Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy
| dc.creator | Kastening, Boris | |
| dc.date | 1999-08-26 | |
| dc.date | 2000-01-21 | |
| dc.date.accessioned | 2026-07-07T06:33:52Z | |
| dc.date.available | 2026-07-07T06:33:52Z | |
| dc.description | The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into recursion relations for the connected Greens functions in a loop expansion. These relations amount to a simple proof that W[G,J] generates only connected graphs and can be used to find all such graphs with their combinatoric weights. A Legendre transformation with respect to the external current converts the functional differential equations for the free energy into those for the effective energy Gamma[G,Phi], which is considered as a functional of the free correlation function G and the field expectation Phi. These equations are turned into recursion relations for the one-particle irreducible Greens functions. These relations amount to a simple proof that Gamma[G,J] generates only one-particle irreducible graphs and can be used to find all such graphs with their combinatoric weights. The techniques used also allow for a systematic investigation into resummations of classes of graphs. Examples are given for resumming one-loop and multi-loop tadpoles, both through all orders of perturbation theory. Since the functional differential equations derived are non-perturbative, they constitute also a convenient starting point for other expansions than those in numbers of loops or powers of coupling constants. We work with general interactions through four powers in the field. | |
| dc.description | 34 pages; abstract expanded; section IV.E about absorption of tadpoles and one related reference added; eqs. (20) and (23) corrected; further references added; some minor beautifications; to be published by Phys.Rev.E | |
| dc.identifier | https://arxiv.org/abs/hep-th/9908172 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9908172 | |
| dc.identifier | Phys.Rev. E61 (2000) 3501-3528 | |
| dc.identifier | doi:10.1103/PhysRevE.61.3501 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99340 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Statistical Mechanics | |
| dc.subject | High Energy Physics - Phenomenology | |
| dc.title | Recursive Graphical Construction of Feynman Diagrams in phi^4 Theory: Asymmetric Case and Effective Energy | |
| dc.type | text |