Diagonalization of Inclusive Sum Rules and Inclusive Bootstrap

Mak, Se-yuen; Tan, Chung-I

doi:10.1103/physrevd.6.1059

Phys. Rev. D

1972

DOI: 10.1103/physrevd.6.1059

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Diagonalization of Inclusive Sum Rules and Inclusive Bootstrap

Se-yuen Mak

Chung-I Tan

Abstract: We introduce the technique of multi-dimensional Laplace transforms under which the inclusive-like sum rules for discontinuities of multiparticle amplitudes can be diagonglized. The resulting equations are simple constraints on our generalized partial-wave amplitudes, and they can be used to impose unitarity conditions for bootstrap models. A simple· example is given to illustrate '752 -the non-linear nature of this "inclusive bootstrap" program.

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1973

1980

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Cited by 4 publications

References 17 publications

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Optical nutation in a gaussian beam resonator

Rohart

Macke

1980

J. Phys. France

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Reçu le 17 janvier 1980, révisé le 24 mars, accepté le 25 mars 1980) Résumé. 2014 Nous examinons la réponse transitoire d'un résonateur plan-sphérique excité continûment et rempli par un gaz optiquement fin qui est brutalement amené en résonance exacte avec le champ excitateur. Contrairement aux traitements antérieurs, notre approche prend en compte la distribution du champ dans le résonateur 2014 aussi bien axiale que transversale 2014 et les mouvements moléculaires à travers l'onde stationnaire. Ceci est obtenu en projetant la polarisation induite dans le gaz sur le mode gaussien fondamental du résonateur et les résultats sont donnés sous une forme quasi analytique. Une réponse oscillante n'est obtenue que lorsque la fréquence de Rabi est grande devant l'élargissement Doppler et le résonateur de mauvaise qualité. Certaines de nos prévisions théoriques ont été confirmées par une expérience à une longueur d'onde de 6 mm. Abstract. 2014 We examine the transient behaviour of a plane-spherical resonator driven by a continuous wave and filled by an optically thin gas which is suddenly switched on exact resonance with the driving field. Contrary to previous treatments, the axial and transversal field distributions and the molecular motions through the standing wave are taken into account. This is achieved by projecting the induced gas polarization on the fundamental gaussian mode of the resonator and the results are given in a quasi analytic form. An oscillatory response is only obtained when the Rabi frequency is large with respect to the Doppler line width and for a bad quality resonator. Some of the theoretical predictions have been supported by an experiment at a 6 mm-wavelength.

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Optical nutation in a gaussian beam resonator

Rohart

Macke

1980

J. Phys. France

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Inclusive Approach to the Multiplicity Distribution

Mak

Tan

1973

Phys. Rev. D

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Starting with the Mueller-Regge assumption, a multiperipheral-like integral equation for the multiplicity generating function is constructed and solved. The integral equation, therefore, involves inclusive parameters only. A one-to-one correspondence between our result and that of an exclusive multiperipheral model is established through a proper orthogonal matrix. Explicit expressions for the multiplicity distribution and correlations are obtained. Possible appGcations and generalizations are discussed within the framework of a two-component picture of hadronic productions.

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Rapidity Clusterings in Hadronic Production

Tan¹

1973

Phys. Rev. D

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We elaborate on the role of secondary Regge singularities in the framework of the shortrange correlation picture of hadronic production. Their presence is seen to imply the existence of 'local clusterings" in the rapidity distributions of events with a fixed multiplicity. In this scheme, the approach to the scaling limit in the central region is a manifestation of the "threshold" effect of "cluster" formation. An explicit model is constructed where the scaling limit can be approached from below. This i s then explained from the point of view of Markovian walk in one dimension.

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Diagonalization of Inclusive Sum Rules and Inclusive Bootstrap

Cited by 4 publications

References 17 publications

Optical nutation in a gaussian beam resonator

Optical nutation in a gaussian beam resonator

Inclusive Approach to the Multiplicity Distribution

Rapidity Clusterings in Hadronic Production

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