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 entire ultrametric box is especially defined through the round filters and the monotonous filters on D, particularly 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 can be utilized to the differential equation y'=hy (y,h analytic components on D), analytic interpolation, p-adic team duality on meromorphic items and to the p-adic Fourier rework 1. 30 Years in Mathematical Physics -- 2. Perturbation idea for Gauge-Invariant Fields / V.N. Popov and L. Faddev -- three. The Feynman quintessential for Singular Lagrangians -- four. Covariant Quantization of the Gravitational box / V.N. Popov and L. Faddev -- five. creation to useful equipment -- 6. Inverse challenge of Quantum Scattering idea. II -- 7. Quantum thoroughly Integrable versions in box conception -- eight. The Quantum approach to the Inverse challenge and the Heisenberg XYZ version / L.A. Takhtadzhan and L. Faddev -- nine. Integrable types 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 conception of Gravitation -- 14. Lagrangian Mechanics in Invariant shape / A.M. Vershik and L. Faddev

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8) the factor <«C(x)that really does not depend on F Jo and perform a translation F{o - FF ^ 3f d • c,us inducing the transformations: Let c 0 be a solution of the equation: which can be expressed by a Green's function depending on B (cf. Ref. the S -function appears asTj^(CC + 6 C B* , d-C]) and we can put c = 0 everywhere except when equal to the argument of this function. 8) can be transformed, up to an infinite factor, to the form where and The relations obtained look like the usual formulae of quantization of a classical Hamiltonian system using Feynman method (cf.

Transl. (2) 60 (1967). b) On expansions in functions that are solutions of a scattering problem, Dokl. Akad. Nauk SSSR 104 (1955), 360-363. (Russian) 27 30 YEARS IN MATHEMATICAL PHYSICS 27 5. Norman Levinson, On the uniqueness of the potential in a Schrodinger equation for a given asymptotic phase, Danske Vid. Selsk. -Fys. Medd. 25 (1949), no. 9. 6. I. M. Gel'fand and B. M. Levitan, On the determination of a differential equation from its spectral function, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 309-360; English transl.

Phys. Rev. 101, 1957, (1956). "Garrod, C, Rev. Mod. Phys. 38, 483, (1966). 12 Matthews, P. , Relativistic Quantum Theory of the Interactions of the Elemen tary Particles, Russian translation (1959). , The Theory of Space, Time and Gravitation, issued by the State Publishing Department, Moscow, 1955 (in Russian). 52 THE FEYNMAN INTEGRAL FOR SINGULAR LAGRANGIANS L. D. F a d d e e v A generalization is obtained for the continual Feynman integral, adapted for the quantization of a mechanical system describable by a singular Lagrangian.

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