The exponential of i divided by h-bar times this quantity defines the propagator in the (*) Feynman path integral approach.
For a string tracing out a worldsheet, this quantity is proportional to the tension of the string times the area of the sheet, in which case it is invariant under reparametrizations. Because that version named for Nambu and Goto is difficult to quantize, another version of this quantity named for Polyakov is often used instead. A formalism that promotes this quantity to the status of operator and expresses it as the difference of two generators at different times was developed by Julian Schwinger. The exponential of i divided by h-bar times this quantity defines the propagator in the (*) Feynman path integral approach. When evaluated as a definite integral, Hamilton's principal function has the same value as this quantity. According to the Euler-Lagrange equation, the actual path followed by a conservative system is the one that minimizes this quantity. For 10 points, name this functional given by the time integral of the Lagrangian along a system trajectory.
For a string tracing out a worldsheet, this quantity is proportional to the tension of the string times the area of the sheet, in which case it is invariant under reparametrizations.
action