Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ||z;alpha> defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ||z;alpha><−z;alpha||. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible alpha dependence of this minimum value is considered. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Group portrait at the farewell banquet for Dr. William Antopol from the laboratory staff of Mount Sinai Hospital; Ken's Chop House, New York city Portraits Groups

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Group US Army military portrait including Dr. William Levison (top row, third from left); Schofield Barracks, Hawaii Portraits Groups Men

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Embedding Of Non-Simple Lie-Groups, Coupling-Constant Relations And Non-Uniqueness Of Models Of Unification

A general derivation of the coupling constant relations which result on embedding a non-simple group like SU L (2) @ U(1) in a larger simple group (or graded Lie group) is given. It is shown that such relations depend only on the requirement (i) that the multiplet of vector fields form an irreducible representation of the unifying algebra and (ii) the transformation properties of the fermions under SU L (2). This point is illustrated in two ways, one by constructing two different unification groups containing the same fermions and therefore have same Weinberg angle; the other by putting different SU L (2) structures on the same fermions and consequently have different Weinberg angles. In particular the value sin~0=3/8 is characteristic of the sequential doublet models or models which invoke a large number of additional leptons like E 6, while addition of extra charged fermion singlets can reduce the value of sin ~ 0 to 1/4. We point out that at the present time the models of grand unification are far from unique.

Group portrait, unidentified co-educational Jewish public school.

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Outdoor group portrait of attendees of the International Meeting of the World Union for Progressive Judaism; London.

Includes Rabbi Leo Baeck, E.L. Ehrlich of Basel, Herbert Strauss of Bern, and Rabbi Eugen Messinger of Bern

Understanding and management of resistance to Group M, L and I Herbicides

This project will develop better understanding of resistance to glyphosate, paraquat and Group I herbicides to better inform weed management. The project will develop a range of tools for farm advisors to improve their confidence in decision making with respect to reducing the risk of glyphosate, Group I and paraquat resistance. These will include risk assessments, case studies and scenario exploring tools. The project will discuss with commercial providers the potential for new herbicide registrations. The project will establish farm advisor learning groups to work on the application of the research in local areas where resistance is already a major problem and to improve adoption of research outcomes from this and other projects.

Class picture of Gisela Kleinermann Portraits Group

The photograph shows Gisela Kleinermann (standing at the right end of the line) with her class at the ‘Juedische Schule’ in Dresden, late summer of 1938, as she and her mother were preparing for her immigration to the USA. Most other children were deported in October 1938 and perished in the Holocaust. The teacher, Jacob Blum (center back) emigrated to Palestine.

Albert Einstein with unidentified group; City College, New York Portraits Groups; Men

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Group portrait, 50th Anniversary of the Saxony-Anhalt chapter of German Engineers; Bernburg Portraits Groups

Caption: Zur Erinnerung an das fuenfzigjaehrige Gruendungsfest Saechsisch Anhaltinischen Bezirksvereins Deutscher Ingenieure am 11. und 12. Mai 1912 in Bernburg.

Albert Einstein with unidentified group Portraits Groups

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Unidentified Group on Beach at Swinemuende Portraits; Groups

Album 4

Unidentified Group at Swimming Pool; Pioneer Youth Camp Portraits Groups

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Leo Baeck with group; Boston Portraits; Groups; Men

Page 58 of the "American Jewish Cavalcade" scrapbook of Leo Baeck in New York found in ROS 10 Folder 3