By Faddeev L.D.

ISBN-10: 9810221983

ISBN-13: 9789810221980

ISBN-10: 9810221991

ISBN-13: 9789810221997

The behaviour of the analytic components on an infraconnected set D in ok an algebraically closed whole ultrametric box is especially defined via the round filters and the monotonous filters on D, in particular the T-filters: zeros of the weather, Mittag-Leffler sequence, factorization, Motzkin factorization, greatest precept, injectivity, algebraic houses of the algebra of the analytic parts on D, difficulties of analytic extension. this is often utilized to the differential equation y'=hy (y,h analytic parts on D), analytic interpolation, p-adic workforce duality on meromorphic items and to the p-adic Fourier remodel 1. 30 Years in Mathematical Physics -- 2. Perturbation conception for Gauge-Invariant Fields / V.N. Popov and L. Faddev -- three. The Feynman fundamental for Singular Lagrangians -- four. Covariant Quantization of the Gravitational box / V.N. Popov and L. Faddev -- five. advent to useful equipment -- 6. Inverse challenge of Quantum Scattering thought. II -- 7. Quantum thoroughly Integrable types in box idea -- eight. The Quantum approach to the Inverse challenge and the Heisenberg XYZ version / L.A. Takhtadzhan and L. Faddev -- nine. Integrable versions in (1+1)-Dimensional Quantum box conception -- 10. From Integrable versions to Conformal box concept through Quantum teams -- eleven. the quest for Multidimensional Solitons -- 12. Hamiltonian method of the speculation of Anomalies -- thirteen. The strength challenge in Einstein's concept of Gravitation -- 14. Lagrangian Mechanics in Invariant shape / A.M. Vershik and L. Faddev

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Much more painful are missed opportunities (as Dyson put it). It is difficult to suppress the jealousy when a result you were close to is obtained by another. You cannot help asking yourself what led you astray, what kind of blinders obscured your imagination. Such speculations could be useful for future scientific activities. In my life the role of the blinders has been played in the most dramatic cases by my hostility toward spontaneous breakdown of symmetry. Recently with Polyakov I came to see clearly how the education in statistical physics he got in his youth helped him to work in quantum field theory.

REFERENCES 1Bogoliubov and Shirkov, An Introduction to the Theory of Quantized Fields, Moscow 1957 (in Russian). 2 Feynman, R. P. Acta Phys, Polonica, 24, 6 (12), (1963). 3 De Witt, B. , Relativity, Groups and Topology, London, (1964). , Phys. Rev. 125, 1043, (1962); Phys. Rev. 127, 321, (1962). 5 Feynman, R. , Phys. Rev. 80, 440, (1950). 6 Ward, J. C, Phys. Rev. 77, 293L, (1950); Phys. Rev. 78, 182L, (1950). , Phys. , 115, 721, (1959). 8 Yang, C. N. and Mills, R. , Phys. Rev. 96, 191, (1959). 'Glashow, S.

P. Novikov for constructive and stimulating competition. My students V. S. Buslaev, V. N. Popov, 0. A. Yakubovskii, B. S. Pavlov, P. P. Kulish, and S. P. Merkur'ev, now over forty, the younger A. V. Venkov, I. Ya. Arefeva, M. M. Skriganov, V. V. Matveev, L. A. Takhtadzhyan, M. A. SemenovTyan-Shanskii, A. G. Relman, and V. E. Korepin, and the scientific youths E. K. Sklyanin, F. A. Smirnov, N. Yu. Reshetikhin, V. O. Tarasov, and S. L. Shatashvili make up a group to be proud of. My association and joint work with them constitute the basic substance of my present scientific life.

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