Hamilton's Turns for the Lorentz Group

Hamilton in the course of his studies on quaternions came up with an elegant geometric picture for the group SU(2). In this picture the group elements are represented by ``turns'', which are equivalence classes of directed great circle arcs on the unit sphere $S^2$, in such a manner that the rule for composition of group elements takes the form of the familiar parallelogram law for the Euclidean translation group. It is only recently that this construction has been generalized to the simplest noncompact group $SU(1,1) = Sp(2, R) = SL(2,R)$, the double cover of SO(2,1). The present work develops a theory of turns for $SL(2,C)$, the double and universal cover of SO(3,1) and $SO(3,C)$, rendering a geometric representation in the spirit of Hamilton available for all low dimensional semisimple Lie groups of interest in physics. The geometric construction is illustrated through application to polar decomposition, and to the composition of Lorentz boosts and the resulting Wigner or Thomas rotation.Comment: 13 pages, Late

Caratterizzazione e applicazione dei fasci laser

Dottorato di ricerca in elettromagnetismo applicato a scienze elettrofisiche. 7. ciclo. Coordinatore Giogio Gerosa. Docente guida Franco GoriConsiglio Nazionale delle Ricerche - Biblioteca Centrale - P.le Aldo Moro, 7, Rome; Biblioteca Nazionale Centrale - P.za Cavalleggeri, 1, Florence / CNR - Consiglio Nazionale delle RichercheSIGLEITItal

Improving the efficiency of the interactive Guy Fawkes protocol

In the Guy Fawkes protocol, messages on an insecure channel are authenticated without any shared secret or public key. Each part generates a sequence of secret keys and authenticates its commitment to the first key. Then each message is authenticated by hashing with the current key and the commitment to the next one, both to be disclosed afterwards. This mechanism forces two interacting parts to commit to responses before receiving and authenticating the corresponding requests. By consequence, not all the exchanged messages can be significant, but only 1/3 of them. A modified version of the protocol is presented that improves efficiency (1/2 of the messages can be significant) while retaining security

Twisted Gaussian Schell-model beams: a superposition model

We present a simple model in which a twisted Gaussian Schell-model beam is produced by an incoherent superposition of ordinary Gaussian beams. The meaning and some direct consequences of the model are given

Space intensity distribution and projections of the cross-spectral density

It is shown that, in the paraxial approximation, the intensity distribution produced throughout the space by a partially coherent field depends only on certain projection integrals of the cross spectral density. These projections, in tum, can be recovered from knowledge of the spatial distribution of the optical intensity. This result can enlighten the recently evidentiated fact that two fields in different states of coherence can give rise to the same intensity everywhere. Some examples are discussed

A new method for measuring diffusivity of liquid binary mixtures using DSPI

A simple and compact digital speckle pattem interferometer is proposed to measure the isothermal diffusion coefficient in transparent mixtures. The diffusion constant is determined directly from the skeletonized video correlogram. An example of diffusion coefficient measurement of a binary liquid mixture demonstrates the usefulness of the metho

A new method for measuring the diffusivity of liquid binary mixtures using DSPI

A simple and compact digital speckle pattern interferometer is proposed to measure the isothermal diffusion coefficient in transparent mixtures. The diffusion constant is determined directly from the skeletonized video correlogram. An example of diffusion coefficient measurement of a binary liquid mixture demonstrates the usefulness of the metho