A Rejoinder on Quaternionic Projective Representations

In a series of papers published in this Journal (J. Math. Phys.), a discussion was started on the significance of a new definition of projective representations in quaternionic Hilbert spaces. The present paper gives what we believe is a resolution of the semantic differences that had apparently tended to obscure the issues.Comment: AMStex, 6 Page

Alternative Descriptions in Quaternionic Quantum Mechanics

We characterize the quasianti-Hermitian quaternionic operators in QQM by means of their spectra; moreover, we state a necessary and sufficient condition for a set of quasianti-Hermitian quaternionic operators to be anti-Hermitian with respect to a uniquely defined positive scalar product in a infinite dimensional (right) quaternionic Hilbert space. According to such results we obtain two alternative descriptions of a quantum optical physical system, in the realm of quaternionic quantum mechanics, while no alternative can exist in complex quantum mechanics, and we discuss some differences between them.Comment: 16 page

Unbounded normal operators in octonion Hilbert spaces and their spectra

Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.Comment: 50 page

New classical properties of quantum coherent states

A noncommutative version of the Cramer theorem is used to show that if two quantum systems are prepared independently, and if their center of mass is found to be in a coherent state, then each of the component systems is also in a coherent state, centered around the position in phase space predicted by the classical theory. Thermal coherent states are also shown to possess properties similar to classical ones

Projective Group Representations in Quaternionic Hilbert Space

We extend the discussion of projective group representations in quaternionic Hilbert space which was given in our recent book. The associativity condition for quaternionic projective representations is formulated in terms of unitary operators and then analyzed in terms of their generator structure. The multi--centrality and centrality assumptions are also analyzed in generator terms, and implications of this analysis are discussed.Comment: 16 pages, no figures, plain Te

Quasi-permutable normal operators in octonion Hilbert spaces and spectra

Families of quasi-permutable normal operators in octonion Hilbert spaces are investigated. Their spectra are studied. Multiparameter semigroups of such operators are considered. A non-associative analog of Stone's theorem is proved.Comment: 20 page

Nonabelian special K-flows

AbstractThe Kolmogorov-Sinai theory of special K-flows is enlarged to a class of nonabelian dynamical systems whose stochastic behavior is analyzed. The main result of this paper is that these dynamical systems retain the fundamental property of having homogeneous Lebesgue spectrum with countably infinite multiplicity

Recent Results Regarding Affine Quantum Gravity

Recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non-classical modification of the ground state wave function leads to a result that eliminates term-by-term divergences that arise in a conventional perturbation analysis. After a brief review of both the scalar field story and the affine quantum gravity program, examination of the procedures used in the latter surprisingly shows an analogous formulation which already implies that affine quantum gravity is not plagued by divergences that arise in a standard perturbation study. Additionally, guided by the projection operator method to deal with quantum constraints, trial reproducing kernels are introduced that satisfy the diffeomorphism constraints. Furthermore, it is argued that the trial reproducing kernels for the diffeomorphism constraints may also satisfy the Hamiltonian constraint as well.Comment: 32 pages, new features in this alternative approach to quantize gravity, minor typos plus an improved argument in Sec. 9 suggested by Karel Kucha