9) where r are the Dirac matrices, and an overdot indicates a derivative with respect to the arbitrary worldline coordinate t. The "einbein" e is a Lagrange multiplier for the mass-shell constraint. For the explanation of the rest of the notations one can consult [193]. [193] detaillates two observation

describing the system, and the constraints are typically linear or convex functions, so that this maximization implicitly calculates shadow prices (Lagrange multipliers) for each of the constraints, which are uniform over the subsystems and characterize its important properties in equilibrium. One might

ics and science. His work in the ca/culus of variations led to the development of a system of algebraic manipulations seeking the value of constants, Lagrange multipliers, in place of solving Euler’s differential equations. It makes it possible to immediately write down a computable expression for the maxim