Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1856198 | Annals of Physics | 2012 | 30 Pages |
Interacting fourth order quantum mechanics is in the Ostrogradski formalism afflicted by an instability involving the decay of the vacuum. When treating such systems as 1+01+0-dimensional Euclidean field theories in the transfer operator formalism the ‘instability problem’ and the ‘unitarity problem’ are distinct and decoupled. The instability problem is shown to be absent: a stable ground state always exists and is typically normalizable and strictly positive. The generator HH of the transfer operator replaces the Ostrogradski Hamiltonian and is non-Hermitian but selfadjoint with respect to a Krein structure, which also ensures consistency with the Lagrangian functional integral. The case of a scalar quartic derivative interaction is treated in detail. Variational perturbation theory, a strong coupling expansion, and direct diagonalization of matrix truncations are used to compute the spectrum of HH in this case.
► The Ostrogradski instability problem is resolved. ► A new Hamiltonian HH replaces Ostrogradski’s HOstr. ►HH in contrast to HOstr provenly always has a ground state. ► Computational techniques for the spectrum of HH are developed. ► Lagrangian correlators are expressed as exp{−τH}exp{−τH} matrix elements.