The Heisenberg-Pauli canonical formalism of quantum field theory in the rigorous setting of nonlinear generalized functions (Part I)
| dc.creator | Colombeau, Jean-Francois | |
| dc.creator | Gsponer, Andre | |
| dc.date | 2008-07-02 | |
| dc.date | 2008-09-07 | |
| dc.date.accessioned | 2026-07-07T10:00:55Z | |
| dc.date.available | 2026-07-07T10:00:55Z | |
| dc.description | The unmodified Heisenberg-Pauli canonical formalism of quantum field theory applied to a self-interacting scalar boson field is shown to make sense mathematically in a framework of generalized functions adapted to nonlinear operations. The free-field operators, their commutation relations, and the free-field Hamiltonian operator are calculated by a straightforward transcription of the usual formalism expressed in configuration space. This leads to the usual results, which are essentially independent of the regularization, with the exception of the zero-point energy which may be set to zero if a particular regularization is chosen. The calculations for the self-interacting field are more difficult, especially because of the well-known problems due to the unboundness of the operators and their time-dependent domains. Nevertheless, a proper methodology is developed and a differentiation on time-dependent domains is defined. The Heisenberg equations and the interacting-field equation are shown to be mathematically meaningful as operator-valued nonlinear generalized functions, which therefore provide an alternative to the usual Bogoliubov-Wightman interpretation of quantized fields as operator-valued distributions. The equation for the time-evolution operator is proved using two different methods, but no attempt is made to calculate the scattering operator, and the applications to perturbation theory are left to a subsequent report. | |
| dc.description | 108 pages. Section on zero-point energy revised and expanded | |
| dc.identifier | https://arxiv.org/abs/0807.0289 | |
| dc.identifier | http://arxiv.org/abs/0807.0289 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168469 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81Q99 (Primary); 35D99, 35Q40, 46F30, 81T99 (Secondary) | |
| dc.title | The Heisenberg-Pauli canonical formalism of quantum field theory in the rigorous setting of nonlinear generalized functions (Part I) | |
| dc.type | text |