A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules
Traditionally, the dynamics of a quantum physical system is described on the basis of the field models, where the fundamental role is played by the algebra of quantized fields and its automorphisms (forming a compact group). However, despite this important role of quantized fields, the fields are un...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2017-06-01
|
| Series: | Учёные записки Казанского университета. Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/a-simple-algebraic-model-for-few-nucleon-systems_309940.html |
| _version_ | 1797984125639983104 |
|---|---|
| author | M.I. Kirillov A.S. Nikitin A.S. Sitdikov |
| author_facet | M.I. Kirillov A.S. Nikitin A.S. Sitdikov |
| author_sort | M.I. Kirillov |
| collection | DOAJ |
| description | Traditionally, the dynamics of a quantum physical system is described on the basis of the field models, where the fundamental role is played by the algebra of quantized fields and its automorphisms (forming a compact group). However, despite this important role of quantized fields, the fields are unobservable quantities.
As shown by R. Haag, a quantum physical system can also be described in a dual way, where the algebra of observables and the semigroup (category) of its endomorphisms are taken as the initial object. Both approaches should provide practically the same information about the physical system, but the second approach is more natural, because it is based only on the experimentally observed information. In this case, the concept of duality reduces to the existence of a dual object to a compact group: in the case of the Abelian group, this is a group of its characters (Pontryagin duality); in the case of the non-Abelian group, this is the category of representations of the given group (Tannaka–Krein duality). From the physical point of view, the dual object describes charges (Abelian charges in the case of the Abelian compact group and non-Abelian ones in the case of the non-Abelian group) and, hence, the superselected structure of the physical system.
We have developed a model for describing non-Abelian isotopic charges of nucleon systems. The category of representations of the compact isotopic rotation group describes the superselected structure by isospin, and each irreducible representation is indexed by one of the numbers {0; 1/2; 1; 3/2; 2;…}. It has been shown that a special projection operator belonging to the algebra of endomorphisms of a fixed object of the category allows to obtain a bound state of nucleons by projecting onto antisymmetric subspace. The states of such nucleons obey parastatistics of the order 2. It has been also demonstrated that the intertwining operators of objects with a vacuum sector correspond to the fields carrying isotopic charges.
Since the model takes into account the conservation of isospin, it is also applicable to the study of resonances, which are under heated discussions at the present time. |
| first_indexed | 2024-04-11T06:56:35Z |
| format | Article |
| id | doaj.art-4854d70289c144a68d90894c09b9485d |
| institution | Directory Open Access Journal |
| issn | 2541-7746 2500-2198 |
| language | English |
| last_indexed | 2024-04-11T06:56:35Z |
| publishDate | 2017-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета. Серия Физико-математические науки |
| spelling | doaj.art-4854d70289c144a68d90894c09b9485d2022-12-22T04:38:59ZengKazan Federal UniversityУчёные записки Казанского университета. Серия Физико-математические науки2541-77462500-21982017-06-011592191203A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection RulesM.I. Kirillov0A.S. Nikitin1A.S. Sitdikov2Kazan State Power Engineering University, Kazan, 420066 RussiaKazan State Power Engineering University, Kazan, 420066 RussiaKazan State Power Engineering University, Kazan, 420066 RussiaTraditionally, the dynamics of a quantum physical system is described on the basis of the field models, where the fundamental role is played by the algebra of quantized fields and its automorphisms (forming a compact group). However, despite this important role of quantized fields, the fields are unobservable quantities. As shown by R. Haag, a quantum physical system can also be described in a dual way, where the algebra of observables and the semigroup (category) of its endomorphisms are taken as the initial object. Both approaches should provide practically the same information about the physical system, but the second approach is more natural, because it is based only on the experimentally observed information. In this case, the concept of duality reduces to the existence of a dual object to a compact group: in the case of the Abelian group, this is a group of its characters (Pontryagin duality); in the case of the non-Abelian group, this is the category of representations of the given group (Tannaka–Krein duality). From the physical point of view, the dual object describes charges (Abelian charges in the case of the Abelian compact group and non-Abelian ones in the case of the non-Abelian group) and, hence, the superselected structure of the physical system. We have developed a model for describing non-Abelian isotopic charges of nucleon systems. The category of representations of the compact isotopic rotation group describes the superselected structure by isospin, and each irreducible representation is indexed by one of the numbers {0; 1/2; 1; 3/2; 2;…}. It has been shown that a special projection operator belonging to the algebra of endomorphisms of a fixed object of the category allows to obtain a bound state of nucleons by projecting onto antisymmetric subspace. The states of such nucleons obey parastatistics of the order 2. It has been also demonstrated that the intertwining operators of objects with a vacuum sector correspond to the fields carrying isotopic charges. Since the model takes into account the conservation of isospin, it is also applicable to the study of resonances, which are under heated discussions at the present time.https://kpfu.ru/a-simple-algebraic-model-for-few-nucleon-systems_309940.htmlcuntz algebratensor monoidal c*-categorydibaryon systemisospinsuperselection rules |
| spellingShingle | M.I. Kirillov A.S. Nikitin A.S. Sitdikov A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules Учёные записки Казанского университета. Серия Физико-математические науки cuntz algebra tensor monoidal c*-category dibaryon system isospin superselection rules |
| title | A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules |
| title_full | A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules |
| title_fullStr | A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules |
| title_full_unstemmed | A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules |
| title_short | A Simple Algebraic Model for Few-Nucleon Systems in the Presence of Non-Abelian Superselection Rules |
| title_sort | simple algebraic model for few nucleon systems in the presence of non abelian superselection rules |
| topic | cuntz algebra tensor monoidal c*-category dibaryon system isospin superselection rules |
| url | https://kpfu.ru/a-simple-algebraic-model-for-few-nucleon-systems_309940.html |
| work_keys_str_mv | AT mikirillov asimplealgebraicmodelforfewnucleonsystemsinthepresenceofnonabeliansuperselectionrules AT asnikitin asimplealgebraicmodelforfewnucleonsystemsinthepresenceofnonabeliansuperselectionrules AT assitdikov asimplealgebraicmodelforfewnucleonsystemsinthepresenceofnonabeliansuperselectionrules AT mikirillov simplealgebraicmodelforfewnucleonsystemsinthepresenceofnonabeliansuperselectionrules AT asnikitin simplealgebraicmodelforfewnucleonsystemsinthepresenceofnonabeliansuperselectionrules AT assitdikov simplealgebraicmodelforfewnucleonsystemsinthepresenceofnonabeliansuperselectionrules |