Series: Modern Birkhauser Classics
Reprint of the 1994 Edition., 1994, XVI, 335 p.
Softcover, ISBN 978-3-0348-0173-7
Due: July 31, 2011
First complete historical description of Unified field theories in this era
Addresses historically interested physicists and mathematicians
The extensive bibliography of original papers also includes important but little known contributions
Despite the rapidly expanding ambit of physical research and the continual appearance of new branches of physics, the main thrust in its development has been the attempt at a theoretical synthesis of the entire body of physical knowledge. Vladimir Vizgin's work presents perhaps the first systematic historico-scientific study of the formation and development of the unified field theories in the general context of 20th century physics. Concentrating on the first three decades of the century and drawing extensively on Russian sources, the author analyses the first successes, failures and paths of further development of the unified field theories. He presents the evolution of these theories as a process of interaction/competition between the geometric field and quantum research programs, and ascertains the relevance of these theories for fundamental concepts in modern field theory.
Preface.- Introduction.- 1 The Electromagnetic Program for the Synthesis of Physics.- 2 The General Theory of Relativity: The Core of the Program of Unified Field Theory.- 3 Weyl's Theory: The First Truly Geometrized Unified Field Theory.- 4 1921: The Pivotal Year of Unified Geometrized Field Theories.- 5 Einstein's Decade of Hopes and Disappointments.- 6 The Role of Unified Geometrized Field Theories in the Genesis and Development of Quantum Theory.- Concluding Remarks.- Bibliography.
Series: Modern Birkhauser Classics
Reprint of the 1995 Edition., 1995, XI, 334 p. 16 illus.
Softcover, ISBN 978-3-0348-0176-8
Due: July 31, 2011
Presents person and work of a distinguished scientific “eccentric Provides a historical account of how Heaviside’s ideas originated Deals with one of the most periods in the history of physics
Oliver Heaviside’s contributions to electromagnetism, electrical engineering, and applied mathematics have consistently attracted attention. Of late they have become a major source for the study of the development of field theory after Maxwell.
From Obscurity to Enigma: The Work of Oliver Heaviside, 1872-1889 is a systematic, in-depth study of the most creative period in Heaviside’s scientific career. During this period he wrote the essays and articles that constitute his two-volume Electrical Papers. Here he presented his novel reformulation of Maxwell’s equations, created the elements of vector algebra, produced the first comprehensive theory of transmission lines, suggested the inductive ≪loading≫ of telegraph and telephone lines to improve long-distance communications, introduced his innovative version of the operational calculus, and made several important contributions to the electrodynamics of moving bodies. From Obscurity to Enigma traces the evolution of Heaviside’s ideas against the background of growing knowledge in basic electromagnetic theory, telegraphy, and telephony at the time. It reveals the thematic coherence that unifies his various publications, and sheds considerable light on the reason for the exclamations of incomprehension that greeted his work from the time of its publication to the present.
I The Enigmatic Legacy of Oliver Heaviside.- II Outlining the Way.- III The Maxwellian Outlook.- IV From Obscurity to Enigma.- Appendix 3.1 Heaviside's Extended Theorem of Divergence.- Appendix 3.2 Unification of Electricity and Magnetism.- Appendix 3.3 Note on Heaviside's Derivation of the Mutual Energy of Two Current Systems.- Appendix 4.1 The KR Law and the Distortionless Condition.- Appendix 4.2 Notes on Heaviside's Operational Calculus.- Bibliography.- Index.
Series: Algebra and Applications, Vol. 15
1st Edition., 2011, XII, 401 p. 6 illus.
Hardcover, ISBN 978-0-85729-715-0
The modular representation theory of Iwahori-Hecke algebras and this theory's connection to groups of Lie type is an area of rapidly expanding interest; it is one that has also seen a number of breakthroughs in recent years. In classifying the irreducible representations of Iwahori-Hecke algebras at roots of unity, this book is a particularly valuable addition to current research in this field. Using the framework provided by the Kazhdan-Lusztig theory of cells, the authors develop an analogue of James' (1970) "characteristic-free'' approach to the representation theory of Iwahori-Hecke algebras in general.
Presenting a systematic and unified treatment of representations of Hecke algebras at roots of unity, this book is unique in its approach and includes new results that have not yet been published in book form. It also serves as background reading to further active areas of current research such as the theory of affine Hecke algebras and Cherednik algebras.
The main results of this book are obtained by an interaction of several branches of mathematics, namely the theory of Fock spaces for quantum affine Lie algebras and Ariki's theorem, the combinatorics of crystal bases, the theory of Kazhdan-Lusztig bases and cells, and computational methods.
This book will be of use to researchers and graduate students in representation theory as well as any researchers outside of the field with an interest in Hecke algebras.
Series: Trends in Logic, Vol. 31
2011, VIII, 194 p. 24 illus.
Hardcover, ISBN 978-94-007-1475-5
The book is a monograph devoted to paradoxes of reasoning in the European tradition of philosophical logic. For each paradox, it analyses important attempts at its solution.The content is arranged according to the new classification of paradoxes presented by the author. The paradoxes discussed in the first three chapters can be called intra-linguistic ones. The first chapter analyzes paradoxes resulting from a clash between a logically correct reasoning and previously accepted opinions. The second one is devoted to paradoxes resulting from the error of ambiguity. The third one analyzes reasonings, whose paradoxical character originates in self-referent language constructions. Chapter four discusses paradoxes which are called ontological ones, whose existence results from a confrontation between the language description of reality and that reality itself.
The book is written in a clear way and does not require advanced knowledge of logic. It is addressed to readers with either humanist or scientific educational background and deals with important problems of language, cognition and reasoning in an accessible way.
Preface.- Introduction.- 1. Sophisms and paralogisms (paradoxes of: horses, Newcomb, Fitch).- 2. Wrong intuition’s paradoxes (paradoxes of: common birthday, approximation, Stevenson’s bottle, Hempel, infinity).- 3. Paradoxes coming from ambiguity (paradoxes of Protagoras, Elektra, horn-headed man, the club without a name, God’s omnipotence, stone) .- 4. Paradoxes of self-reference (Mobius ribbon (band), Klein’s bottle, liar paradox, Buridan, barber, Richard, Berry, Grelling and Nelson, unexpected examination, crocodile).- 5. Ontological paradoxes.- 6. Epilogue.- Bibliography.- Subject index.- Name index.
Series: Advanced Courses in Mathematics - CRM Barcelona
2011, VIII, 150 p. 16 illus. in color.
Softcover, ISBN 978-3-0348-0190-4
Due: July 29, 2011
The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrodinger and wave equations. Several powerful methods from recent top research articles are described in a careful and expository manner.
Content Level ≫ Graduate
Keywords ≫ Boltzmann equations - hyperbolic equations - statistical mechanics
Related subjects ≫ Dynamical Systems & Differential Equations
Foreword. 1 The De Giorgi Method for Nonlocal Fluid Dynamics.- 2 Recent Results on the Periodic Lorentz Gas.- 3 The Boltzmann Equation in Bounded Domains.- 4 The Concentration-Compactness/Rigidity Method for Critical Dispersive and Wave Equations.