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Author: Julian Lawrynowicz Publisher: Springer Science & Business Media ISBN: 9401118965 Category : Mathematics Languages : en Pages : 470
Book Description
This volume presents a collection of papers on geometric structures in the context of Hurwitz-type structures and applications to surface physics. The first part of this volume concentrates on the analysis of geometric structures. Topics covered are: Clifford structures, Hurwitz pair structures, Riemannian or Hermitian manifolds, Dirac and Breit operators, Penrose-type and Kaluza--Klein-type structures. The second part contains a study of surface physics structures, in particular boundary conditions, broken symmetry and surface decorations, as well as nonlinear solutions and dynamical properties: a near surface region. For mathematicians and mathematical physicists interested in the applications of mathematical structures.
Author: Julian Lawrynowicz Publisher: Springer Science & Business Media ISBN: 9401118965 Category : Mathematics Languages : en Pages : 470
Book Description
This volume presents a collection of papers on geometric structures in the context of Hurwitz-type structures and applications to surface physics. The first part of this volume concentrates on the analysis of geometric structures. Topics covered are: Clifford structures, Hurwitz pair structures, Riemannian or Hermitian manifolds, Dirac and Breit operators, Penrose-type and Kaluza--Klein-type structures. The second part contains a study of surface physics structures, in particular boundary conditions, broken symmetry and surface decorations, as well as nonlinear solutions and dynamical properties: a near surface region. For mathematicians and mathematical physicists interested in the applications of mathematical structures.
Author: K. Kodaira Publisher: Springer Science & Business Media ISBN: 1461385903 Category : Mathematics Languages : en Pages : 476
Book Description
This book is an introduction to the theory of complex manifolds and their deformations. Deformation of the complex structure of Riemann surfaces is an idea which goes back to Riemann who, in his famous memoir on Abelian functions published in 1857, calculated the number of effective parameters on which the deformation depends. Since the publication of Riemann's memoir, questions concerning the deformation of the complex structure of Riemann surfaces have never lost their interest. The deformation of algebraic surfaces seems to have been considered first by Max Noether in 1888 (M. Noether: Anzahl der Modulen einer Classe algebraischer Fliichen, Sitz. K6niglich. Preuss. Akad. der Wiss. zu Berlin, erster Halbband, 1888, pp. 123-127). However, the deformation of higher dimensional complex manifolds had been curiously neglected for 100 years. In 1957, exactly 100 years after Riemann's memoir, Frolicher and Nijenhuis published a paper in which they studied deformation of higher dimensional complex manifolds by a differential geometric method and obtained an important result. (A. Fr61icher and A. Nijenhuis: A theorem on stability of complex structures, Proc. Nat. Acad. Sci., U.S.A., 43 (1957), 239-241).
Author: Volker Dietrich Publisher: Springer Science & Business Media ISBN: 9401150362 Category : Mathematics Languages : en Pages : 458
Book Description
Clifford Algebras continues to be a fast-growing discipline, with ever-increasing applications in many scientific fields. This volume contains the lectures given at the Fourth Conference on Clifford Algebras and their Applications in Mathematical Physics, held at RWTH Aachen in May 1996. The papers represent an excellent survey of the newest developments around Clifford Analysis and its applications to theoretical physics. Audience: This book should appeal to physicists and mathematicians working in areas involving functions of complex variables, associative rings and algebras, integral transforms, operational calculus, partial differential equations, and the mathematics of physics.
Author: Stancho Dimiev Publisher: World Scientific ISBN: 9810245971 Category : Mathematics Languages : en Pages : 220
Book Description
This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings will be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields.
Author: Stancho Dimiev Publisher: World Scientific ISBN: 9814491217 Category : Mathematics Languages : en Pages : 220
Book Description
This workshop brought together specialists in complex analysis, differential geometry, mathematical physics and applications for stimulating cross-disciplinary discussions. The lectures presented ranged over various current topics in those fields. The proceedings will be of value to graduate students and researchers in complex analysis, differential geometry and theoretical physics, and also related fields.
Author: E. Ramirez de Arellano Publisher: Birkhäuser ISBN: 3034886985 Category : Mathematics Languages : en Pages : 282
Book Description
This volume, addressed to researchers and postgraduate students, compiles up-to-date research and expository papers on different aspects of complex analysis, including relations to operator theory and hypercomplex analysis. Subjects include the Schrödinger equation, subelliptic operators, Lie algebras and superalgebras, among others.
Author: Rafal Ablamowicz Publisher: Springer Science & Business Media ISBN: 1461213681 Category : Mathematics Languages : en Pages : 470
Book Description
The plausible relativistic physical variables describing a spinning, charged and massive particle are, besides the charge itself, its Minkowski (four) po sition X, its relativistic linear (four) momentum P and also its so-called Lorentz (four) angular momentum E # 0, the latter forming four trans lation invariant part of its total angular (four) momentum M. Expressing these variables in terms of Poincare covariant real valued functions defined on an extended relativistic phase space [2, 7J means that the mutual Pois son bracket relations among the total angular momentum functions Mab and the linear momentum functions pa have to represent the commutation relations of the Poincare algebra. On any such an extended relativistic phase space, as shown by Zakrzewski [2, 7], the (natural?) Poisson bracket relations (1. 1) imply that for the splitting of the total angular momentum into its orbital and its spin part (1. 2) one necessarily obtains (1. 3) On the other hand it is always possible to shift (translate) the commuting (see (1. 1)) four position xa by a four vector ~Xa (1. 4) so that the total angular four momentum splits instead into a new orbital and a new (Pauli-Lubanski) spin part (1. 5) in such a way that (1. 6) However, as proved by Zakrzewski [2, 7J, the so-defined new shifted four a position functions X must fulfill the following Poisson bracket relations: (1.
Author: Rafał Abłamowicz Publisher: Springer Science & Business Media ISBN: 9780817641825 Category : Mathematics Languages : en Pages : 500
Book Description
The first part of a two-volume set concerning the field of Clifford (geometric) algebra, this work consists of thematically organized chapters that provide a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. algebras and their applications in physics. Algebraic geometry, cohomology, non-communicative spaces, q-deformations and the related quantum groups, and projective geometry provide the basis for algebraic topics covered. Physical applications and extensions of physical theories such as the theory of quaternionic spin, a projective theory of hadron transformation laws, and electron scattering are also presented, showing the broad applicability of Clifford geometric algebras in solving physical problems. Treatment of the structure theory of quantum Clifford algebras, the connection to logic, group representations, and computational techniques including symbolic calculations and theorem proving rounds out the presentation.
Author: Vladimir Dotsenko Publisher: Cambridge University Press ISBN: 1108967027 Category : Mathematics Languages : en Pages : 188
Book Description
Covering an exceptional range of topics, this text provides a unique overview of the Maurer—Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a new conceptual treatment of the twisting procedure, guiding the reader through various versions with the help of plentiful motivating examples for graduate students as well as researchers. Topics covered include a novel approach to the twisting procedure for operads leading to Kontsevich graph homology and a description of the twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras using the biggest deformation gauge group ever considered. The book concludes with concise surveys of recent applications in areas including higher category theory and deformation theory.
Author: Julian Lawrynowicz
Author: Julian Lawrynowicz
Author: K. Kodaira
Author: Julian Lawrynowicz
Author: Volker Dietrich
Author: Stancho Dimiev
Author: Stancho Dimiev
Author: E. Ramirez de Arellano
Author: Rafal Ablamowicz
Author: Rafał Abłamowicz
Author: Vladimir Dotsenko