By Faddeev L.D.

ISBN-10: 9810221983

ISBN-13: 9789810221980

ISBN-10: 9810221991

ISBN-13: 9789810221997

The behaviour of the analytic parts on an infraconnected set D in okay an algebraically closed whole 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 components 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 crew 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 indispensable for Singular Lagrangians -- four. Covariant Quantization of the Gravitational box / V.N. Popov and L. Faddev -- five. creation to sensible tools -- 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 types in (1+1)-Dimensional Quantum box thought -- 10. From Integrable versions to Conformal box conception through Quantum teams -- eleven. the hunt for Multidimensional Solitons -- 12. Hamiltonian method of the speculation of Anomalies -- thirteen. The power challenge in Einstein's idea of Gravitation -- 14. Lagrangian Mechanics in Invariant shape / A.M. Vershik and L. Faddev

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Ann. Phys. 15, 437, (1961). ( Phys. Rev. 101, 1957, (1956). "Garrod, C, Rev. Mod. Phys. 38, 483, (1966). 12 Matthews, P. , Relativistic Quantum Theory of the Interactions of the ElemenĀ 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.

32 214 I. INTRODUCTION It is well known that certain difficulties are involved in the quantization of gauge-invariant fields, and that they are due to the singular nature of the Lagrangian concerned. 1 But this technique does not work in the case of a non-abelian gauge group. 2 He noted, for instance, that diagrams with closed loops depend non-trivially on the ongitudinal parts of Green's functions (in internal lines), and the scattering ampliudes obtained were neither unitary nor transverse. 3 As far as we are aware, however, these ules have not been generalized for arbitrary diagrams.

I add only that in 1967 we were scientifically and socially too shy to try to publish such a long article as Paper 2 in some physical journal. I am sure that JETP would have rejected it, and publishing abroad was still very difficult. So we were quite satisfied that at least a short letter was published in Physics Letters and we jumped at the opportunity to publish a detailed exposition of our approach in the preprint series of a new institute of theoretical physics, established by N. N. Bogolyubov in Kiev.

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