The Theory of SpinorsCourier Corporation, 1 févr. 1981 - 157 pages Describes orthgonal and related Lie groups, using real or complex parameters and indefinite metrics. Develops theory of spinors by giving a purely geometric definition of these mathematical entities. Covers generalities on the group of rotations in n-dimensional space, the theory of spinors in spaces of any number of dimensions and much more. |
Table des matières
TENSORS LINEAR REPRESENTATIONS OF GROUPS MATRICES | 21 |
SPINORS IN THREEDIMENSIONAL SPACE | 41 |
LINEAR REPRESENTATIONS OF THE GROUP OF ROTATIONS IN | 52 |
SPINORS IN THE SPACE E2v+1 | 79 |
The fundamental polar in the space of spinors pvectors defined by | 88 |
Case of real Euclidean space Sections 112115 | 101 |
SPINORS IN THE SPACE OF SPECIAL RELATIVITY MINKOWSKI SPACE | vii |
LINEAR REPRESENTATIONS OF THE LORENTZ GROUP | 9 |
SPINORS AND DIRACS EQUATIONS IN RIEMANNIAN GEOMETRY | ix |
25582 | 6 |
| 12 | |
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Expressions et termes fréquents
algebra applied basis vectors bivector co-ordinates coefficients complex conjugate complex rotations compound index conjugate spinors consider corresponding covariant components decomposes decomposition defined denote determinant dimensions Dirac's equations eigenvalue equal Euclidean space form F formula frame of reference fundamental form geometric given gives group G group of proper group of rotations H₁ H₂ identically zero infinitesimal rotation irreducible linear representations irreducible representations irreducible tensors isotropic v-plane isotropic v-vectors linear combinations linear representation linear substitutions linear transformation matrix associated matrix of degree non-zero number of indices obtained odd number orthogonal p-vector P₁ parameters permutation polynomial proper rotations pseudo-Euclidean space pure spinor quadratic form real Euclidean space reference frame reproduced multiplied result rotation group rotations and reversals scalar product scalar square second type Section semi-spinors semi-v-vector space E2 space of special space-like special relativity theory time-like trivector unimodular unit vector unitary unitary matrix variables