/ 9 60 30 24 v 1 2 8 M ar 1 99 6 Skew Symmetric Bundle Maps on Space - Time Daniel

ar X iv : g r - qc / 9 40 30 41 v 1 2 1 M ar 1 99 4 Global structure of Witten ’ s 2 + 1 gravity on R × T 2

We investigate the space M of classical solutions to Witten’s formulation of 2+1 gravity on the manifold R×T . M is connected, but neither Hausdorff nor a manifold. However, removing from M a set of measure zero yields a connected manifold which is naturally viewed as the cotangent bundle over a non-Hausdorff base space. Avenues towards quantizing the theory are discussed in view of the relatio...

Skew Symmetric Bundle Maps on Space-time

We study the “Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices, Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .

ar X iv : c on d - m at / 9 60 31 90 v 1 2 9 M ar 1 99 6 The Four - Dimensional XY Spin Glass

ar X iv : q - a lg / 9 60 80 20 v 1 2 3 A ug 1 99 6 SHIFTED JACK POLYNOMIALS , BINOMIAL FORMULA , AND APPLICATIONS

In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it. 1. Jack polynomials ([M,St]). In this note we use the parameter θ = 1/α inverse to the standard parameter α for Jack polynomials. Jack symmetric polynomials Pλ(x1, . . . , xn; θ) are eigenfunctions of Sekiguchi differential operators D(u; θ) = V (x) det [

Skew Symmetric Bundle Maps on Space - Time August 19 , 1997

We study the ”Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices , Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .