Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way
During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean func...
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todo:paper_11266708_v2013_n8_p_Gueron2023-10-03T16:07:01Z Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way Gueron, J. Leston, M. Field Theories in Lower Dimensions Nonperturbative Effects During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of λΦ4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example - although does not capture all the difficulties in the constructive quantum field theory approach - allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach. © 2013 SISSA, Trieste, Italy. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_11266708_v2013_n8_p_Gueron |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
Field Theories in Lower Dimensions Nonperturbative Effects |
| spellingShingle |
Field Theories in Lower Dimensions Nonperturbative Effects Gueron, J. Leston, M. Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way |
| topic_facet |
Field Theories in Lower Dimensions Nonperturbative Effects |
| description |
During the '70, several relativistic quantum field theory models in D = 1 + 1 and also in D = 2 + 1 have been constructed in a non-perturbative way. That was done in the so-called constructive quantum field theory approach, whose main results have been obtained by a clever use of Euclidean functional methods. Although in the construction of a single model there are several technical steps, some of them involving long proofs, the constructive quantum field theory approach contains conceptual insights about relativistic quantum field theory that deserved to be known and which are accessible without entering in technical details. The purpose of this note is to illustrate such insights by providing an oversimplified schematic exposition of the simple case of λΦ4 (with m > 0) in D = 1 + 1. Because of the absence of ultraviolet divergences in its perturbative version, this simple example - although does not capture all the difficulties in the constructive quantum field theory approach - allows to stress those difficulties inherent to the non-perturbative definition. We have made an effort in order to avoid several of the long technical intermediate steps without missing the main ideas and making contact with the usual language of the perturbative approach. © 2013 SISSA, Trieste, Italy. |
| format |
JOUR |
| author |
Gueron, J. Leston, M. |
| author_facet |
Gueron, J. Leston, M. |
| author_sort |
Gueron, J. |
| title |
Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way |
| title_short |
Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way |
| title_full |
Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way |
| title_fullStr |
Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way |
| title_full_unstemmed |
Non-perturbative λΦ4 in D = 1 + 1: An example of the constructive quantum field theory approach in a schematic way |
| title_sort |
non-perturbative λφ4 in d = 1 + 1: an example of the constructive quantum field theory approach in a schematic way |
| url |
http://hdl.handle.net/20.500.12110/paper_11266708_v2013_n8_p_Gueron |
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AT gueronj nonperturbativelph4ind11anexampleoftheconstructivequantumfieldtheoryapproachinaschematicway AT lestonm nonperturbativelph4ind11anexampleoftheconstructivequantumfieldtheoryapproachinaschematicway |
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