کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1856198 | 1529894 | 2012 | 30 صفحه PDF | دانلود رایگان |
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.
Journal: Annals of Physics - Volume 327, Issue 2, February 2012, Pages 329–358