complex tangent vector. This relation is based upon
quantizing the classical evolution equations, and identifying wavefunctions
with sections of the symmetric tensor bundle and Noether charges with geometric
operators. In general curved spaces these operators obey a deformation of the
Fourier-Jacobi Lie algebra of sp(2,R). These results have already been
generalized by the authors to arbitrary tensor and spinor bundles using
supersymmetric quantum mechanical models and have also been applied to the
theory of higher spin particles. These Proceedings review these results in
their simplest, symmetric tensor setting. New results on a novel and extremely
useful reformulation of the rank 2 deformation of the Fourier-Jacobi Lie
algebra in terms of an associative algebra are also presented. This new algebra
was originally motivated by studies of operator orderings in enveloping
algebras. It provides a new method that is superior in many respects to common
techniques such as Weyl or normal ordering.Comment: This is a contribution to the Proceedings of the 2007 Midwest
Geometry Conference in honor of Thomas P. Branson, published in SIGMA
(Symmetry, Integrability and Geometry: Methods and Applications) at
http://www.emis.de/journals/SIGMA
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