Physics – Mathematical Physics
Scientific paper
2009-03-31
Symmetry, Integrability and Geometry: Methods and Applications 5 (2009) 096 (15 pages)
Physics
Mathematical Physics
20 pages, 6 figures, 1 table; Version 2 - slightly polished, updated references; Version 3 - published version in SIGMA
Scientific paper
10.3842/SIGMA.2009.096
Recently, a number of interesting relations have been discovered between generalised Pauli/Dirac groups and certain finite geometries. Here, we succeeded in finding a general unifying framework for all these relations. We introduce gradually necessary and sufficient conditions to be met in order to carry out the following programme: Given a group $\vG$, we first construct vector spaces over $\GF(p)$, $p$ a prime, by factorising $\vG$ over appropriate normal subgroups. Then, by expressing $\GF(p)$ in terms of the commutator subgroup of $\vG$, we construct alternating bilinear forms, which reflect whether or not two elements of $\vG$ commute. Restricting to $p=2$, we search for ``refinements'' in terms of quadratic forms, which capture the fact whether or not the order of an element of $\vG$ is $\leq 2$. Such factor-group-generated vector spaces admit a natural reinterpretation in the language of symplectic and orthogonal polar spaces, where each point becomes a ``condensation'' of several distinct elements of $\vG$. Finally, several well-known physical examples (single- and two-qubit Pauli groups, both the real and complex case) are worked out in detail to illustrate the fine traits of the formalism.
Havlicek Hans
Odehnal Boris
Saniga Metod
No associations
LandOfFree
Factor-Group-Generated Polar Spaces and (Multi-)Qudits 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 Factor-Group-Generated Polar Spaces and (Multi-)Qudits, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Factor-Group-Generated Polar Spaces and (Multi-)Qudits will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-20363