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Phys. Rev. A 73, 032104 (2006) [6 pages]

Maps for Lorentz transformations of spin

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Thomas F. Jordan*
Physics Department, University of Minnesota, Duluth, Minnesota 55812, USA

Anil Shaji and E. C. G. Sudarshan
The University of Texas at Austin, Center for Statistical Mechanics, 1 University Station C1609, Austin, Texas 78712, USA

Received 8 November 2005; published 13 March 2006

Lorentz transformations of spin density matrices for a particle with positive mass and spin 1∕2 are described by maps of the kind used in open quantum dynamics. They show how the Lorentz transformations of the spin depend on the momentum. Since the spin and momentum generally are not independent, the maps generally are not completely positive and act in limited domains. States with two momentum values are considered, so the maps are for the spin qubit correlated with the qubit made from the two momentum values, and results from the open quantum dynamics of two coupled qubits can be applied. Inverses are used to show that every Lorentz transformation completely removes the spin polarization, and so completely removes the information, from a number of spin density matrices. The size of the spin polarization that is removed is calculated for particular cases.

© 2006 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevA.73.032104
DOI:
10.1103/PhysRevA.73.032104
PACS:
03.30.+p, 03.65.Yz

*Email address: tjordan@d.umn.edu

Present address: The University of New Mexico, Department of Physics and Astronomy, 800 Yale Blvd. NE, Albuquerque, NM 87131, USA. Email address: shaji@unm.edu

Email address: sudarshan@physics.utexas.edu