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1	Author	Emil Wolf	Requires cookie*
	Title	Sudarshan's Optical Researches
	Abstract	As is evident from the scope of this meeting, Sudar-shan's scientific interests and contributions have cov-ered a broad area of physics. Among them optics plays a very prominent role. I say optics rather than quan-tum optics, as is so fashionable these days, because many of Sudarshan's investigations have been partic-ularly concerned with some striking analogies and some remarkable similarities which were found to exist between these two fields, particularly in the do-main of optical coherence. In fact some of Sudarshan's contributions to this area have been largely responsi-ble 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 inter-est in this field.
	Reference	Z. Naturforsch. 52a, 2 (1997)
	Published	1997
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	Identifier	ZNA-1997-52a-0002
	Volume	52

2	Author	R. E. Marshak	Requires cookie*
	Title	The Pain and Joy of a Major Scientific Discovery
	Abstract	This three-day workshop is being held on the occa-sion of George Sudarshan's 60th birthday to do honor to his significant and many-faceted contributions to theoretical physics. The nature and extent of these contributions are being covered by a host of distin-guished 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 four-fermion interaction, otherwise known as the universal V-A theory of weak interactions. George Sudarshan's the-sis problem turned out to be so exciting that his pro-fessor entered as a part-time 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 thirty-four 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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0003.pdf
	Identifier	ZNA-1997-52a-0003
	Volume	52

3	Author	Iwo Bialynicki-Birula, P. J. Morrison	Requires cookie*
	Title	Quantum Mechanics as a Generalization of Nambu Dynamics to the Weyl-Wigner 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 Weyl-Wigner 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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0009.pdf
	Identifier	ZNA-1997-52a-0009
	Volume	52

4	Author	Berthold-Georg Englert	Requires cookie*
	Title	Time Reversal Symmetry and Humpty-Dumpty
	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 Stern-Gerlach interferometer demonstrates that even undoing the evolution partially only may require sub-microscopic precision in controlling a macroscopic apparatus.
	Reference	Z. Naturforsch. 52a, 13—14 (1997)
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0013.pdf
	Identifier	ZNA-1997-52a-0013
	Volume	52

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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0015.pdf
	Identifier	ZNA-1997-52a-0015
	Volume	52

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 spin-1/2 EPR gedanken-experiment is possible using the spin-1/2 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 excitation-ionization 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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0020.pdf
	Identifier	ZNA-1997-52a-0020
	Volume	52

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. Experimen-tal tests of new predictions are discussed.
	Reference	Z. Naturforsch. 52a, 25—30 (1997); received November 11 1995
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0025.pdf
	Identifier	ZNA-1997-52a-0025
	Volume	52

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 so-called "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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0031.pdf
	Identifier	ZNA-1997-52a-0031
	Volume	52

9	Author	ArjenduK. Pattanayak, WilliamC. Schieve	Requires cookie*
	Title	Predicting Two Dimensional Hamiltonian Chaos
	Abstract	We use geometrical analysis to show that the Toda-Brumer-Duff criterion for transition to chaos is a simple application of Jacobi's equation. Further, we propose a new criterion for this transition for two-dimensional hamiltonian systems and summarize the results.
	Reference	Z. Naturforsch. 52a, 34—36 (1997)
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0034.pdf
	Identifier	ZNA-1997-52a-0034
	Volume	52

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 meth-ods 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 non-unitary 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 co-workers. 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 corre-sponds 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 S-matrix theory.
	Reference	Z. Naturforsch. 52a, 37—45 (1997)
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0037.pdf
	Identifier	ZNA-1997-52a-0037
	Volume	52

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 non-unitary as well as unitary transforma-tions. The principle leads to a non-unitary 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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	Identifier	ZNA-1997-52a-0046
	Volume	52

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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0049.pdf
	Identifier	ZNA-1997-52a-0049
	Volume	52

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 semi-classical solutions for a spin-boson Hamiltonian system. We obtain quantum averages by numerically integrating the appropriate Liouville-Von Neumann equations of motion and find these averages to be less erratic than the corresponding chaotic semi-classical 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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0053.pdf
	Identifier	ZNA-1997-52a-0053
	Volume	52

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 <jr-factors 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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0059.pdf
	Identifier	ZNA-1997-52a-0059
	Volume	52

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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0063.pdf
	Identifier	ZNA-1997-52a-0063
	Volume	52

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 non-trivial geometry of the fiber bundle: Hilbert space space of states. The analysis is performed working in the general non-adiabatic setting.
	Reference	Z. Naturforsch. 52a, 66—68 (1997); received July 26 1995
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0066.pdf
	Identifier	ZNA-1997-52a-0066
	Volume	52

17	Author	J. R. Klauder	Requires cookie*
	Title	Coherent States and Coordinate-Free 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 coordinate-free a form as holds in classical mechanics.
	Reference	Z. Naturforsch. 52a, 69—75 (1997)
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0069.pdf
	Identifier	ZNA-1997-52a-0069
	Volume	52

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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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0076.pdf
	Identifier	ZNA-1997-52a-0076
	Volume	52

19	Author	L. O 'raifeartaigh	Requires cookie*
	Title	W-Algebras
	Abstract	W-algebras are defined as polynomial extensions of the Virasoro algebra by primary fields, and they occur in a natural manner in the context of two-dimensional 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 first-class constraints are placed on Kac-Moody algebras. In particular, their occurrence in 2-dimensional Toda theories is explained by the fact that the Toda theories can be regarded as constrained Wess-Zumino-Novikov-Witten (WZNW) theories. The general form of such first-class constraint for WZNW theories is investigated, and is shown to lead to a wider class of two-dimensional integrable systems, all of which have W-algebras as symmetry algebras.
	Reference	Z. Naturforsch. 52a, 79—85 (1997)
	Published	1997
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	TEI-XML for	default:Reihe_A/52/ZNA-1997-52a-0079.pdf
	Identifier	ZNA-1997-52a-0079
	Volume	52

20	Author	Claudio Teitelboim	Requires cookie*
	Title	Gravitation Theory in Path Space* *
	Abstract	A formulation of gravitation theory originally proposed by Mandelstam is re-examined. 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 transfor-mations 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 com-ments are offered on the possibility of developing an invariant description of loops regarded as boundaries of two-dimensional surfaces.
	Reference	Z. Naturforsch. 52a, 86—96 (1997)
	Published	1997
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	Identifier	ZNA-1997-52a-0086
	Volume	52

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