Invariance identitites associated with finite gauge transformations and the uniqueness of the equations of motion of a particle in a classical gauge field

Journal Article · Sat Jan 01 00:00:00 EST 1983 · Found. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01889414· OSTI ID:5539819

Rund, H

A certain class of geometric objects is considered against the background of a classical gauge field associated with an arbitrary structural Lie group. It is assumed that the components of these objects depend on the gauge potentials and their first derivatives, and also on certain gauge-dependent parameters whose properties are suggested by the interaction of an isotopic spin particle with a classical Yang-Mills field. It is shown that the necessary and sufficient conditions for the invariance of the given objects under a finite gauge transformation are embodied in a set of three relations involving the derivatives of their components. As a special case these so-called invariance identities indicate that there cannot exist a gauge-invariant Lagrangian that depends on the gauge potentials, the interaction parameters, and the 4-velocity components of a test particle. However, the requirement that the equations of motion that result from such a Lagrangian be gauge-invariant, uniquely determines the structure of these equations.

• Research Organization: Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721
• OSTI ID: 5539819
• Journal Information: Found. Phys.; (United States), Vol. 13:1
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
FIELD THEORIES
GAUGE INVARIANCE
ELEMENTARY PARTICLES
EQUATIONS OF MOTION
INVARIANCE PRINCIPLES
LAGRANGIAN FUNCTION
LIE GROUPS
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SYMMETRY GROUPS
645400* - High Energy Physics- Field Theory