310 research outputs found
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
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