Titlebook: Quantum Field Theory: Perspective and Prospective; Cécile DeWitt-Morette,Jean-Bernard Zuber Book 1999 Springer Science+Business Media Dord

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The Peierls Bracket,isson bracket of field theory. It is applicable to bosonic and fermionic observables equally. It is as well defined for systems with constraints as those without. If the constraints are associated with local invariances it is defined for observables (invariants) only, and its use avoids the necessit

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Quantized Branes and Symmetries of String Theory,e the origin of the four-dimensional interactions and their gauge bosons from ten or eleven-dimensional coordinate invariance. Supersymmetry provides the origin of fermions. Supersymmetry breaking will provide the origin of mass. In addition, several discrete symmetry groups, including the modular g

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Instructive History of the Quantum Inverse Scattering Method,s described in a short and famous now research letter by Gardner, Green, Kruskal and Miura [2] in 1967. Its quantum version which is ten years younger was devised mostly in Leningrad (now St. Petersburg). In what follows I shall underline some highlights and lessons of this latter development.

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The Electron is Inexhaustible,University, in 1996. It has first been published in the proceedings of this conference, edited by Hugo Rossi and published by the American Mathematical Society in 1999. It summarizes some of the modest contributions of the author and his collaborators in two areas of mathematical physics that have s

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Exact Solution of Random Tiling Models,icrystalline phase. For systems where entropy plays the dominant role, random tiling models are the appropriate description. These are discrete statistical models, without an underlying lattice. Several, though very few, quasicrystalline random tilings have been solved exactly, in the sense that the

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Dimensionally Reduced Chern-Simons Terms and Their Solitons,t equations of motion are derived and reduced dimensionally in time or in space. Interesting solitonic equations emerge and their solutions are described. Finally, we consider a Chern-Simons term in three-dimensional Euclidean space, reduced by spherical symmetry, and we discuss its effect on monopo

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BPS Branes in Supergravity,ogomol’ny-Prasad-Sommerfield bounds on their energy densities and are the carriers of the .-form charges that appear in the supersymmetry algebra. The simplest such solutions have the character of (. + 1)-dimensional Poincaré-invariant hyperplanes in spacetime, .branes. Topics covered include the re

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