Instability of higher-difference initial-value theories

Phys. Rev. D 40, 465 – Published 15 July 1989
D. A. Eliezer and R. P. Woodard


Temporal discretization is developed as a means of studying the nonperturbative stability of nonlocal actions such as those of string theory and third-quantized gravity. An algorithm is derived for constructing the classical canonical Hamiltonian which generates the natural interpolation of continuous time evolution for Lagrangian higher-difference theories. Using this quantity we prove the analog of Ostrogradski's result for continuum higher derivatives: namely, that every nondegenerate, deterministic higher-difference theory is unstable. This result is nonperturbative and survives quantization. An explicit construction is given for the energy of a general quadratic Lagrangian with arbitrarily high differences.


  • Received 9 December 1988
  • Published in the issue dated 15 July 1989

© 1989 The American Physical Society

Authors & Affiliations

D. A. Eliezer*

  • Department of Physics, University of California, Santa Barbara, California 93106

R. P. Woodard

  • Department of Physics, Brown University, Providence, Rhode Island 02912

  • *Address after 31 August 1989: Department of Physics, University of British Columbia, Vancouver, BC V6T 2A6, Canada.
  • Address after 10 August 1989: Department of physics, University of Florida, Gainesville, FL 32611.

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