ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
The infinitesimal canonical transformations which map solutions of the total Hamiltonian equations of motion into each other are investigated. For that, the generating function Ψ of such transformations should satisfy certain conditions. In general, Ψ is a function which depends on the coordinates, the momenta, and the Lagrange multipliers λ. However, it is shown that the requirement of independence of the function Ψ on the Lagrange multipliers is sufficient for the existence of gauge invariant transformations in the Lagrange formalism. It is shown that the condition that the Poisson brackets between Ψ and all the primary first-class constraints are a linear combination of the latter ones provides the λ independence of the function Ψ. The existence of such a λ-independent function Ψ is proven for some systems. In particular, this is proven for the relevant case of systems having primary and secondary first-class constraints. The authors suggest the possibility that for some specific systems a λ-independent generating function Ψ cannot be constructed. This conclusion concerns the systems with more than primary and secondary constraints.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.530275
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