Quantization of second-order Lagrangians: Model problem

R. A. Moore and T. C. Scott
Phys. Rev. A 44, 1477 – Published 1 August 1991
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Abstract

Many aspects of a model problem, the Lagrangian of which contains a term depending quadratically on the acceleration, are examined in the regime where the classical solution consists of two independent normal modes. It is shown that the techniques of conversion to a problem of Lagrange, generalized mechanics, and Dirac’s method for constrained systems all yield the same canonical form for the Hamiltonian. It is also seen that the resultant canonical equations of motion are equivalent to the Euler-Lagrange equations. In canonical form, all of the standard results apply, quantization follows in the usual way, and the interpretation of the results is straightforward. It is also demonstrated that perturbative methods fail, both classically and quantum mechanically, indicating the need for the nonperturbative techniques applied herein. Finally, it is noted that this result may have fundamental implications for certain relativistic theories.

  • Received 11 March 1991

DOI:https://doi.org/10.1103/PhysRevA.44.1477

©1991 American Physical Society

Authors & Affiliations

R. A. Moore

  • Guelph-Waterloo Programme for Graduate Work in Physics, Waterloo Campus, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

T. C. Scott

  • Institute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, Massachusetts 02138

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Issue

Vol. 44, Iss. 3 — August 1991

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