Introduction to Octonion and Other Non-Associative Algebras in PhysicsCambridge University Press, 1995-08-03 - 136 psl. In this book, the author aims to familiarize researchers and graduate students in both physics and mathematics with the application of non-associative algebras in physics.Topics covered by the author range from algebras of observables in quantum mechanics, angular momentum and octonions, division algebra, triple-linear products and YangSHBaxter equations. The author also covers non-associative gauge theoretic reformulation of Einstein's general relativity theory and so on. Much of the material found in this book is not available in other standard works. |
Turinys
1 Introduction | 1 |
2 Nonassociative algebras | 11 |
3 Hurwitz theorems and octonions | 21 |
4 ParaHurwitz and pseudooctonion algebras | 40 |
5 Real division algebras and real Clifford algebra | 51 |
6 ClebschGordan algebras | 64 |
7 Algebra of physical observables | 80 |
8 Triple products and ternary systems | 89 |
9 Nonassociative gauge theory | 115 |
10 Concluding remark | 130 |
| 131 | |
| 135 | |
Kiti leidimai - Peržiūrėti viską
Introduction to Octonion and Other Non-Associative Algebras in Physics Susumo Okubo Peržiūra negalima - 2005 |
Pagrindiniai terminai ir frazės
A₁ alternative algebra associative algebra assume B₂(x B₂(y bi-linear form bi-linear product calculate Chern-Simon form Clifford algebra commutative complex numbers composition algebra condition construction derivation Lie algebra Dim Hom dimension dimensional division algebra eight-dimensional ejek equation of motion field F flexible algebra Fuv(x G₂ Günaydin h₁ Heisenberg equation Hurwitz algebra identity implies irreducible representation Jacobi identity Jordan algebra Jour Levi-Civita symbol Lie-admissible Math Moreover multiplication table non-associative algebra non-degeneracy non-degenerate form obtain octonion algebra Okubo para-Hurwitz algebra Phys physics power-associative product xy pseudo-octonion algebra quantum mechanics quaternion algebra quaternion and octonion relation Remark rewritten satisfies Eq seven-dimensional side of Eq solution symmetric bi-linear tensor Theorem totally anti-symmetric traceless triple product triple system unit element validity of Eq vector space W₁ W₂ xy|xy Yang-Mills μν