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Iagolnitzer, D.

CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique

CEA Centre d'Etudes Nucleaires de Saclay, 91 - Gif-sur-Yvette (France). Service de Physique Theorique

AbstractAbstract

[en] An introduction to recent works, in S-matrix theory and axiomatic field theory, on the analysis and derivation of momentum-space analyticity properties of the multiparticle S matrix is presented. It includes an historical survey, which outlines the successes but also the basic difficulties encountered in the sixties in both theories, and the evolution of the subject in the seventies

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Feb 1981; 77 p; 20. Schladming winter school of theoretical physics; Schladming, Austria; 15 - 27 Feb 1981

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[en] This paper intends to investigate the axiomatic foundations of algebra, as they were presented in the book of algebra of al-Khwarizmi (9 th century), and as they were developed in many subsequent Arabic works. The paper gives also a description of algebra evolution towards a discipline independent ofgeometry and arithmetic: the two disciplines whosemarriage had led to its birth.By an in depth reading of some details in the text of al Khwarizmi , we concluded that this mathematician intended to lay down the axiomatic foundations of that new discipline. His resort to arithmetical and geometrical means was a way of making his theory more accessible. He used them to justify the axioms: those that were not explicitly introduced per se, and those that were remained implicit. The paper also relies on some unedited writingsof al-Khwarizmi's successors, which could shedlight on the ways they used to consolidate the foundations of algebra and improve its methods. (author)

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Al-Khwarizmi et le fondement axiomatique de l'algèbre

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28 refs.

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Lebanese Science Journal; ISSN 1561-3410; ; (16,1); p. 107-126

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[en] A framework is proposed in which supersymmetries can be defined in the language of axiomatic quantum field theory. This framework contains a nuclear *-algebra into which the Borchers' algebra of a general supermultiplet is embedded through a map which, in some sense, generalizes the concept of a superfield. The algebra of supersymmetry is represented on the constructed nuclear *-algebra as an algebra of graded derivations. Since a graded derivation cannot be integrated to a usual automorphism group (only to a formal group), it is assumed that conditions at the Lie algebraic level are strong enough to produce supersymmetric behavior. Thus it is conjectured that if a functional of the nuclear *-algebra is annihilated by the algebra of supersymmetry, and if this functional is related to a state of the Borchers' algebra through the embedding map, this state through the GNS construction gives rise to a supersymmetric Wightman theory. This supersymmetric condition produces an infinite number of correlations among the n-point functions. The 2-point Wightman functions for a general supermultiplet are completely analyzed and it is found that their behavior is similar to the perturbative results. Finally it is proved that the free fields satisfy these supersymmetric conditions

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J. Math. Phys. (N.Y.); ISSN 0022-2488; ; v. 22(3); p. 590-599

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Fonseca, Renato M.; Malinský, Michal; Staub, Florian, E-mail: renato.fonseca@ist.utl.pt, E-mail: malinsky@ipnp.troja.mff.cuni.cz, E-mail: fnstaub@th.physik.uni-bonn.de

arXiv e-print [ PDF ]

arXiv e-print [ PDF ]

AbstractAbstract

[en] We work out a set of simple rules for adopting the two-loop renormalization group equations of a generic gauge field theory given in the seminal works of Machacek and Vaughn to the most general case with an arbitrary number of Abelian gauge factors and comment on the extra subtleties possibly encountered upon matching a set of effective gauge theories in such a framework

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S0370-2693(13)00773-9; Available from http://dx.doi.org/10.1016/j.physletb.2013.09.042; Copyright (c) 2013 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

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[en] The main point of this presentation is to explain a connection between the now celebrated work of Yang and Mills on gauge fields and some work of the authors which goes back to the same period. The work of Yang and Mills was published in 1954 and the main results were independently found by Shaw and included in his 1954 Ph.D. thesis. The authors work was done in the early 1950's, but was first published in 1963 in a long survey article on group representations. This article was based on lectures given in 1961. This work did not overlap with that of Yang, Mills, and Shaw and was done in a completely different spirit. The connection between the two is explained later in the paper. The so-called 'Yang-Mills trick' emerges naturally from a development of the authors old work on the axiomatics of quantum mechanical free particles, and in such a way as to make at least one ad hoc definition appear naturally

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International Journal of Theoretical Physics; ISSN 0020-7748; ; CODEN IJTPBM; v. 32(10); p. 1643-1659

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Raptis, I.

Newcastle upon Tyne Univ. (United Kingdom)

Newcastle upon Tyne Univ. (United Kingdom)

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No abstract available

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May 1996; [vp.]; Available from British Library Document Supply Centre- DSC:DXN015238; Thesis (Ph.D.)

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[en] Exploiting the properties of the Jost-Lehmann-Dyson representation, it is shown that in 1+2 or more spacetime dimensions, a nonempty smallest localization region can be associated with each local observable (except for the c-numbers) in a theory of local observables in the sense of Araki, Haag, and Kastler. Necessary and sufficient conditions are given that observables with spacelike separated localization regions commute (locality of the net alone does not imply this yet). (orig.)

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26 refs.

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[en] The author characterizes functions on an Abelian group which satisfy certain algebraic conditions. This result is then applied to obtain generalizations of the Jordan-von Neumann theorem on quadratic forms. These last results are then used to prove a theorem on observable systems in axiomatic quantum mechanics. (Auth.)

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Letters in Mathematical Physics; ISSN 0377-9017; ; v. 3(2); p. 127-133

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[en] The authors study the modular pairs of a complete orthomodular lattice i.e. a CROC. They propose the concept of m-morphism as a mapping which preserves the lattice structure, the orthogonality and the property to be a modular pair. A characterization of the m-morphisms in the case of the complex Hilbert space is given to justify this concept. (Auth.)

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Letters in Mathematical Physics; ISSN 0377-9017; ; v. 3(1); p. 1-10

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[en] The study examines general axiomatics of Balinski and Young and analyzes existed proportional representation methods using this approach. The second part of the paper provides new axiomatics based on rational choice models. New system of axioms is applied to study known proportional representation systems. It is shown that there is no proportional representation method satisfying a minimal set of the axioms (monotonicity and neutrality).

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ICNAAM 2010: International conference of numerical analysis and applied mathematics 2010; Rhodes (Greece); 19-25 Sep 2009; (c) 2010 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

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