Action principle and equations of motion for nonabelian monopoles

Journal Article · Tue Apr 01 04:00:00 EST 1986 · Ann. Phys. (N.Y.); (United States)

DOI:https://doi.org/10.1016/0003-4916(86)90209-5· OSTI ID:5523549

Hong-Mo, C; Scharbach, P; Tsun, T S

Monopoles in gauge theories have an intrinsic interaction with the gauge field. The definition of a monopole as a topological charge implies a certain constraint coupling the gauge field to the coordinates of a particle carrying that charge. Hence, even starting with the free action, the constraint will give equations of motion in which field and particle interact. Applied to electromagnetism, this procedure gives the Maxwell and Lorentz equations. In this paper, we apply the same idea to nonabelian monopoles to deduce their equations of motion which are otherwise unknown. To surmount certain technical difficulties connected with patching, loop space techniques are developed to solve the variational problem. A closed set of equations are obtained, which are analogous to the Maxwell and Lorentz equations, and bear also a formal resemblance to the Wong equations for a ''classical'' point source of Yang-Mills fields.

• Research Organization: Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, England
• OSTI ID: 5523549
• Journal Information: Ann. Phys. (N.Y.); (United States), Journal Name: Ann. Phys. (N.Y.); (United States) Vol. 167:2; ISSN APNYA
• Country of Publication: United States
• Language: English

Related Subjects

645400* -- High Energy Physics-- Field Theory
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
DIFFERENTIAL EQUATIONS
EQUATIONS
EQUATIONS OF MOTION
GAUGE INVARIANCE
INVARIANCE PRINCIPLES
LIE GROUPS
MATHEMATICS
MONOPOLES
PARTIAL DIFFERENTIAL EQUATIONS
SU GROUPS
SYMMETRY GROUPS
TOPOLOGY
YANG-MILLS THEORY