Gauge theories and relativistic membranes

In the course of its time evolution, a relativistic point particle algebra traces out a ''worldwide'' ω in Minkowski spacetime (M,η). This provides us with an immersion of ω into M, by virtue of which the Minkowski metric η of M induces a metric on ω. For a segment of the worldline with endpoints A and B we take the particle's action, S, to be the length, in the induced metric, of the segment. The constant m is (in units where the speed of light is unity) the particle's mass. The Euler-Langrange equations that follow from this action imply that ω is a geodesic. This paper is about simplifications and generalizations of the connections of the relativistic membrane with Yang-Mills gauge theories. Other connections between membranes and gauge theories are also considered. (author)