Laws of trigonometry on SU(3)
In this paper we will study triangles in SU(3). The orbit space of congruence classes of triangles in SU(3) has dimension 8. Each corner is made up of a pair of tangent vectors (X,Y), and we consider the 8 functions trX{sup 2}, i trX{sup 3}, trY{sup 2}, i trY{sup 3}, trXY, i trY{sup 2}Y, i trXY{sup 2}, trX{sup 2}Y{sup 2} which are invariant under the full isometry group of SU(3). We show that these 8 corner invariants determine the isometry class of the triangle. We give relations (laws of trigonometry) between the invariants at the different corners, enabling us to determine the invariants at the remaining corners, including the values of the remaining side and angles, if we know one set of corner invariants. The invariants that only depend on one tangent vector we will call side invariants, while those that depend on two tangent vectors will be called angular invariants. For each triangle we then have 6 side invariants and 12 angular invariants. Hence we need 18 {minus} 8 = 10 laws of trigonometry. The basic tool for deriving these laws is a formula expressing tr(exp X exp Y) in terms of the corner invariants.
- Research Organization:
- California Univ., Berkeley, CA (USA)
- OSTI ID:
- 7142145
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
Similar Records
Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=({+-}1,0)
Metric-connection theories of gravity
Related Subjects
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
STRING MODELS
MATHEMATICAL OPERATORS
CALCULATION METHODS
INVARIANCE PRINCIPLES
MATHEMATICAL MANIFOLDS
SYMMETRY
TRIANGULAR CONFIGURATION
COMPOSITE MODELS
CONFIGURATION
EXTENDED PARTICLE MODEL
MATHEMATICAL MODELS
PARTICLE MODELS
QUARK MODEL
653000* - Nuclear Theory
657000 - Theoretical & Mathematical Physics
645400 - High Energy Physics- Field Theory