Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics
Mostafazadeh, Ali
arXiv, 0302050 / Harvested from arXiv
Text on arXiv
We consider pseudo-unitary quantum systems and discuss various properties of pseudo-unitary operators. In particular we prove a characterization theorem for block-diagonalizable pseudo-unitary operators with finite-dimensional diagonal blocks. Furthermore, we show that every pseudo-unitary matrix is the exponential of $i=\sqrt{-1}$ times a pseudo-Hermitian matrix, and determine the structure of the Lie groups consisting of pseudo-unitary matrices. In particular, we present a thorough treatment of $2\times 2$ pseudo-unitary matrices and discuss an example of a quantum system with a $2\times 2$ pseudo-unitary dynamical group. As other applications of our general results we give a proof of the spectral theorem for symplectic transformations of classical mechanics, demonstrate the coincidence of the symplectic group $Sp(2n)$ with the real subgroup of a matrix group that is isomorphic to the pseudo-unitary group U(n,n), and elaborate on an approach to second quantization that makes use of the underlying pseudo-unitary dynamical groups.
Publié le : 2003-02-21
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Quantum Physics 
@article{0302050,
     author = {Mostafazadeh, Ali},
     title = {Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0302050}
}

Mostafazadeh, Ali. Pseudo-Unitary Operators and Pseudo-Unitary Quantum Dynamics. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0302050/