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:
| Дата: | 2006 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2006
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.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| id |
irk-123456789-146427 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1464272019-02-10T01:24:20Z 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. 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. 2006 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/146427 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. |
| spellingShingle |
Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. Functional Integral Approaches to the Bosonization of Effective Multi-Quark Interactions with UA(1) Breaking Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Hiller, B. Osipov, A.A. Bernard, V. Blin, A.H. |
| author_sort |
Hiller, B. |
| title |
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_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_sort |
functional integral approaches to the bosonization of effective multi-quark interactions with ua(1) breaking |
| publisher |
Інститут математики НАН України |
| publishDate |
2006 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146427 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT hillerb functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking AT osipovaa functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking AT bernardv functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking AT blinah functionalintegralapproachestothebosonizationofeffectivemultiquarkinteractionswithua1breaking |
| first_indexed |
2023-05-20T17:24:22Z |
| last_indexed |
2023-05-20T17:24:22Z |
| _version_ |
1796153217988427776 |