 1  Author
 Emil Wolf  Requires cookie*   Title
 Sudarshan's Optical Researches    Abstract
 As is evident from the scope of this meeting, Sudarshan's scientific interests and contributions have covered a broad area of physics. Among them optics plays a very prominent role. I say optics rather than quantum optics, as is so fashionable these days, because many of Sudarshan's investigations have been particularly concerned with some striking analogies and some remarkable similarities which were found to exist between these two fields, particularly in the domain of optical coherence. In fact some of Sudarshan's contributions to this area have been largely responsible for the clarifications of several subtle questions, which in the 1960s soon after the invention of the laser were rather controversial. I take some pride in having been responsible together with my colleague Leonard Mandel for stimulating Sudarshan's interest in this field.   
Reference
 Z. Naturforsch. 52a, 2 (1997)   
Published
 1997   
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2  Author
 R. E. Marshak  Requires cookie*   Title
 The Pain and Joy of a Major Scientific Discovery    Abstract
 This threeday workshop is being held on the occasion of George Sudarshan's 60th birthday to do honor to his significant and manyfaceted contributions to theoretical physics. The nature and extent of these contributions are being covered by a host of distinguished speakers and, hence, I shall limit my banquet remarks to George Sudarshan's early scientific career in particle physics which culminated in his remarkable doctoral dissertation on the nature of the fourfermion interaction, otherwise known as the universal VA theory of weak interactions. George Sudarshan's thesis problem turned out to be so exciting that his professor entered as a parttime participant. This was easy to do because George was brought up in the Indian tradition which instills great respect on the part of the student towards his teacher. In any case, Sudarshan's thesis was issued as a jointly authored University of Rochester preprint on September 16, 1957, the data of George's 26th birthday, just thirtyfour years ago. This evening I should like to recall those early years of close association with George Sudarshan and describe ever so briefly the pain and joy of a major scientific discovery.   
Reference
 Z. Naturforsch. 52a, 3—8 (1997)   
Published
 1997   
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3  Author
 Iwo BialynickiBirula, P. J. Morrison  Requires cookie*   Title
 Quantum Mechanics as a Generalization of Nambu Dynamics to the WeylWigner Formalism* *    Abstract
 It is shown that Nambu dynamics can be generalized to any number of dimensions by replacing the 0(3) algebra, a prominent feature of Nambu's formulation, by an arbitrary Lie algebra. For the infinite dimensional algebra of rotations in phase space one obtains quantum mechanics in the WeylWigner representation from the generalized Nambu dynamics. Also, this formulation can be cast into a canonical Hamiltonian form by a natural choice of canonically conjugate variables.   
Reference
 Z. Naturforsch. 52a, 9—12 (1997)   
Published
 1997   
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4  Author
 BertholdGeorg Englert  Requires cookie*   Title
 Time Reversal Symmetry and HumptyDumpty    Abstract
 It is argued that the quantal evolution of a physical system is fundamentally irreversible although the dynamical equations are symmetric under time reversal. The example of spin coherence in a SternGerlach interferometer demonstrates that even undoing the evolution partially only may require submicroscopic precision in controlling a macroscopic apparatus.   
Reference
 Z. Naturforsch. 52a, 13—14 (1997)   
Published
 1997   
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5  Author
 Y. Aharonov, J. Anandan  Requires cookie*   Title
 Is There a Preferred Canonical Quantum Gauge?* *    Abstract
 The interaction between a long solenoid and a quantized charged particle in the field free region outside it is studied treating both systems quantum mechanically. This leads to a paradox which suggests that when the electromagnetic field is quantized, there may be a preferred quantum gauge for the vector potential. This paradox is resolved by canonically quantizing the system in a different gauge in which the classical Lagrangian contains an acceleration dependent term.   
Reference
 Z. Naturforsch. 52a, 15—19 (1997)   
Published
 1997   
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6  Author
 Thomas Walther, EdwardS. Fry  Requires cookie*   Title
 On Some Aspects of an Hg Based EPR Experiment    Abstract
 An experimental realization of Bohm's spin1/2 EPR gedankenexperiment is possible using the spin1/2 nuclei of the isotope 199 Hg. The dissociation of dimers of the 199 Hg 2 isotopomer, using a spectroscopically selective stimulated Raman process, leads to the generation of an entangled state between the two 199 Hg atoms. The measurement of nuclear spin correlations between the two atoms in this entangled state is achieved by detection of the atoms using a spin state selective two photon excitationionization scheme. The experiment will not only close the detector efficiency loophole, but in addition will permit enforcement of the locality condition. Effects of imperfect analyzers will also be discussed.   
Reference
 Z. Naturforsch. 52a, 20—24 (1997); received October 12 1995   
Published
 1997   
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7  Author
 J. P. Hsu  Requires cookie*   Title
 Fuzzy Transitions from Quantum to Classical Mechanics and New Phenomena of Mesoscopic Objects* *    Abstract
 A new "phase invariant" equation of motion for both microscopic and macroscopic objects is proposed. It reduces to the probabilistic wave equation for small masses and the deterministic classical equation for large masses. The motions of mesoscopic objects and fuzzy transitions between quantum and classical mechanics are discussed on the basis of the generalized equation. Experimental tests of new predictions are discussed.   
Reference
 Z. Naturforsch. 52a, 25—30 (1997); received November 11 1995   
Published
 1997   
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8  Author
 R. G. Hulet, N.W M Ritchie, J. G. Story  Requires cookie*   Title
 Measurement of a Weak Value    Abstract
 "Weak measurements" are measurements in which the coupling between the measuring device and the observable to be measured is so weak that the eigenvalues of the observable are not resolved. Under certain circumstances the corresponding eigenfunctions can be made to interfere, producing a measurement result which is outside the allowed range of the observable's eigenvalues. We present the first measurement of this socalled "weak value" using an optical experiment. In our experiment, the small displacement between the two orthogonally polarized components of a laser beam passed through a birefringence crystal is measured. We use a numerical simulation to show that this phenomenon may be practical for detecting and amplifying small effects.   
Reference
 Z. Naturforsch. 52a, 31—33 (1997)   
Published
 1997   
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9  Author
 ArjenduK. Pattanayak, WilliamC. Schieve  Requires cookie*   Title
 Predicting Two Dimensional Hamiltonian Chaos    Abstract
 We use geometrical analysis to show that the TodaBrumerDuff criterion for transition to chaos is a simple application of Jacobi's equation. Further, we propose a new criterion for this transition for twodimensional hamiltonian systems and summarize the results.   
Reference
 Z. Naturforsch. 52a, 34—36 (1997)   
Published
 1997   
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10  Author
 Ilya Prigogine  Requires cookie*   Title
 From Poincare's Divergences to Quantum Mechanics with Broken Time Symmetry    Abstract
 We discuss the spectral property of unstable dynamical systems in both classical and quantum mechanics. An important class of unstable dynamical systems corresponds to the Large Poincare Systems (LPS). Conventional perturbation technique leads then to divergences. We introduce methods for the elimination of Poincare divergences to obtain a solution of the spectral problem analytic in the coupling constant. To do so, we have to enlarge the class of permissible transformations, to include nonunitary transformations as well as to extend the Hilbert space. A simple example refers to the Friedrichs model, which was studied independently by George Sudarshan and his coworkers. However, our main interest is the irreducible representations in the Liouville space. In these representations the central quantity is the density matrix, and the eigenfunctions of the Liouville operator cannot be expressed in terms of the wave functions. We suggest that this situation corresponds to quantum chaos. Indeed, classical chaos does not mean that Newton's equation becomes "wrong" but that trajectories loose their operational meaning. Similarly, whenever we have an irreducible representation in the Liouville space this means that the wave function description looses its operational meaning. Additional statistical features appear. A simple example corresponds to persistent interactions in the scattering problem which cannot be treated in the frame of usual Smatrix theory.   
Reference
 Z. Naturforsch. 52a, 37—45 (1997)   
Published
 1997   
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11  Author
 Oktay Sinanoğlu  Requires cookie*   Title
 A Principal of Linear Covariance for Quantum Mechanics and Its Consequences Taking one Beyond Symmetry    Abstract
 A Principle of Linear Covariance is stated which follows from the "superposition principle" of quantum mechanics. Accordingly, quantum mechanical equations should be written in linearly covariant form which makes them look the same under nonunitary as well as unitary transformations. The principle leads to a nonunitary classification of all molecules (and clusters and solids) into distinct equivalence classes giving hitherto unknown relations between isomeric molecules. One also gets kinetic and thermic selection rules for chemical reactions. All these are independent of, and far more general than any unitary or point group symmetries. The invariants found for each class of molecules or clusters allow qualitative electronic deductions and are more generally applicable than symmetry based quantum numbers.   
Reference
 Z. Naturforsch. 52a, 46—48 (1997)   
Published
 1997   
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12  Author
 Georg Süssmann  Requires cookie*   Title
 Uncertainty Relation: From Inequality to Equality    Abstract
 The uncertainty area (5 (p, q): — [J W(p, q) 2 dp dq] ~ 1 is proposed in place of äp • Öq, and it is shown that each pure quantum state is a minimum uncertainty state in this sense: S (p, q) = 2 n h. For mixed states, on the other hand, d(p, q) > 2nh. In a phase space of 2F(=6N) dimensions, S: = k B • log[<5 f (p, q)/(2nh) F ]with S F (p, q):= [J W(p, q) 2 d pd F q]' 1 is considered as an alternative to von Neumann's entropy S:=k B • trclog~ 1)].   
Reference
 Z. Naturforsch. 52a, 49—52 (1997)   
Published
 1997   
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13  Author
 BruceJ. West, Paolo Grigolini, Luca Bonci, Roberto Roncaglia  Requires cookie*   Title
 Quantum Irreversibility and Chaos    Abstract
 Herein we establish a relation between quantum irreversibility and the chaotic semiclassical solutions for a spinboson Hamiltonian system. We obtain quantum averages by numerically integrating the appropriate LiouvilleVon Neumann equations of motion and find these averages to be less erratic than the corresponding chaotic semiclassical trajectories. However, the quantum averages are shown to be dissipative as measured by the entropy of the spin subsystem and to suppress the phenomenon of "revivals".   
Reference
 Z. Naturforsch. 52a, 53—58 (1997)   
Published
 1997   
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14  Author
 L. C. Biedenharn, K. Srinivasa, Rao  Requires cookie*   Title
 Understanding the ^Factors in Quantum Group Symmetry    Abstract
 A characteristic feature of quantum groups is the occurrence of ^factors (factors of the form <7*, A:eIR), which implement braiding symmetry. We show how the <jrfactors in matrix elements of elementary ^tensor operators (for all U q {n)) may be evaluated, without explicit calculation, directly from structural symmetry properties.   
Reference
 Z. Naturforsch. 52a, 59—62 (1997)   
Published
 1997   
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15  Author
 LouisJ. Boya  Requires cookie*   Title
 Rays and Phases: A Paradox?    Abstract
 Dedicatory It is an honor to be able to speak in this meeting celebrating George Sudarshan's birthday; to know him and to discuss physics with him has been a great privilege for me   
Reference
 Z. Naturforsch. 52a, 63—65 (1997)   
Published
 1997   
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16  Author
 B. Kendrick  Requires cookie*   Title
 The Quantum Phase    Abstract
 The geometrical nature of the quantum phase is introduced. This phase is shown to originate from the nontrivial geometry of the fiber bundle: Hilbert space space of states. The analysis is performed working in the general nonadiabatic setting.   
Reference
 Z. Naturforsch. 52a, 66—68 (1997); received July 26 1995   
Published
 1997   
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17  Author
 J. R. Klauder  Requires cookie*   Title
 Coherent States and CoordinateFree Quantization* *    Abstract
 The usual quantization procedures interpret canonical transformations in an active way linking them with unitary transformations, while the quantization procedure offered by coherent states completely separates classical canonical transformations and unitary operator transformations. By exploiting this property, along with a physically motivated shadow metric, it is seen how to realize the quantization process in as coordinatefree a form as holds in classical mechanics.   
Reference
 Z. Naturforsch. 52a, 69—75 (1997)   
Published
 1997   
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18  Author
 Susumu Okubo  Requires cookie*   Title
 Poisson Brackets and Nijenhuis Tensor    Abstract
 Many integrable models satisfy the zero Nijenhuis tensor condition. Although its application for discrete systems is then straightforward, there exist some complications to utilize the condition for continuous infinite dimensional models. A brief sketch of how we deal with the problem is explained with an application to a continuous Toda lattice. 1. Let M be a symplectic manifold with a Poisson bracket [A,BR=F^D^ADVB (1)   
Reference
 Z. Naturforsch. 52a, 76—78 (1997)   
Published
 1997   
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19  Author
 L. O 'raifeartaigh  Requires cookie*   Title
 WAlgebras    Abstract
 Walgebras are defined as polynomial extensions of the Virasoro algebra by primary fields, and they occur in a natural manner in the context of twodimensional integrable systems, notably in the KdV and Toda systems. Their occurrence in those theories can be traced to their being the residual symmetry algebras when certain firstclass constraints are placed on KacMoody algebras. In particular, their occurrence in 2dimensional Toda theories is explained by the fact that the Toda theories can be regarded as constrained WessZuminoNovikovWitten (WZNW) theories. The general form of such firstclass constraint for WZNW theories is investigated, and is shown to lead to a wider class of twodimensional integrable systems, all of which have Walgebras as symmetry algebras.   
Reference
 Z. Naturforsch. 52a, 79—85 (1997)   
Published
 1997   
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20  Author
 Claudio Teitelboim  Requires cookie*   Title
 Gravitation Theory in Path Space* *    Abstract
 A formulation of gravitation theory originally proposed by Mandelstam is reexamined. The idea is to avoid the use of coordinates while staying in the continuum. This is accomplished by regarding a point as the end of a path. The theory is then formulated in the space of all paths. The analysis relies on the properties of path deformations. These deformations play the role of gauge transformations in path space. Their algebra is established. It closes if and only if the defining conditions of a riemannian geometry hold (Bianchi identity and vanishing of the antisymmetric part of the Riemann tensor in three of its indices). Two problems faced by Mandelstam are solved: (i) An explicit formula is given which establishes when two neighboring paths end at the same point, (ii) An action principle is given, in terms of a functional integral over path space. It is also indicated how to reconstruct the metric from the curvature through gauge fixing in path space. Brief comments are offered on the possibility of developing an invariant description of loops regarded as boundaries of twodimensional surfaces.   
Reference
 Z. Naturforsch. 52a, 86—96 (1997)   
Published
 1997   
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