Double Scaling Limits and Catastrophes of the zerodimensional O(N) Vector Sigma Model: The A-Series

We evaluate the partition functions in the neighbourhood of catastrophes by saddle point integration and express them in terms of generalized Airy functions.Comment: 20 pages, LaTeX, two figures available from author on reques

The Value of Friendship for Education

In lieu of an abstract, here is the article\u27s first paragraph: Western philosophers have enthusiastically praised friendship. A few intellectuals have raised doubts about it, such as Thomas Hobbes and Søren Kierkegaard, but friendship has inspired many others, including Aristotle, Francis Bacon, C.S. Lewis, and Mary E. Hunt, who have esteemed its benefits, especially the reciprocal commitment to nurture each friend\u27s \u27best self\u27

Thoreau as Liberation Thinker

In lieu of an abstract, here is the article\u27s first paragraph: Henry David Thoreau’s claim to be “a mystic, a transcendentalist, and a natural philosopher” took an unexpected turn for me. Spending much time with A Week on the Concord and Merrimack Rivers (my dissertation addresses the idea of religion found between its covers), I encountered a “liberation thinker” resisting the limitations of American culture while honoring the natural world and indigenous peoples. Thoreau’s epigraph reveals how he wants the muse of his dead brother to inspire him, but the book also discloses how he wants the muse of indigenous peoples to inspirit and improve American culture. Impressively, he esteems nature as more than a symbol pointing to a distant divinity as he experiences its inherent sacredness. Natural creation is at once our house and being; we are immersed in and part of its continuous regenerative processes, which suggests familial bonds of sacredness uniting humans and nonhumans. Thoreau offers an alternative to social structures and outlooks that devalue human and nonhuman existence

An exactly solvable model of the Calogero type for the icosahedral group

We construct a quantum mechanical model of the Calogero type for the icosahedral group as the structural group. Exact solvability is proved and the spectrum is derived explicitly.Comment: 13 pages, no figures, latex 2epsilo

Sigma models with AkA_k singularities in Euclidean spacetime of dimension 0<=D<4 and in the limit N->infinity

For the case of the single-O($N$)-vector linear sigma models the critical behaviour following from any $A_k$ singularity in the action is worked out in the double scaling limit $N \rightarrow \infty$, $f_r \rightarrow f_r^c$, $2 \leq r \leq k$. After an exact elimination of Gaussian degrees of freedom, the critical objects such as coupling constants, indices and susceptibility matrix are derived for all $A_k$ and spacetime dimensions $0 \leq D < 4$. There appear exceptional spacetime dimensions where the degree $k$ of the singularity $A_k$ is more strongly constrained than by the renormalizability requirement.Comment: LaTeX, 25 pages, no figure

Critical O(N) - vector nonlinear sigma - models: A resume of their field structure

The classification of quasi - primary fields is outlined. It is proved that the only conserved quasi - primary currents are the energy - momentum tensor and the O(N) - Noether currents. Derivation of all quasi - primary fields and the resolution of degeneracy is sketched. Finally the limits d=2 and d=4 of the space dimension are discussed. Whereas the latter is trivial the former is only almost so.Comment: 16 pages, Latex. To appear in the Proceedings of the XXII Conference on Differential Methods in Theoretical Physics, Ixtapa, Mexico, September 20-24, 199

UV and VUV spectroscopy and photochemistry of small molecules in a supersonic jet

UV and VUV absorption and emission spectroscopy is used to probe jet cooled molecules, free radicals, and clusters in the gas phase. Due to efficient cooling inhomogeneous effects on spectral line widths are eliminated. Therefore from these spectra, both structural and dynamical information is obtained. The photoproducts of these reactions are probed by resonance enhanced multiphoton ionization

Local cubic vertex functions for three massless higher even spin fields on spaces AdS_D: An analytic approach

Local cubic vertex functions of three higher even spin fields on AdS_D are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV divergence as the residue of the highest order pole in the dimensional regularization parameter \epsilon. The method works for even D and maintains covariance at any step. The resulting formula is quite concise.Comment: 9 page

Double Scaling Limits, Airy Functions and Multicritical Behaviour in O(N) Vektor Sigma Models

O(N) vector sigma models possessing catastrophes in their action are studied. Coupling the limit N --> infinity with an appropriate scaling behaviour of the coupling constants, the partition function develops a singular factor. This is a generalized Airy function in the case of spacetime dimension zero and the partition function of a scalar field theory for positive spacetime dimension.Comment: 14 pages, LaTe