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Gauge symmetry and W-algebra in higher derivative systems. (English) Zbl 1298.81153
Summary: The problem of gauge symmetry in higher derivative Lagrangian systems is discussed from a Hamiltonian point of view. The number of independent gauge parameters is shown to be in general $$less$$ than the number of independent primary first classc onstraints, thereby distinguishing it from conventional first order systems. Different models have been considered as illustrative examples. In particular we show a direct connection between the gauge symmetry and the W-algebra for the rigid relativistic particle.

##### MSC:
 81T13 Yang-Mills and other gauge theories in quantum field theory 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, $$W$$-algebras and other current algebras and their representations 70S05 Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems 70H45 Constrained dynamics, Dirac’s theory of constraints
##### Keywords:
gauge symmetry; conformal and W symmetry
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