detailed contents is added through MasterPDF
Author(s): Geoffrey M. Dixon
Series: Mathematics and Its Applications, 290
Publisher: Springer
Year: 1994
Language: English
Commentary: detailed contents is added through MasterPDF
Pages: 242
Contents
Preface
1. Underpinnings
1.1. The Argument.
SCREED I
SCREED II
SCREEDIII
1.2. Clifford Aigebras.
1.3. Conjugations and Spinors
NILPOTENT CLIFFORD ALGEBRAS
SYMPLECTIC NILPOTENT CLIFFORD ALGEBRA
1.4. Aigebraic Fundamentals ofthe Standard Model
2. Division Algebras Alone.
2.1. Mostly Octonions.
2.2. Adjoint algebras.
2.3. Clifford Algebras, Spinors
2.4. Resolving the Identity of O_L
2.5. Lie Algebras, Lie Groups, from O_L
2.6. From Galois Fields to Division Aigebras: An Insight.
3. Tensor Algebras
3.1. Tensoring Two: Clifford Aigebras and Spinors.
3.2. Tensoring Two: Spinor Inner Product.
3.3. Tensoring Three: Clifford Aigebras and Spinors
3.4. Tensoring Three: Spinor Inner Product
RESOLVING THE IDENTITY OF T
THE TRACE OF X
3.5. Derivation of the Standard Symmetry.
3.6. SU(2) X SU(3) Multiplets, and U(1)
4. Connecting to Physics.
4.1. Connecting to Geometry
DIMENSIONAL REDUCTION
4.2. Connecting to Particles
4.3. Parity N onconservation
LEFTHANDED DIRAC OPERATOR
4.4. Gauge Fields.
4.5. Weak Mixing.
4.6. Gauging SU(3).
5. Spontaneous Symmetry Breaking.
5.1. Scalar Fields.
5.2. Scalar Lagrangians.
5.3. Fermions and Scalars
6. 10 Dimensions
6.1. Fermion Lagrangian.
MATTER/ ANTIMATTER MIXING
6.2. More SU(3).
6.3. Freedom from Matter-Antimatter Mixing.
6.4. (1,9)-Scalar Lagrangian
6.5. Charge Conjugation on T_L (2)
6.6. Charge Conjugation on T^2
THE MEANING OF MAJORANA
6.7. 10 Other Dimensions.
THE CLIFFORD ALGEBRA
7. Doorways.
7.1. Moufang and other Identities
TWO IDENTITIES
THE MOUFANG IDENTITIES
7.2. Spheres and Lie Algebras.
SPHERE FIBRATIONS
7.3. Triality.
TRIALITY REPRESENTATIONS OF so(8)
THE Tri IN TRIALITY
FREUDENTHAL'S PRINCIPLE OF TRIALITY
7.4. LG2 and Tri.
LG2 TRIALITY TRIPLET
7.5. LG2 Triplets and the X-Product
LG^X_2 GENERAL SOLUTION
LG^X_2 AND THE X-ADJOINT ALGEBRA O_{LX}
8. Corridors.
8.1. Magie Square.
8.2. The Ten MS_{KK'}.
R®R
R®C
R®Q
R®O
C®C
C®Q
C®O
Q®Q
Q®O
O®O
8.3. Spinor_{KK'} Outer Products
C OUTER PRODUCTS
Q OUTER PRODUCTS
O OUTER PRODUCTS
8.4. LF_4 ~ MS_{RO}.
8.5. J^O_3 and F_4
8.6. More Magie Square
Appendix i. O_L Actions: Product Rule e_a * e_{a+1} = e_{a+5}.
Appendix ii. O_R Actions: Product Rule e_a * e_{a+1} = e_{a+5}.
Appendix iii. O_L Actions: Product Rule e_a * e_{a+1} = e_{a+3}.
Appendix iv. O_R Actions: Product Rule e_a * e_{a+1} = e_{a+3}
Bibliography
Index
