A Generalization of the Bargmann's Theory of Ray Representations

The paper contains a complete theory of factors for ray representations acting in a Hilbert bundle, which is a generalization of the known Bargmann's theory. With the help of it we have reformulated the standard quantum theory such that the gauge freedom emerges naturally from the very nature of quantum laws. The theory is of primary importance in the investigations of covariance (in contradistinction to symmetry) of a quantum theory which possesses a nontrivial gauge freedom. In that case the group in question is not any symmetry group but it is a covariance group only - that case which has not been deeply investigated. It is shown on the paper that the factor of its representation depends on space and time when the system in question possesses a gauge freedom. In the nonrelativistic theories the factor depends on the time only. In the relativistic theory the Hilbert bundle is over the spacetime in the nonrelativistic one it is over the time. We explain two applications of this generalization: in a theory of a quantum particle in the nonrelativistic limit and in the quantum electrodynamics.Comment: 37 pages, LateX, revised version, submitted to Comm. Math. Phy

Why odd-space and odd-time dimensions in even-dimesional spaces?

We are answering the question why 4-dimensional space has the metric 1+3 by making a general argument from a certain type of equations of motion linear in momentum for any spin (except spin zero) in any even dimension d. All known free equations for non-zero spin for massless fields belong to this type of equations. Requiring Hermiticity(This is a generalization of an earlier work which shows that without assuming the Lorentz invariance -which in the present work is assumed- the Weyl equation follows using Hermiticity.) of the equations of motion operator as well as irreducibility with respect to the Lorentz group representation, we prove that only metrics with the signature corresponding to q time + (d - q) space dimensions with q being odd exist. Correspondingly, in four dimensional space, Nature could only make the realization of 1+3 dimensional space.Comment: (only small corrections made

Fidelity preserving maps on density operators

We prove that any bijective fidelity preserving transformation on the set of all density operators on a Hilbert space is implemented by an either unitary or antiunitary operator on the underlying Hilbert space.Comment: This is corrected version of the paper math.OA/0108060. The paper has already appeared in ROMP (vol. 48 (2001), 299-303

Parity violating vertices for spin-3 gauge fields

The problem of constructing consistent parity-violating interactions for spin-3 gauge fields is considered in Minkowski space. Under the assumptions of locality, Poincar\'e invariance and parity non-invariance, we classify all the nontrivial perturbative deformations of the abelian gauge algebra. In space-time dimensions $n=3$ and $n=5$, deformations of the free theory are obtained which make the gauge algebra non-abelian and give rise to nontrivial cubic vertices in the Lagrangian, at first order in the deformation parameter $g$. At second order in $g$, consistency conditions are obtained which the five-dimensional vertex obeys, but which rule out the $n=3$ candidate. Moreover, in the five-dimensional first order deformation case, the gauge transformations are modified by a new term which involves the second de Wit--Freedman connection in a simple and suggestive way.Comment: 27 pages, 1 table, revtex4, typos correcte

Neuroscience: Comraderie and Nostalgia in Nematodes

Two recent papers on social rearing and olfactory imprinting show that early developmental experiences can lead to long-lasting changes in behaviour of the model nematode Caenorhabditis elegans

Parametric statistics of zeros of Husimi representations of quantum chaotic eigenstates and random polynomials

Local parametric statistics of zeros of Husimi representations of quantum eigenstates are introduced. It is conjectured that for a classically fully chaotic systems one should use the model of parametric statistics of complex roots of Gaussian random polynomials which is exactly solvable as demonstrated below. For example, the velocities (derivatives of zeros of Husimi function with respect to an external parameter) are predicted to obey a universal (non-Maxwellian) distribution ${d P(v)}/{dv^2} = 2/(\pi\sigma^2)(1 + |v|^2/\sigma^2)^{-3},$ where $\sigma^2$ is the mean square velocity. The conjecture is demonstrated numerically in a generic chaotic system with two degrees of freedom. Dynamical formulation of the ``zero-flow'' in terms of an integrable many-body dynamical system is given as well.Comment: 13 pages in plain Latex (1 figure available upon request

\u3cb\u3eWoven Bands, Medicines and Recipes: Cod. Pal. Germ. 551.\u3c/b\u3e \u3ci\u3eThe Adventures, Provenance and Contents of a 15\u27 Century Manuscript Held at the Library of Heidelberg University in Germany.\u3c/i\u3e

Today, we are going to visit Heidelberg, the city where the earliest German University was founded in 1386. On account of its romantic setting, it became one of the internationally popular institutions in the 19th century. Here, we will visit the University Library, where the manuscript we are to discuss today is housed. It is on the shelf in the Department of Manuscripts, bound in a modest working cover of the 19th century. History. - We shall embark on a journey of more than 500 years into the past and through some very trying times that helped shape present-day Central Europe. Finding the manuscript was not an earth-shaking discovery, but rather the following of the Haensel-and- Gretel trail of crumbs which were dropped by a book on medieval trades by Gerhard Eis. and the later mention of the manuscript by Leonie von Wilckens, the now deceased Curator of Textiles at the Germanisches Nationalmuseum in Nuremberg. It is part of the famous Palatina Collection of the University of Heidelberg, that is to say, it once belonged to a prince of the Palatinate. The manuscript was collected some time before the 1550\u27s by Ottheinrich (1502-1559), then count Palatine of Palatinate-Neuburg. He was a lavish Protestant Renaissance Prince, a notable collector and bibliophile. This ran him into great financial trouble - especially in view of his pocket-size realm - and his eclectic art collection counting many famous Italian paintings and objets d\u27art wound up on the auction block, since the trades no longer consented to support his extravagant lifestyle by paying his debt. He had to lie low and leave the country for a while. His magnificent castle from that time at Neuburg can still be admired today. He was able to hold on to his collection of books, though. Many of his book acquisitions were a direct result of the many closings of monasteries and convents due to the wave of the Reformation that swept Germany - in most cases these collections were thus saved from destruction. In 1556, he succeeded to the hereditary title of Elector Palatine, thus joining the rather powerful club of princes that elected the Emperor of the Holy Roman Empire. Ottheinrich immediately proceeded to remodel Heidelberg Castle in the Renaissance style, and he combined his library with that of the University and placed it into the upper story of the Church of the Holy Ghost, to be made available to scholars and other interested folks who were able to read. He also provided a generous endowment, so that the library could continue to be developed and prosper. Here, the collection served the university, which was reborn as a reformation institution with Philip Melanchthon at the helm

\u3cb\u3eWoven Bands, Medicines and Recipes: Cod. Pal. Germ. 551.\u3c/b\u3e \u3ci\u3eThe Adventures, Provenance and Contents of a 15\u27 Century Manuscript Held at the Library of Heidelberg University in Germany.\u3c/i\u3e

Today, we are going to visit Heidelberg, the city where the earliest German University was founded in 1386. On account of its romantic setting, it became one of the internationally popular institutions in the 19th century. Here, we will visit the University Library, where the manuscript we are to discuss today is housed. It is on the shelf in the Department of Manuscripts, bound in a modest working cover of the 19th century. History. - We shall embark on a journey of more than 500 years into the past and through some very trying times that helped shape present-day Central Europe. Finding the manuscript was not an earth-shaking discovery, but rather the following of the Haensel-and- Gretel trail of crumbs which were dropped by a book on medieval trades by Gerhard Eis. and the later mention of the manuscript by Leonie von Wilckens, the now deceased Curator of Textiles at the Germanisches Nationalmuseum in Nuremberg. It is part of the famous Palatina Collection of the University of Heidelberg, that is to say, it once belonged to a prince of the Palatinate. The manuscript was collected some time before the 1550\u27s by Ottheinrich (1502-1559), then count Palatine of Palatinate-Neuburg. He was a lavish Protestant Renaissance Prince, a notable collector and bibliophile. This ran him into great financial trouble - especially in view of his pocket-size realm - and his eclectic art collection counting many famous Italian paintings and objets d\u27art wound up on the auction block, since the trades no longer consented to support his extravagant lifestyle by paying his debt. He had to lie low and leave the country for a while. His magnificent castle from that time at Neuburg can still be admired today. He was able to hold on to his collection of books, though. Many of his book acquisitions were a direct result of the many closings of monasteries and convents due to the wave of the Reformation that swept Germany - in most cases these collections were thus saved from destruction. In 1556, he succeeded to the hereditary title of Elector Palatine, thus joining the rather powerful club of princes that elected the Emperor of the Holy Roman Empire. Ottheinrich immediately proceeded to remodel Heidelberg Castle in the Renaissance style, and he combined his library with that of the University and placed it into the upper story of the Church of the Holy Ghost, to be made available to scholars and other interested folks who were able to read. He also provided a generous endowment, so that the library could continue to be developed and prosper. Here, the collection served the university, which was reborn as a reformation institution with Philip Melanchthon at the helm