An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors

This book is unique compared to the existing literature.

Author: Roldao Da Rocha, Jr.

Publisher: Oxford University Press

ISBN: 9780198782926

Category:

Page: 256

View: 130

This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.
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Clifford Algebras and Spinors

Clifford Algebras and Spinors

This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors.

Author: Pertti Lounesto

Publisher: Cambridge University Press

ISBN: 9780521005517

Category: Mathematics

Page: 338

View: 598

This is the second edition of a popular work offering a unique introduction to Clifford algebras and spinors. The beginning chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.
Categories: Mathematics

Clifford Algebras An Introduction

Clifford Algebras  An Introduction

A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.

Author: D. J. H. Garling

Publisher: Cambridge University Press

ISBN: 9781107096387

Category: Mathematics

Page: 200

View: 809

A straightforward introduction to Clifford algebras, providing the necessary background material and many applications in mathematics and physics.
Categories: Mathematics

Clifford Algebras and their Applications in Mathematical Physics

Clifford Algebras and their Applications in Mathematical Physics

Leading experts in the rapidly evolving field of Clifford (geometric) algebras have contributed to this comprehensive two-volume text.

Author: Rafał Abłamowicz

Publisher: Springer Science & Business Media

ISBN: 0817641823

Category: Mathematics

Page: 461

View: 900

Leading experts in the rapidly evolving field of Clifford (geometric) algebras have contributed to this comprehensive two-volume text. Consisting of thematically organized chapters, the volume is a broad overview of cutting-edge topics in mathematical physics and the physical applications of Clifford algebras. Volume I 'Algebra and Physics' is devoted to the mathematical aspects of Clifford algebras and their applications in physics. Algebraic geometry, cohomology, non-commutative 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, Dirac theory of electron, plane waves and wave packets in electrodynamics, 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, twistor phase space, introduction of a Kaluza--Klein type theory related to Finsler geometry, the connection to logic, group representations, and computational techniques--including symbolic calculations and theorem proving--round out the presentation. Volume 2 'Clifford Analysis' is an up-to-date survey of most aspects of modern-day Clifford analysis. Topics range from applications such as complex-distance potential theory, supersymmetry, and fluid dynamics to Fourier analysis, the study of boundary value problems, and applications to mathematical physics and Schwarzian derivatives in Euclidean space. Among the mathematical topics examined are generalized Dirac operators, monogenic and hypermonogenic functions and their derivatives, Euclidean Beltrami equations, Fourier theory under M\'{o}bius transformations, and applications to operator theory and scattering theory. Given the careful balance of mathematical theory and applications to physics, the two volumes are accessible to graduate students and specialists in the general area of Clifford algebras and their applications.
Categories: Mathematics

An Introduction to Spinors and Geometry with Applications in Physics

An Introduction to Spinors and Geometry with Applications in Physics

This graduate textbook dealing with the modern mathematical techniques of differential geometry and Clifford algebras is written with students of theoretical physics in mind.

Author: Ian M. Benn

Publisher: Adam Hilger

ISBN: STANFORD:36105030473511

Category: Mathematics

Page: 358

View: 548

"...The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of differential geometry and Clifford algebras in classical field theory..."--back cover.
Categories: Mathematics

Clifford Algebras and Lie Theory

Clifford Algebras and Lie Theory

This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator.

Author: Eckhard Meinrenken

Publisher: Springer Science & Business Media

ISBN: 9783642362163

Category: Mathematics

Page: 321

View: 758

This monograph provides an introduction to the theory of Clifford algebras, with an emphasis on its connections with the theory of Lie groups and Lie algebras. The book starts with a detailed presentation of the main results on symmetric bilinear forms and Clifford algebras. It develops the spin groups and the spin representation, culminating in Cartan’s famous triality automorphism for the group Spin(8). The discussion of enveloping algebras includes a presentation of Petracci’s proof of the Poincaré–Birkhoff–Witt theorem. This is followed by discussions of Weil algebras, Chern--Weil theory, the quantum Weil algebra, and the cubic Dirac operator. The applications to Lie theory include Duflo’s theorem for the case of quadratic Lie algebras, multiplets of representations, and Dirac induction. The last part of the book is an account of Kostant’s structure theory of the Clifford algebra over a semisimple Lie algebra. It describes his “Clifford algebra analogue” of the Hopf–Koszul–Samelson theorem, and explains his fascinating conjecture relating the Harish-Chandra projection for Clifford algebras to the principal sl(2) subalgebra. Aside from these beautiful applications, the book will serve as a convenient and up-to-date reference for background material from Clifford theory, relevant for students and researchers in mathematics and physics.
Categories: Mathematics

Spinor Construction of Vertex Operator Algebras Triality and E8 1

Spinor Construction of Vertex Operator Algebras  Triality  and E8 1

Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory. This book accomplishes several goals.

Author: Alex J. Feingold

Publisher: American Mathematical Soc.

ISBN: 9780821851289

Category: Mathematics

Page: 146

View: 938

The theory of vertex operator algebras is a remarkably rich new mathematical field which captures the algebraic content of conformal field theory in physics. Ideas leading up to this theory appeared in physics as part of statistical mechanics and string theory. In mathematics, the axiomatic definitions crystallized in the work of Borcherds and in Vertex Operator Algebras and the Monster, by Frenkel, Lepowsky, and Meurman. The structure of monodromies of intertwining operators for modules of vertex operator algebras yields braid group representations and leads to natural generalizations of vertex operator algebras, such as superalgebras and para-algebras. Many examples of vertex operator algebras and their generalizations are related to constructions in classical representation theory and shed new light on the classical theory. This book accomplishes several goals. The authors provide an explicit spinor construction, using only Clifford algebras, of a vertex operator superalgebra structure on the direct sum of the basic and vector modules for the affine Kac-Moody algebra $D^{(1)}_n$. They also review and extend Chevalley's spinor construction of the 24-dimensional commutative nonassociative algebraic structure and triality on the direct sum of the three 8-dimensional $D_4$-modules. Vertex operator para-algebras, introduced and developed independently in this book and by Dong and Lepowsky, are related to one-dimensional representations of the braid group. The authors also provide a unified approach to the Chevalley, Griess, and $E_8$ algebras and explain some of their similarities. A third goal is to provide a purely spinor construction of the exceptional affine Lie algebra $E^{(1)}_8$, a natural continuation of previous work on spinor and oscillator constructions of the classical affine Lie algebras. These constructions should easily extend to include the rest of the exceptional affine Lie algebras. The final objective is to develop an inductive technique of construction which could be applied to the Monster vertex operator algebra. Directed at mathematicians and physicists, this book should be accessible to graduate students with some background in finite-dimensional Lie algebras and their representations. Although some experience with affine Kac-Moody algebras would be useful, a summary of the relevant parts of that theory is included. This book shows how the concepts and techniques of Lie theory can be generalized to yield the algebraic structures associated with conformal field theory. The careful reader will also gain a detailed knowledge of how the spinor construction of classical triality lifts to the affine algebras and plays an important role in a spinor construction of vertex operator algebras, modules, and intertwining operators with nontrivial monodromies.
Categories: Mathematics

Clifford Geometric Algebras

Clifford  Geometric  Algebras

This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995.

Author: William E. Baylis

Publisher: Springer Science & Business Media

ISBN: 9781461241041

Category: Science

Page: 517

View: 783

This volume is an outgrowth of the 1995 Summer School on Theoretical Physics of the Canadian Association of Physicists (CAP), held in Banff, Alberta, in the Canadian Rockies, from July 30 to August 12,1995. The chapters, based on lectures given at the School, are designed to be tutorial in nature, and many include exercises to assist the learning process. Most lecturers gave three or four fifty-minute lectures aimed at relative novices in the field. More emphasis is therefore placed on pedagogy and establishing comprehension than on erudition and superior scholarship. Of course, new and exciting results are presented in applications of Clifford algebras, but in a coherent and user-friendly way to the nonspecialist. The subject area of the volume is Clifford algebra and its applications. Through the geometric language of the Clifford-algebra approach, many concepts in physics are clarified, united, and extended in new and sometimes surprising directions. In particular, the approach eliminates the formal gaps that traditionally separate clas sical, quantum, and relativistic physics. It thereby makes the study of physics more efficient and the research more penetrating, and it suggests resolutions to a major physics problem of the twentieth century, namely how to unite quantum theory and gravity. The term "geometric algebra" was used by Clifford himself, and David Hestenes has suggested its use in order to emphasize its wide applicability, and b& cause the developments by Clifford were themselves based heavily on previous work by Grassmann, Hamilton, Rodrigues, Gauss, and others.
Categories: Science

Matrix Gateway to Geometric Algebra Spacetime and Spinors

Matrix Gateway to Geometric Algebra  Spacetime and Spinors

In this book we fully integrate the ideas of geometric algebra directly into the fabric of matrix linear algebra. A geometric matrix is a real or complex matrix which is identified with a unique geometric number.

Author: Garret Sobczyk

Publisher:

ISBN: 1704596629

Category:

Page: 188

View: 660

Geometric algebra has been presented in many different guises since its invention by William Kingdon Clifford shortly before his death in 1879. Our guiding principle is that it should be fully integrated into the foundations of mathematics, and in this regard nothing is more fundamental than the concept of number itself. In this book we fully integrate the ideas of geometric algebra directly into the fabric of matrix linear algebra. A geometric matrix is a real or complex matrix which is identified with a unique geometric number. The matrix product of two geometric matrices is just the product of the corresponding geometric numbers. Any equation can be either interpreted as a matrix equation or an equation in geometric algebra, thus fully unifying the two languages. The first 6 chapters provide an introduction to geometric algebra, and the classification of all such algebras. Exercises are provided. The last 3 chapters explore more advanced topics in the application of geometric algebras to Pauli and Dirac spinors, special relativity, Maxwell's equations, quaternions, split quaternions, and group manifolds. They are included to highlight the great variety of topics that are imbued with new geometric insight when expressed in geometric algebra. The usefulness of these later chapters will depend on the background and previous knowledge of the reader.Matrix Gateway to Geometric Algebra will be of interest to undergraduate and graduate students in mathematics, physics and the engineering sciences, who are looking for a unified treatment of geometric ideas arising in these areas at all levels. It should also be of interest to specialists in linear and multilinear algebra, and to mathematical historians interested in the development of geometric number systems.
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Clifford Algebra in Mathematics and Physics

Clifford Algebra in Mathematics and Physics

For example, complex variables, vectors, quaternions, matrix theory, differential forms, tensor calculus, spinors and twistors, are all subsumed under a common approach.The book begins with a brief historical introduction, followed by a ...

Author: Stefano Spezia

Publisher: Arcler Press

ISBN: 1773611267

Category:

Page: 362

View: 907

The Clifford or geometric algebra (GA) is an algebra generated by a vector space with a bilinear form with some special properties. GA is more efficient than the matrix algebra because of the fact that the components of geometric algebra can be expressed without introducing any arbitrary basis and turned out to be a superior mathematical tool which provides a common mathematical language that aids a unified approach and understanding in topics across mathematics, physics and engineering. For example, complex variables, vectors, quaternions, matrix theory, differential forms, tensor calculus, spinors and twistors, are all subsumed under a common approach.The book begins with a brief historical introduction, followed by a description of the mathematical formalism of Clifford algebra. In particular, definitions, axiom and examples applied to two-dimensional and three-dimensional spaces have been presented. Section 1 gives an overview of the application of GA in Physics, focusing on geometric algebra pictures of both the plane wave solution of the Maxwell equation and special relativity, a toy model of SU(3) symmetry, and some preliminary thoughts about a possible geometric meaning of quantum mechanics. In particular, it is cleared that the internal spin structure of the particle is hidden in both Schrödinger and Dirac equations showing that the classical mechanics combined with zero-point field leads to quantum mechanics. Section 2 discusses the problem of quantization in quantum theory, a natural algebraic alternative definition of time, a coordinate-free formulation of General Relativity, a more unified and systematic description of flux compactifications and of supergravity and string compactifications in general. Finally, the last Section 3 begins with the study of the association of a quaternion algebra to the set of generalized Fibonacci quaternions by using the construction of Clifford algebras and concludes with the study of an important branch of modern analysis: The Clifford analysis.
Categories:

An Introduction to Dirac Operators on Manifolds

An Introduction to Dirac Operators on Manifolds

; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.

Author: Jan Cnops

Publisher: Springer Science & Business Media

ISBN: 9781461200659

Category: Mathematics

Page: 211

View: 859

The chapters on Clifford algebra and differential geometry can be used as an introduction to the topics, and are suitable for senior undergraduates and graduates. The other chapters are also accessible at this level.; This self-contained book requires very little previous knowledge of the domains covered, although the reader will benefit from knowledge of complex analysis, which gives the basic example of a Dirac operator.; The more advanced reader will appreciate the fresh approach to the theory, as well as the new results on boundary value theory.; Concise, but self-contained text at the introductory grad level. Systematic exposition.; Clusters well with other Birkhäuser titles in mathematical physics.; Appendix. General Manifolds * List of Symbols * Bibliography * Index
Categories: Mathematics

Lectures on Quantum Mechanics

Lectures on Quantum Mechanics

Clifford. Algebras. and. Spin. Representations. ⋆. No one fully understands
spinors. Their algebra is formally understood ... We will present a very quick
introduction to the abstract theory of Clifford algebras before specializing to the
Clifford ...

Author: Philip L. Bowers

Publisher: Cambridge University Press

ISBN: 9781108670791

Category: Science

Page:

View: 229

Quantum mechanics is one of the principle pillars of modern physics. It also remains a topic of great interest to mathematicians. Since its discovery it has inspired and been inspired by many topics within modern mathematics, including functional analysis and operator algebras, Lie groups, Lie algebras and their representations, principle bundles, distribution theory, and much more. Written with beginning graduate students in mathematics in mind, this book provides a thorough treatment of (nonrelativistic) quantum mechanics in a style that is leisurely, without the usual theorem-proof grammar of pure mathematics, while remaining mathematically honest. The author takes the time to fully develop the required mathematics and employs a consistent mathematical presentation to clarify the often-confusing notation of physics texts. Along the way the reader encounters several topics requiring more advanced mathematics than found in many discussions of the subject, making for a fascinating course in how mathematics and physics interact.
Categories: Science

Clifford Algebras and Spinor Structures

Clifford Algebras and Spinor Structures

Introduction. In this paper we review two methods of constructing spinor spaces
as minimal onesided ideals in Clifford algebras. The first method is applicable to
quadratic spaces endowed with a quadratic form of maximum Witt index, hence, ...

Author: Rafal Ablamowicz

Publisher: Springer Science & Business Media

ISBN: 0792333667

Category: Mathematics

Page: 421

View: 424

This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry.
Categories: Mathematics

The Spinorial Chessboard

The Spinorial Chessboard

The presentation is detailed and mathematically rigorous. Not only students but also researchers will welcome this book for the clarity of its style and for the straightforward way it applies mathematical concepts to physical theory.

Author: Paolo Budinich

Publisher: Springer Science & Business Media

ISBN: 9783642834073

Category: Science

Page: 128

View: 151

Spinor theory is an important tool in mathematical physics in particular in the context of conformal field theory and string theory. These lecture notes present a new way to introduce spinors by exploiting their intimate relationship to Clifford algebras. The presentation is detailed and mathematically rigorous. Not only students but also researchers will welcome this book for the clarity of its style and for the straightforward way it applies mathematical concepts to physical theory.
Categories: Science

Clifford Algebras and Their Applications in Mathematical Physics

Clifford Algebras and Their Applications in Mathematical Physics

The spinor spaces obtained thus are related to a Clifford subalgebra of the parent
algebra. Classification of real Clifford algebras and interior products of spinors
together with their isometry groups are discussed. 1. INTRODUCTION Clifford ...

Author: J.S.R. Chisholm

Publisher: Springer Science & Business Media

ISBN: 9789400947283

Category: Mathematics

Page: 592

View: 568

William Kingdon Clifford published the paper defining his "geometric algebras" in 1878, the year before his death. Clifford algebra is a generalisation to n-dimensional space of quaternions, which Hamilton used to represent scalars and vectors in real three-space: it is also a development of Grassmann's algebra, incorporating in the fundamental relations inner products defined in terms of the metric of the space. It is a strange fact that the Gibbs Heaviside vector techniques came to dominate in scientific and technical literature, while quaternions and Clifford algebras, the true associative algebras of inner-product spaces, were regarded for nearly a century simply as interesting mathematical curiosities. During this period, Pauli, Dirac and Majorana used the algebras which bear their names to describe properties of elementary particles, their spin in particular. It seems likely that none of these eminent mathematical physicists realised that they were using Clifford algebras. A few research workers such as Fueter realised the power of this algebraic scheme, but the subject only began to be appreciated more widely after the publication of Chevalley's book, 'The Algebraic Theory of Spinors' in 1954, and of Marcel Riesz' Maryland Lectures in 1959. Some of the contributors to this volume, Georges Deschamps, Erik Folke Bolinder, Albert Crumeyrolle and David Hestenes were working in this field around that time, and in their turn have persuaded others of the importance of the subject.
Categories: Mathematics

Clifford Algebras and their Applications in Mathematical Physics

Clifford Algebras and their Applications in Mathematical Physics

The condition that the covariant derivatives of the Clifford algebra generators
vanish , Duvv = 0 , then insures that the Riemann ... Introduction : Clifford Algebra
in General Relativity The incorporation of spinors into general relativity ( 1 ) was ...

Author: F. Brackx

Publisher: Springer Science & Business Media

ISBN: 0792323475

Category: Science

Page: 411

View: 880

This International Conference on Clifford AlgebrfU and Their Application, in Math ematical Phy,ic, is the third in a series of conferences on this theme, which started at the Univer,ity of Kent in Canterbury in 1985 and was continued at the Univer,iU de, Science, et Technique, du Languedoc in Montpellier in 1989. Since the start of this series of Conferences the research fields under consideration have evolved quite a lot. The number of scientific papers on Clifford Algebra, Clifford Analysis and their impact on the modelling of physics phenomena have increased tremendously and several new books on these topics were published. We were very pleased to see old friends back and to wellcome new guests who by their inspiring talks contributed fundamentally to tracing new paths for the future development of this research area. The Conference was organized in Deinze, a small rural town in the vicinity of the University town Gent. It was hosted by De Ceder, a vacation and seminar center in a green area, a typical landscape of Flanders's "plat pays" . The Conference was attended by 61 participants coming from 18 countries; there were 10 main talks on invitation, 37 contributions accepted by the Organizing Com mittee and a poster session. There was also a book display of Kluwer Academic Publishers. As in the Proceedings of the Canterbury and Montpellier conferences we have grouped the papers accordingly to the themes they are related to: Clifford Algebra, Clifford Analysis, Classical Mechanics, Mathematical Physics and Physics Models.
Categories: Science

Clifford Algebras

Clifford Algebras

Keywords: Clifford algebras, bilinear forms, pure spinors 26. 1 Introduction We
will adopt the spinor geometry as formulated by its discoverer E. Cartan [1], who
specially stressed the mathematical elegance of the spinors he named "simple" ...

Author: Pertti Lounesto

Publisher: Springer Science & Business Media

ISBN: 0817635254

Category: Mathematics

Page: 626

View: 116

In addition, attention is paid to the algebraic and Lie-theoretic applications of Clifford algebras---particularly their intersection with Hopf algebras, Lie algebras and representations, graded algebras, and associated mathematical structures. Symplectic Clifford algebras are also discussed. Finally, Clifford algebras play a strong role in both physics and engineering. The physics section features an investigation of geometric algebras, chiral Dirac equations, spinors and Fermions, and applications of Clifford algebras in classical mechanics and general relativity. Twistor and octonionic methods, electromagnetism and gravity, elementary particle physics, noncommutative physics, Dirac's equation, quantum spheres, and the Standard Model are among topics considered at length.
Categories: Mathematics

Supersymmetry for Mathematicians An Introduction

Supersymmetry for Mathematicians  An Introduction

This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner.

Author: V. S. Varadarajan

Publisher: American Mathematical Soc.

ISBN: 9780821835746

Category: Mathematics

Page: 300

View: 527

Supersymmetry has been the object of study by theoretical physicists since the early 1970's. In recent years it has attracted the interest of mathematicians because of its novelty, and because of significance, both in mathematics and physics, of the main issues it raises. This book presents the foundations of supersymmetry to the mathematically minded reader in a cogent and self-contained manner. It begins with a brief introduction to the physical foundations of the theory, especially the classification of relativistic particles and their wave equations, such as the equations of Dirac and Weyl. It then continues the development of the theory of supermanifolds stressing the analogy with the Grothendieck theory of schemes. All the super linear algebra needed for the book is developed here and the basic theorems are established: differential and integral calculus in supermanifolds, Frobenius theorem, foundations of the theory of super Lie groups, and so on. A special feature of the book is the treatment in depth of the theory of spinors in all dimensions and signatures, which is the basis of all developments of supergeometry both in physics and mathematics, especially in quantum field theory and supergravity.
Categories: Mathematics

The Algebraic Theory of Spinors and Clifford Algebras

The Algebraic Theory of Spinors and Clifford Algebras

INTRODUCTION. When E. Cartan classified the simple representations of all
simple Lie algebras, he discovered a hitherto unknown representation of the
orthogonal Lie algebra g, which could not be obtained from the representation on
the ...

Author: Claude Chevalley

Publisher: Springer Science & Business Media

ISBN: 3540570632

Category: Mathematics

Page: 214

View: 887

In 1982, Claude Chevalley expressed three specific wishes with respect to the publication of his Works. First, he stated very clearly that such a publication should include his non technical papers. His reasons for that were two-fold. One reason was his life long commitment to epistemology and to politics, which made him strongly opposed to the view otherwise currently held that mathematics involves only half of a man. As he wrote to G. C. Rota on November 29th, 1982: "An important number of papers published by me are not of a mathematical nature. Some have epistemological features which might explain their presence in an edition of collected papers of a mathematician, but quite a number of them are concerned with theoretical politics ( . . . ) they reflect an aspect of myself the omission of which would, I think, give a wrong idea of my lines of thinking". On the other hand, Chevalley thought that the Collected Works of a mathematician ought to be read not only by other mathematicians, but also by historians of science.
Categories: Mathematics