Quantization of secondorder Lagrangians: Model problem
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 EulerLagrange 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.
 Publication:

Physical Review A
 Pub Date:
 August 1991
 DOI:
 10.1103/PhysRevA.44.1477
 Bibcode:
 1991PhRvA..44.1477M
 Keywords:

 03.65.Bz;
 02.90.+p;
 03.20.+i;
 Other topics in mathematical methods in physics