دانلود کتاب Mathematical physics 2000

The area of automorphic representations is a natural continuation of studies in the 19th and 20th centuries on number theory and modular forms. A guiding principle is a reciprocity law relating infinite dimensional automorphic representations with finite dimensional Galois representations. Simple relations on the Galois side reflect deep relations on the automorphic side, called “liftings.” This in-depth book concentrates on an initial example of the lifting, from a rank 2 symplectic group PGSp(2) to PGL(4), reflecting the natural embedding of Sp(2,C) in SL(4, C). It develops the technique of comparing twisted and stabilized trace formulae. It gives a detailed classification of the automorphic and admissible representation of the rank two symplectic PGSp(2) by means of a definition of packets and quasi-packets, using character relations and trace formulae identities. It also shows multiplicity one and rigidity theorems for the discrete spectrum. Applications include the study of the decomposition of the cohomology of an associated Shimura variety, thereby linking Galois representations to geometric automorphic representations. To put these results in a general context, the book concludes with a technical introduction to Langlands’ program in the area of automorphic representations. It includes a proof of known cases of Artin’s conjecture Modern mathematical physics - what it should be, L.D. Faddeev; new applications of the chiral anomaly, J. Frohlich and B. Pedrini; fluctuations and entropy-driven space-time intermittency in Navier-Stokes fluids, G. Gallavotti; superstrings and the unification of the physical forces, M.B. Green; questions in quantum physics - a personal view, R. Haag; what good are quantum field theory infinites? R. Jackiw; constructive quantum field theory, A. Jaffe; Fourier's law - a challenge to theorists, F. Bonetto et al; the "corpuscular" structure of the spectra of operators describing large systems, R.A. Minlos; vortex-and magneto-dynamics - a topological perspective, H.K. Moffatt; gauge theory - the gentle revolution, L. O'Raifeartiagh; random matrices as paradigm, L. Pastur; wavefunction collapse as a real gravitational effect, R. Penrose; Schrodinger equations in the 21st century, B. Simon; the classical three-body problem - where is abstract mathematics, physical intuition, computational physics most powerful? H.A. Posch and W. Thirring; infinite particle systems and their scaling limits, S.R.S. Varadhan; supersymmetry - a personal view