Gauge symmetry and W-algebra in higher derivative systems

Abstract

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 {\it{less}} than the number of independent primary first class constraints, 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.Comment: 1+22 pages, 1 figure, LaTeX, v2; title changed, considerably expanded version with new results, to appear in JHE

New Hamiltonian analysis of Regge-Teitelboim minisuperspace cosmology

“…Higher derivative theories were studied and used in different contexts over a long period of time [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Though the classical Hamiltonian formulation of higher derivative theories was worked out by Ostrogradsky long ago [24] and has been refined over the years, specifically in the context of gauge theories certain aspects of the Hamiltonian formulation were not adequately emphasised.…”

“…One such issue is the mismatch between the number of primary first class constraints and the number of independent gauge degrees of freedom in a higher derivative relativistic particle model [9]. Recently it has been demonstrated [11] that under an equivalent first-order formalism [10] which is a variant of the Ostrogradsky approach, the well known algorithmic method of construction of the gauge generator for first-order systems [25,26] can be invoked to settle the issue. The Hamiltonian method developed in BMP of abstracting the independent gauge degrees of freedom of higher derivative systems has been applied to a number of particle and field theoretic models [11,27,28] successfully.…”

“…Recently it has been demonstrated [11] that under an equivalent first-order formalism [10] which is a variant of the Ostrogradsky approach, the well known algorithmic method of construction of the gauge generator for first-order systems [25,26] can be invoked to settle the issue. The Hamiltonian method developed in BMP of abstracting the independent gauge degrees of freedom of higher derivative systems has been applied to a number of particle and field theoretic models [11,27,28] successfully. Note in this context that the anasysis of the RT model in the ambit of higher derivative theory [4] was done from the Ostrogradsky approach and this work is based on the minisuperspace model following from the RT theory.…”

A first-class approach of higher derivative Maxwell–Chern–Simons–Proca model

“…The starting point of the approach developed in [52] consists in converting the original higher derivative theory to an equivalent first order theory by introducing new fields to account for higher derivative terms. To pass from the higher derivative theory to a first order one, we define the variables B μ as…”

“…As the second term in the action (1) contains higher derivative terms ∂ λ ∂ λ A μ , the canonical analysis will be done by a variant of Ostrogradsky method [46][47][48][49][50][51] developed in Ref. [52], based on an equivalent first order formalism [53,54] and applied to a number of particle and field theoretic models [52,[55][56][57]. The Hamiltonian analysis of a higher derivative extension of a theory displays a constraints set with a more complicated structure than the constraints set of the usual theory (where the Lagrangian is a function of the fields and their first derivatives only).…”