Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking
Low energy hadron phenomenology involving the (u,d,s) quarks is often approached through effective multi-quark Lagrangians with the symmetries of QCD. A very successful approach consists in taking the four-quark Nambu-Jona-Lasinio Lagrangian with the chiral UL(3) × UR(3) symmetry in the massless lim...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2006 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2006
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/146427 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking / B. Hiller, A.A. Osipov, V. Bernard, A.H. Blin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862729367306633216 |
|---|---|
| author | Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. |
| author_facet | Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. |
| citation_txt | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking / B. Hiller, A.A. Osipov, V. Bernard, A.H. Blin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Low energy hadron phenomenology involving the (u,d,s) quarks is often approached through effective multi-quark Lagrangians with the symmetries of QCD. A very successful approach consists in taking the four-quark Nambu-Jona-Lasinio Lagrangian with the chiral UL(3) × UR(3) symmetry in the massless limit, combined with the UA(1) breaking six-quark flavour determinant interaction of 't Hooft. We review the present status and some very recent developments related to the functional integration over the cubic term in auxiliary mesonic variables that one introduces to bosonize the system. Various approaches for handling this functional, which cannot be integrated exactly, are discussed: the stationary phase approximation, the perturbative expansion, the loop expansion, their interrelation and importance for the evaluation of the effective action. The intricate group structure rules out the method of Airy's integral. The problem of the instability of the vacuum is stated and a solution given by including eight-quark interactions.
|
| first_indexed | 2025-12-07T19:14:26Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146427 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T19:14:26Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. 2019-02-09T16:50:39Z 2019-02-09T16:50:39Z 2006 Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking / B. Hiller, A.A. Osipov, V. Bernard, A.H. Blin // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 41 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81T10 https://nasplib.isofts.kiev.ua/handle/123456789/146427 Low energy hadron phenomenology involving the (u,d,s) quarks is often approached through effective multi-quark Lagrangians with the symmetries of QCD. A very successful approach consists in taking the four-quark Nambu-Jona-Lasinio Lagrangian with the chiral UL(3) × UR(3) symmetry in the massless limit, combined with the UA(1) breaking six-quark flavour determinant interaction of 't Hooft. We review the present status and some very recent developments related to the functional integration over the cubic term in auxiliary mesonic variables that one introduces to bosonize the system. Various approaches for handling this functional, which cannot be integrated exactly, are discussed: the stationary phase approximation, the perturbative expansion, the loop expansion, their interrelation and importance for the evaluation of the effective action. The intricate group structure rules out the method of Airy's integral. The problem of the instability of the vacuum is stated and a solution given by including eight-quark interactions. B. Hiller is very grateful to the Organizers of the sixth International Conference on “Symmetry in Nonlinear Mathematical Physics”, Kyiv, June 20–26, 2005, for the kind invitation and for the excellent organization which gave rise to a very interesting and pleasant meeting. This work has been supported by grants provided by Funda¸c˜ao para a Ciˆencia e a Tecnologia, POCTI/FNU/50336/2003 and POCI/FP/63412/2005; This research is part of the EU integrated infrastructure initiative Hadron Physics project under contract No.RII3-CT-2004-506078. A.A. Osipov also gratefully acknowledges the Funda¸c˜ao Calouste Gulbenkian for financial support. B. Hiller and A.A. Osipov are very grateful to V. Miransky and V.N. Pervushin for discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking Article published earlier |
| spellingShingle | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. |
| title | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking |
| title_full | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking |
| title_fullStr | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking |
| title_full_unstemmed | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking |
| title_short | Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking |
| title_sort | functional integral approaches to the bosonization of effective multi-quark interactions with ua(1) breaking |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146427 |
| work_keys_str_mv | AT hillerb functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking AT osipovaa functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking AT bernardv functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking AT blinah functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking |