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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.

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
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