Rotating frames in special relativity analyzed in light of a recent article by M. Strauss

The argument of Einstein for non-Euclidity on a rotating disk is analyzed and found valid. The kinematic reason for the non-Euclidean geometry is stated explicitly and provides a kinematic resolution of Ehrenfest's paradox. The transformation from an inertial frameK to a rotating frame, the axis of which is at rest inK, is discussed. It is concluded in favor of the Galilean-like transformation employed by Møller. The method used by Møller in obtaining the intrinsic spatial geometry in any frame is examined. It is found to be adequate, provided that only coordinates with a proper metrical significance are used. In this connection the distinction between global and local geometry is found to be essential.     

Ion beam exposure of resists

Problems caused by the statistical variation of the number of exposing ions in ionbeam lithography are discussed. Using Poisson statistics, the minimum dose required for exposure as a function of resist sensitivity and minimum feature size is calculated. It is found that, although ion-beam resists show a very high sensitivity of 10¹¹ to 10¹³,cm^–2, it would be possible to use still more sensitive resists and obtain submicron linewidth resolution.     

A model for an interacting quantum field

We present here a close nonlinear analog to the free quantum field of Bose statistics, in which the linear one-particle space is replaced by a nonlinear infinite-dimensional Hermitian symmetric space D, and the quantum field is constructed as a Hilbert space of holomorphic functions on D.     

Statistical mechanical model with chemical reaction

We study a mixture of classical particles where unequal particles interact with strong binding forces, while equal particles repel each other with a hard-core interaction. The interactions are constructed so that at most two unequal particles can bind to a molecule. Such a system can be interpreted as one where the basic species react to form diatomic molecules, the equilibrium of which at low densities is governed by the well-known law of mass action. Our results explicate and supplement the approach of Andersen to this problem.     

Superfluidity of 3He in dilute solutions of 3He in liquid 4He

The possibility of superfluidity of ³He in dilute solutions of ³He in liquid ⁴He is investigated, and the corresponding critical temperature is estimated. The results indicate S-state pairing, i.e., for small concentrations of ³He, the highest transition temperature is obtained for L = 0, but the obtained critical temperatures are very low.     

A note on the conformal quasi-invariance of the Laplacian on a pseudo-Riemannian manifold

We consider the Laplacian on a pseudo-Riemannian manifold with constant scalar curvature (e.g. Euclidian space with an arbitrary signed inner product or its conformal compactification and coverings of this) and show that for this minus a constant we have quasi-invariance with respect to an action of the conformal group on functions.     

Spectral representations and density operators for infinite-dimensional homogeneous random fields

A theory of spectral representations and spectral density operators of infinite-dimensional homogeneous random fields is established. Some results concerning the form of the spectral representation are given in the general infinite-dimensional case, while the results pertaining to the density operator are confined to Hilbert space valued fields. The concept of a purely non-deterministic (p.n.d.) field is defined, and necessary and sufficient conditions for the property of p.n.d. are obtained in terms of the spectral density operator. The theory is developed using some isomorphisms induced by families of self-adjoint operators in the linear second order space associated with the field. The method seems to lead to more direct results also in the random process case, and it sheds new light on concepts such as multiplicity of the field and rank of the spectral density operator.