Nonperturbative contributions in quantum-mechanical models: the instantonic approach
| dc.creator | Casahorran, J. | |
| dc.date | 2000-12-05 | |
| dc.date | 2002-10-26 | |
| dc.date.accessioned | 2026-07-07T04:11:05Z | |
| dc.date.available | 2026-07-07T04:11:05Z | |
| dc.description | We review the euclidean path-integral formalism in connection with the one-dimensional non-relativistic particle. The configurations which allow to construct a semiclassical approximation classify themselves into either topological (instantons) and non-topological (bounces) solutions. The quantum amplitudes consist on an exponential associated with the classical contribution multiplied by the fluctuation factor which is given by a functional determinant. The eigenfunctions as well as the energy eigenvalues of the quadratic operators at issue can be written in closed form due to the shape-invariance property. Accordingly we resort to the zeta-function method to compute the functional determinants in a systematic way. The effect of the multi-instantons configurations is also carefully considered. To illustrate the instanton calculus in a relevant model we go to the double-well potential. The second popular case is the periodic-potential where the initial levels split into bands. The quantum decay rate of the metastable states in a cubic model is evaluated by means of the bounce-like solution. | |
| dc.description | To appear in Commun. Math. Scienc | |
| dc.identifier | https://arxiv.org/abs/hep-th/0012038 | |
| dc.identifier | http://arxiv.org/abs/hep-th/0012038 | |
| dc.identifier | Commun.Math.Sci. 1 (2003) 245-268 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/50441 | |
| dc.subject | High Energy Physics - Theory | |
| dc.title | Nonperturbative contributions in quantum-mechanical models: the instantonic approach | |
| dc.type | text |