 Degenerate Lagrangian

A Lagrangian is degenerate when its Hessian with respect to velocities is singular. The momentum–velocity relation then cannot be inverted for every velocity. Some Euler–Lagrange equations can become algebraic constraints rather than independent second-order equations. A massless limit can produce this behaviour; disappearance of an equation at quadratic order does not establish an unconstrained mode of the exact nonlinear model.