Energy Gaps in a Spacetime Crystal

This paper presents an analysis of the band structure of a spacetime potential lattice created by a standing electromagnetic wave. We show that there are energy band gaps. We estimate the effect, and propose a measurement that could confirm the existence of such phenomena.Comment: 8 pages. 2 figure

Lax-Phillips Scattering Theory of a Relativistic Quantum Field Theoretical Lee-Friedrichs Model and Lee-Oehme-Yang-Wu Phenomenology

The one-channel Wigner-Weisskopf survival amplitude may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the pole approximation evolution does not correspond to a semigroup (experiments on the decay of the neutral K-meson system support the semigroup evolution postulated by Lee, Oehme and Yang, and Yang and Wu, to very high accuracy). The scattering theory of Lax and Phillips, originally developed for classical wave equations, has been recently extended to the description of the evolution of resonant states in the framework of quantum theory. The resulting evolution law of the unstable system is that of a semigroup, and the resonant state is a well-defined funtion in the Lax-Phillips Hilbert space. In this paper we apply this theory to relativistically covarant quantum field theoretical form of the (soluble) Lee model. We show that this theory provides a rigorous underlying basis for the Lee-Oehme-Yang-Wu construction.Comment: Plain TeX, 34 page

On quaternionic functional analysis

In this article, we will show that the category of quaternion vector spaces, the category of (both one-sided and two sided) quaternion Hilbert spaces and the category of quaternion $B^*$-algebras are equivalent to the category of real vector spaces, the category of real Hilbert spaces and the category of real $C^*$-algebras respectively. We will also give a Riesz representation theorem for quaternion Hilbert spaces and will extend two results of Kulkarni (namely, we will give the full versions of the Gelfand-Naimark theorem and the Gelfand theorem for quaternion $B^*$-algebras). On our way to these results, we compare, clarify and unify the term "quaternion Hilbert spaces" in the literatures.Comment: to appear in the Mathematical Proceedings of the Cambridge Philosophical Societ

Characterization of avirulent mutant Legionella pneumophila that survive but do not multiply within human monocytes.

Legionella pneumophila, the causative agent of Legionnaires' disease, is a Gram-negative bacterium and a facultative intracellular parasite that multiplies in human monocytes and alveolar macrophages. In this paper, mutants of L. pneumophila avirulent for human monocytes were obtained and extensively characterized. The mutants were obtained by serial passage of wild-type L. pneumophila on suboptimal artificial medium. None of 44 such mutant clones were capable of multiplying in monocytes or exerting a cytopathic effect on monocyte monolayers. Under the same conditions, wild-type L. pneumophila multiplied 2.5-4.5 logs, and destroyed the monocyte monolayers. The basis for the avirulent phenotype was an inability of the mutants to multiply intracellularly. Both mutant and wild-type bacteria bound to and were ingested by monocytes, and both entered by coiling phagocytosis. Thereafter, their intracellular destinies diverged. The wild-type formed a distinctive ribosome-lined replicative phagosome, inhibited phagosome-lysosome fusion, and multiplied intracellularly. The mutant did not form the distinctive phagosome nor inhibit phagosome-lysosome fusion. The mutant survived intracellularly but did not replicate in the phagolysosome. In all other respects studied, the mutant and wild-type bacteria were similar. They had similar ultrastructure and colony morphology; both formed colonies of compact and diffuse type. They had similar structural and secretory protein profiles and LPS profile by PAGE. Both the mutant and wild-type bacteria were completely resistant to human complement in the presence or absence of high titer anti-L. pneumophila antibody. The mutant L. pneumophila have tremendous potential for enhancing our understanding of the intracellular biology of L. pneumophila and other parasites that follow a similar pathway through the mononuclear phagocyte. Such mutants also show promise for enhancing our understanding of immunity to L. pneumophila, and they may serve as prototypes in the development of safe and effective vaccines against intracellular pathogens