Scalar products of pauli spin matrices

Roderich Tumulka

Lawrence Paul Horwitz, Rafael I Arshansky

The authors study a family of Hilbert spaces with positive definite invariant scalar product for the quantum mechanical description of relativistic spin- 1 / 2 particles. The Hermitian and anti-Hermitian parts of the Dirac operator gamma mu p mu are related to energy and helicity. Replacing p mu by p mu -eA mu , the difference between the squares of these operators provides a minimal coupling evolution operator, similar to the second-order Dirac operator, for which F mu nu is coupled to a covariant form of the Pauli spin matrices which generate SU(2) in a space-like surface. No Dirac sea is required for the consistency of the theory.

Pertti Lounesto

Willi-Hans Steeb, Yorick Hardy

Entanglement for the eigenvectors of a nonlinear eigenvalue problem given by the Kronecker product of the Pauli spin matrices is investigated. Fully and partially entangled eigenvectors are found.

Willi-Hans Steeb, Yorick Hardy

Pauli spin matrices, Pauli group, commutators, anti-commutators and the Kronecker product are studied. Applications to eigenvalue problems, exponential functions of such matrices, spin Hamilton operators, mutually unbiased bases, Fermi operators and Bose operators are provided.