Chapter 9: The Generalized Poisson Bracket and Its Applications

The purpose of this chapter is to analyze the properties of the Dirac bracket and of the transformations generated by it. As we have seen in the preceding chapter, to define the Dirac bracket we need to be given an even number of functions, ζ_m, on a 2k-dimensional phase space with canonical coordinates ω^μ, with the property that the matrix of PB's ∥{ζ_m, ζ_m′}∥ is nonsingular. We assume, for simplicity, that this matrix is nonsingular in the entire phase space, and denote its inverse by…