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Author: Harold G. Dales Publisher: Oxford University Press ISBN: 9780198539919 Category : Mathematics Languages : en Pages : 378
Book Description
Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.
Author: Harold G. Dales Publisher: Oxford University Press ISBN: 9780198539919 Category : Mathematics Languages : en Pages : 378
Book Description
Super-fields are a class of totally ordered fields that are larger than the real line. They arise from quotients of the algebra of continuous functions on a compact space by a prime ideal, and generalize the well-known class of ultrapowers, and indeed the continuous ultrapowers. These fields are an important topic in their own right and have many surprising applications in analysis and logic. The authors introduce these exciting new fields to mathematicians, analysts, and logicians, including a natural generalization of the real line R, and resolve a number of open problems. After an exposition of the general theory of ordered fields and a careful proof of some classic theorems, including Kapansky's embedding, they establish important new results in Banach algebra theory, non-standard analysis, and model theory.
Author: H.C. Lee Publisher: Springer Science & Business Media ISBN: 1461309131 Category : Science Languages : en Pages : 594
Book Description
The Super Field Theory Workshop, held at Simon Fraser University, Vancouver, Canada July 25 - August 5, 1986 was originally intended to be a sequel to the 1983 Chalk River Workshop on Kaluza-Klein Theories and the 1985 Workshop on Quantum Field Theories held at the University of Western Ontario. The scope of the workshop was therefore not to be very big, with a program of about 20 papers, an anticipated 30 to 45 participants, and with much time scheduled for discussion and personal contact. These goals were soon changed in the face of wide interest in the workshop, both for participation and for giving talks, so that the workshop materialized with about 90 participants and 40 talks. This volume contains the texts, some considerably expanded from the oral version, of most of the talks pre sented at the workshop. Not included are a few talks whose manuscripts were not made available to the editors. In the last few years the subject of particle physics and unified field theory has developed in a way not witnessed in the last fifty years: a confluence with mathematics, especially in geometry, topology and algebra at an advanced level. This has vastly expanded the horizon of the disci pline and heightened the expectation that a true understanding of the fun damental laws of physics may soon be within reach. Most aspects of this new development are covered, many in pedagogical detail, by articles in this volume.
Author: Max Dickmann Publisher: Cambridge University Press ISBN: 1107146720 Category : Mathematics Languages : en Pages : 652
Book Description
Offers a comprehensive presentation of spectral spaces focussing on their topology and close connections with algebra, ordered structures, and logic.
Author: Arnold Beckmann Publisher: Springer ISBN: 3319401890 Category : Computers Languages : en Pages : 388
Book Description
This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.
Author: Sergio M. Kuzenko Publisher: CRC Press ISBN: 9780750305068 Category : Science Languages : en Pages : 680
Book Description
Ideas and Methods of Supersymmetry and Supergravity: Or a Walk Through Superspace provides a comprehensive, detailed, and self-contained account of four dimensional simple supersymmetry and supergravity. Throughout the book, the authors cultivate their material in detail with calculations and full discussions of the fundamental ideas and motivations. They develop the subject in its superfield formulations but where appropriate for illustration, analogy, and comparison with conventional field theory, they use the component formulation. The book discusses many subjects that, until now, can only be found in the research literature. In addition, it presents a plethora of new results. Combining classical and quantum field theory with group theory, differential geometry, and algebra, the book begins with a solid mathematical background that is used in the rest of the book. The next chapter covers algebraic aspects of supersymmetry and the concepts of superspace and superfield. In the following chapters, the book presents classical and quantum superfield theory and the superfield formulation of supergravity. A synthesis of results and methods developed in the book, the final chapter concludes with the theory of effective action in curved superspaces. After studying this book, readers should be well prepared to pursue independent research in any area of supersymmetry and supergravity. It will be an indispensable source of reference for advanced graduate students, postdoctoral faculty, and researchers involved in quantum field theory, high energy physics, gravity theory, mathematical physics, and applied mathematics.
Author: Daniel S. Freed Publisher: American Mathematical Soc. ISBN: 1470452065 Category : Algebraic topology Languages : en Pages : 186
Book Description
These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Author: McMaster University Publisher: American Mathematical Soc. ISBN: 9780821860083 Category : Mathematics Languages : en Pages : 362
Book Description
Contains the proceedings of the 1983 Seminar on Quadratic and Hermitian Forms held at McMaster University, July 1983. Between 1945 and 1965, most of the work in quadratic (and hermitian) forms took place in arithmetic theory (M Eichler, M Kneser, O T O'Meara).
Author: Yoshiaki Tanii Publisher: Springer ISBN: 4431548289 Category : Science Languages : en Pages : 134
Book Description
This book is a pedagogical introduction to supergravity, a gravitational field theory that includes supersymmetry (symmetry between bosons and fermions) and is a generalization of Einstein's general relativity. Supergravity provides a low-energy effective theory of superstring theory, which has attracted much attention as a candidate for the unified theory of fundamental particles, and it is a useful tool for studying non-perturbative properties of superstring theory such as D-branes and string duality. This work considers classical supergravities in four and higher spacetime dimensions with their applications to superstring theory in mind. More concretely, it discusses classical Lagrangians (or field equations) and symmetry properties of supergravities. Besides local symmetries, supergravities often have global non-compact symmetries, which play a crucial role in their applications to superstring theory. One of the main features of this book is its detailed discussion of these non-compact symmetries. The aim of the book is twofold. One is to explain the basic ideas of supergravity to those who are not familiar with it. Toward that end, the discussions are made both pedagogical and concrete by stating equations explicitly. The other is to collect relevant formulae in one place so as to be useful for applications to string theory. The subjects discussed in this book include the vielbein formulation of gravity, supergravities in four dimensions, possible types of spinors in various dimensions, superalgebras and supermultiplets, non-linear sigma models for non-compact Lie groups, electric-magnetic duality symmetries, supergravities in higher dimensions, dimensional reductions, and gauged and massive supergravities.
Author: Harold G. Dales
Author: Harold G. Dales
Author: Dales
Author: H.C. Lee
Author: Max Dickmann
Author: Arnold Beckmann
Author: Sergio M. Kuzenko
Author: Daniel S. Freed
Author: 
Author: McMaster University
Author: Yoshiaki Tanii