Total Hamiltonian and Extended Hamiltonian for Constrained Hamilton Systems

Abstract

For constrained Hamiltonian systems, the motion equations are deduced from total Hamiltonian and extended Hamiltonian with Lagrangian multipliers depending on time t and canonical variables q i and p i . When the multipliers reduced to only depend on time t, the motion equations exactly agree with the old results. Under the same conditions (Lagrangian multipliers depend on time t and canonical variables q i and p i ), the relation equations of coefficients in the generator of gauge transformation are deduced, but the equations have an additive term besides the well-known results. This additive term is from Lagrangian multipliers depending on canonical variables, and it might perform the gauge symmetries that needs to be discussed further.