Yank-Mills fields and hypersurface twistors

Thesis/Dissertation · Sun Jan 01 04:00:00 EST 1989

OSTI ID:5219333

Fioravanti, M A

The author establishes a one-to-one correspondence between (not necessarily self-dual) solutions of the non-abelian source-free Yang-Mills equations on Minkowski space, and pairs of cohomology classes ({gamma}), ({phi}). If O(n) is the sheaf of holomorphic sections of the n{sup th} tensor power of the hyperplane line bundle over C P{sup 1}, and g is the Lie algebra of the gauge group, ({gamma}) {var epsilon} H{sub CR}{sup 1} (PN circumflex,g) and defines a deformation C-R({gamma}) of the canonical C-R structure on a principal bundle over PN circumflex, the subset of null twistor space PN, representing unscaled null geodesics in Minkowski space. ({phi}) {var epsilon} H{sub CR({gamma})}{sup 1} (PN,O({minus}4) {direct product} g). The spin-bundle over Minkowski space is used in the construction. This bundle is foliated by a congruence of lines; each of these lines projects into a null geodesic in Minkowski space, and corresponds to a point in N. The restriction S of the spin-bundle to a spacelike hyperplane in Minkowski space is transversal to this foliation, and PN is identified with S. ({gamma}) encodes certain components of the Yang-Mills connection on S, and ({phi}) encodes the self-dual part of the field on S. They give initial values for a system of evolution equations in the spin-bundle. This system is composed by four first order ordinary differential equations along the lines in the foliation of the spin-bundle, with some of the right-hand sides given by integrals on the fiber over a point in Minkowski space, and a partial differential equation on this fiber. The evolution equations simplify largely in the case of an abelian gauge group. In the case of anti-self-dual fields, the system reduces to two ordinary differential equations along the lines in the foliation of the spin-bundle, and the differential equation on the fiber over each point in Minkowski space. He studies the modifications in the construction when sources are present.

• Research Organization: Pittsburgh Univ., PA (United States)
• OSTI ID: 5219333
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ALGEBRA
DIFFERENTIAL EQUATIONS
EQUATIONS
FIELD EQUATIONS
GRADED LIE GROUPS
LIE GROUPS
MATHEMATICAL SPACE
MATHEMATICS
MINKOWSKI SPACE
MODIFICATIONS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
SYMMETRY GROUPS
YANG-MILLS THEORY