## Electronic Theses and Dissertations

#### Title

Quantum mechanics in the real Pauli algebra.

1991

Thesis

M.Sc.

Physics

Baylis, W. E.

#### Keywords

Physics, Elementary Particles and High Energy.

CC BY-NC-ND 4.0

#### Abstract

In this thesis, real quantum mechanics (QM) is constructed over the field ${\cal F}\sb{P\sb0\oplus P\sb3}$ in the Pauli algebra, where the trivector $i = \sigma\sb1\sigma\sb2\sigma\sb3$ arises naturally as a product of the unit basis vectors in 3-dimensional Euclidean space. In this scheme, i is the volume element of the algebra with $i\sp2 = -1$ and has geometrical meaning. Components of the state vector in Hilbert space take the form of a real element in the field ${\cal F}\sb{P\sb0\oplus P\sb3}$ and the hermitean conjugate of the state vector is just its transpose, so that all the observables, represented by hermitean operators, are symmetric; i itself is an anti-hermitean operator. In this construction, the time reversal operator ${\cal T}$ is a combination of the transpose "+" and the unitary operator which changes the sign of t. Since ${\cal T}$ is an anti-automorphism the interpretation of its action must be carefully analyzed in terms of the state vectors and their inner products. Furthermore, the parity transformation is not represented by the spatial inversion $\tilde\Pi$ (an antilinear, anti-unitary transformation). Instead, the spatial reversal $\bar\Pi$ (an anti-automorphic, linear transformation) is proposed as a parity operator. It is unitary as well as hermitean, and it commutes with the Hamiltonian, H, of a system, thus, it is a constant of motion. This thesis mainly deals with non-relativistic QM for spinless particles.Dept. of Physics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1991 .W444. Source: Masters Abstracts International, Volume: 31-01, page: 0331. Chair: W. E. Baylis. Thesis (M.Sc.)--University of Windsor (Canada), 1991.

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