# Bulletin of the American Physical Society

# APS April Meeting 2011

## Volume 56, Number 4

## Saturday–Tuesday, April 30–May 3 2011; Anaheim, California

### Session K1: Poster Session II (2:00-5:00PM)

2:00 PM,
Sunday, May 1, 2011

Room: Imperial/Regal Rooms

Sponsoring
Unit:
APS

Abstract ID: BAPS.2011.APR.K1.29

### Abstract: K1.00029 : New Aspects of Angular Momentum Quantization in Curved Geometries

Preview Abstract Abstract

#### Author:

Felix T. Smith

(SRI International)

Curvature in velocity space affects angular momentum through the Thomas precession, observable through quantum effects. When position space is curved too, a similar angular momentum effect arises, with an even smaller curvature parameter. In a phase space view of dynamics and group theory the two effects appear through a direct product of two Lorentz groups, one centered on Lorentz boosts and the other on translations in a hyperbolic position space. The usual tensor representation must now be extended to $8\times 8$ matrices arising from position and velocity submatrices. The rotation subgroup becomes a direct product group $R\left( 3 \right)_{\mbox{vel}} \otimes R\left( 3 \right)_{\mbox{pos}} $. Its matrices recouple into a total angular momentum of standard form and a new contra-angular momentum $Q$ represented by $6\times 6$ matrices whose Lie algebra and quantization properties have been derived (Smith, F. T., Ann. Fond. L. de Broglie, \textbf{30}, 179 (2010)). It has quantum numbers $q,m_q $ whose connections with elementary particles are as yet undetermined. Transitions will be highly forbidden except in regions of high gravitational curvature or high relative velocity.

To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.APR.K1.29

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