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From Physical Concept to Mathematical Structure : An Introduction to Theoretical Physics /
The text takes an innovative approach to theoretical physics. It surveys the field in a way that emphasizes perspective rather than content per se, and identifies certain common threads, both conceptual and methodological, which run through the fabric of the subject today.
| Autores principales: | , |
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| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Toronto :
University of Toronto Press,
[1979]
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| Colección: | Book collections on Project MUSE.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; PREFACE; ACKNOWLEDGMENTS; 1 INTRODUCTION; 1.1 General remarks; 1.2 Linear theories; 1.3 Linear operators and transformation groups; 2 CARTESIAN TENSORS AND TRANSFORMATION GROUPS; 2.1 The position vector and its generalization: the rotation group in 2-dimensions; 2.2 Inner and outer products of vectors: tensors; 2.3 Moment of inertia as a second-rank tensor; 2.4 Tensors as multilinear maps; References; Problems; 3 ROTATIONS, REFLECTIONS, AND MORE ABOUT TENSORS; 3.1 Introduction; 3.2 Representation of the group of rotations in 3-dimensional space
- 3.3 A double-valued representation of the group of rotations in 3-dimensional space3.4 Rotations in quaternion form; 3.5 Spinors; 3.6 Reflections and inversions
- pseudotensors; 3.7 Invariant tensors; 3.8 Axial vectors in 3-space as second-rank tensors; 3.9 Vector and tensor fields; 3.10 Covariance of physical laws; References; Problems; 4 CARTESIAN TENSORS AT WORK; 4.1 Theory of elastic continua; (a) Local rotations, compressions, and shears
- the strain tensor; (b) Dilatations; (c) The stress tensor; (d) Hooke's law
- a linear approximation; (e) Principal stresses and strains
- (F) Isotropic cubic crystals4.2 Wave propagation in elastic solids; 4.3 Hydrodynamics; References; Problems; 5 TENSORS AS A BASIS OF GROUP REPRESENTATIONS; 5.1 Introduction; 5.2 The abstract notion of a group; 5.3 The symmetric group Sn; 5.4 Representations of groups; 5.5 Irreducible representations of the symmetric group Sn; 5.6 Product representations; 5.7 Representations of the general linear group; 5.8 Representations of the full orthogonal group; References; Problems; 6 QUANTUM MECHANICS AS A LINEAR THEORY; 6.1 Introduction; 6.2 Eigenfunction expansions for self-adjoint operators
- 6.3 Postulates of quantum mechanics6.4 Matrix mechanics; 6.5 An example
- the simple harmonic oscillator; 6.6 Particles with inner structure; 6.7 Quantization of orbital momentum; 6.8 Rotation operator and representation of the special orthogonal (rotation) group; 6.9 Many-particle systems; References; Problems; 7 GENERALIZED TENSORS IN RIEMANNIAN GEOMETRY; 7.1 Introduction; 7.2 Gauss's introduction to non-Euclidean geometry; 7.3 Curvilinear coordinates; (a) General considerations; (b) Spherical polar coordinates; (c) Lengths, areas, and volumes; 7.4 Riemannian geometry
- 7.5 Change of coordinates
- generalized tensors7.6 Tensor algebra; 7.7 The scalar product; 7.8 Tensors as multilinear maps; References; Problems; 8 SPECIAL RELATIVITY; 8.1 Introduction; 8.2 Preliminaries; 8.3 Galilean relativity; 8.4 Postulates of special relativity; 8.5 Properties of the Poincare group and its subgroups; 8.6 Minkowski space; 8.7 Maxwell's equations in covariant form; 8.8 Two relativistic invariants; 8.9 Covariance of the Lorentz force equation
- conservation laws; 8.10 Relativistic mechanics; 8.11 Applications of relativistic mechanics; (a) Doppler effect; (b) Compton effect