Physics
Scientific paper
May 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009aps..dmp.y1011s&link_type=abstract
American Physical Society, 40th Annual Meeting of the APS Division of Atomic, Molecular and Optical Physics, May 19-23,2009, abs
Physics
Scientific paper
The Einstein addition law of velocities implies a hyperbolic geometry for relativistic velocity and momentum space. The simplest model of an open, expanding universe implies a hyperbolic geometry for position space. It is natural to investigate the kinematics of a phase space combining hyperbolic geometries in both the velocity-momentum manifold H(3)vel and the position manifold H(3)pos. Each of these sustains its own Lorentz subgroup, Lvel = O(1,3)vel and Lpos = O(1,3)pos. These form a direct product group L^2 = Lvel x Lpos, a 12-parameter group, represented by 8 x8 matrices. Among its operators are a subgroup Lboost of Lorentz velocity boosts that operate on the elements of Lvel by Einstein addition and on those of Lpos by the Lorentz transformation. There is also a conjugate subgroup Lshift of hyperbolic translational shifts that operate on the elements of Lpos translationally, and on those of Lvel to describe the Hubble effect of distance on velocity vectors. The structure, symmetries, Lie algebra and important operators and quantum numbers of the resulting representation of L^2 will be reported. (See also F.T. Smith, Ann. Fond. L. de Broglie, 30, 179 (2005).)
No associations
LandOfFree
Lorentz Symmetries of a Doubly Hyperbolic Phase Space does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Lorentz Symmetries of a Doubly Hyperbolic Phase Space, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Lorentz Symmetries of a Doubly Hyperbolic Phase Space will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-778415