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Đây là bộ sách tiếng anh về chuyên ngành vật lý gồm các lý thuyết căn bản và lý liên quan đến công nghệ nano ,công nghệ vật liệu ,công nghệ vi điện tử,vật lý bán dẫn. Bộ sách này thích hợp cho những ai đam mê theo đuổi ngành vật lý và muốn tìm hiểu thế giới vũ trụ và hoạt độn ra sao.
Geometric Algebra and its Application to Mathematical Physics Chris J L Doran Sidney Sussex College A dissertation submitted for the degree of Doctor of Philosophy in the University of Cambridge February 1994 Preface This dissertation is the result of work carried out in the Department of Applied Mathematics and Theoretical Physics between October 1990 and October 1993 Sections of the dissertation have appeared in a series of collaborative papers 1] | 10] Except where explicit reference is made to the work of others, the work contained in this dissertation is my own Acknowledgements Many people have given help and support over the last three years and I am grateful to them all I owe a great debt to my supervisor, Nick Manton, for allowing me the freedom to pursue my own interests, and to my two principle collaborators, Anthony Lasenby and Stephen Gull, whose ideas and inspiration were essential in shaping my research I also thank David Hestenes for his encouragement and his company on an arduous journey to Poland Above all, I thank Julie Cooke for the love and encouragement that sustained me through to the completion of this work Finally, I thank Stuart Rankin and Margaret James for many happy hours in the Mill, Mike and Rachael, Tim and Imogen, Paul, Alan and my other colleagues in DAMTP and MRAO I gratefully acknowledge nancial support from the SERC, DAMTP and Sidney Sussex College To my parents Contents Introduction 1.1 Some History and Recent Developments : : : : : 1.2 Axioms and De nitions : : : : : : : : : : : : : : : 1.2.1 The Geometric Product : : : : : : : : : : 1.2.2 The Geometric Algebra of the Plane : : : 1.2.3 The Geometric Algebra of Space : : : : : : 1.2.4 Re ections and Rotations : : : : : : : : : 1.2.5 The Geometric Algebra of Spacetime : : : 1.3 Linear Algebra : : : : : : : : : : : : : : : : : : : 1.3.1 Linear Functions and the Outermorphism 1.3.2 Non-Orthonormal Frames : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 2.1 Grassmann Algebra versus Cli ord Algebra : : : : : : : 2.2 The Geometrisation of Berezin Calculus : : : : : : : : 2.2.1 Example I The \Grauss" Integral : : : : : : : : 2.2.2 Example II The Grassmann Fourier Transform 2.3 Some Further Developments : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Grassmann Algebra and Berezin Calculus Lie Groups and Spin Groups : : : : : : : : : : : : : : : : : : : : 3.1 Spin Groups and their Generators : : : : : : : : : : : : : : : : 3.2 The Unitary Group as a Spin Group : : : : : : : : : : : : : : 3.3 The General Linear Group as a Spin Group : : : : : : : : : : 3.3.1 Endomorphisms of