附註:Includes bibliographical references (pages 353-361) and index.
Cover -- Table of Contents -- Preface -- Acknowledgments -- Introduction -- Part I Point Particles -- 1. THE SPINLESS POINT PARTICLE -- 1.1 Point particles versus worldlines -- 1.2 Classical theory -- 1.3 First quantization -- 1.4 Second quantization -- 2. POINT PARTICLES AND CLIFFORD ALGEBRA -- 2.1 Introduction to geometric calculus based on Clifford algebra -- 2.2 Algebra of spacetime -- 2.3 Physical quantities as polyvectors -- 2.4 The unconstrained action from the polyvector action -- 2.5 Quantization of the polyvector action -- 2.6 On the second quantization of the polyvector action -- 2.7 Some further important consequences of Clifford algebra -- 2.8 The polyvector action and De Witt ... Rovelli material reference system -- 3. HARMONIC OSCILLATOR IN PSEUDO-EUCLIDEAN SPACE -- 3.1 The 2-dimensional pseudo-Euclidean harmonic oscillator -- 3.2 Harmonic oscillator in d-dimensional pseudo-Euclidean space -- 3.3 A system of scalar fields -- 3.4 Conclusion -- Part II Extended Objects -- 4. GENERAL PRINCIPLES OF MEMBRANE KINEMATICS AND DYNAMICS -- 4.1 Membrane space M -- 4.2 Membrane dynamics -- 4.3 More about the interconnections among various membrane actions -- 5. MORE ABOUT PHYSICS IN M -SPACE -- 5.1 Gauge fields in M-space -- 5.2 Dynamical metric field in M-space -- 6. EXTENDED OBJECTS AND CLIFFORD ALGEBRA -- 6.1 Mathematical preliminaries -- 6.2 Dynamical vector field in M-space -- 6.3 Full covariance in the space of parameters f A -- 7 . QUANTIZATION -- 7.1 The quantum theory of unconstrained membranes -- 7.2 Clifford algebra and quantization -- Part III Brane World -- 8. SPACETIME AS A MEMBRANE IN A HIGHER-DIMENSIONAL SPACE -- 8.1 The brane in a curved embedding space -- 8.2 A system of many intersecting branes -- 8.3 The origin of matter in the brane world -- 8.4 Comparison with the Randall ... Sundrum model -- 9. THE EINSTEIN ... HILBERT ACTION ON THE BRANE AS THE EFFECTIVE ACTION -- 9.1 The classical model -- 9.2 The quantum model -- 9.3 Conclusion -- 10.
摘要:This book attempts to provide a synthetic view of fundamental theoretical physics. It describes the ingredients which may have to be used in order to build a theory which will unify general relativity, quantum field theory, and the known fundamental interactions. The books written so far have either considered a specialized topic in much detail, or they were too superficial and general. This book unites both approaches: it provides enough detail to start with, but does not go too far in developing a particular special field. Instead it turns to another special field and then shows how different fields are interrelated in a fascinating way. Many surprising new findings are revealed. Audience: This book will be of interest to those who would like to explore how the `Theory of Everything' could possibly be formulated. It will be of interest to researchers and students. A background in general relativity and quantum mechanics is recommended. The introductory sections, and especially Part IV: Beyond the Horizon, need no such background knowledge. They are intended for the reader who is interested in the conceptual and even philosophical questions.
