On geometric bases for quantum A-polynomials of knots
A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum A- and C-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in muc...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-01-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S037026932400697X |
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| author | Dmitry Galakhov Alexei Morozov |
| author_facet | Dmitry Galakhov Alexei Morozov |
| author_sort | Dmitry Galakhov |
| collection | DOAJ |
| description | A simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum A- and C-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising. |
| format | Article |
| id | doaj-art-dc0f945a233f498b81a824dda00034ee |
| institution | Kabale University |
| issn | 0370-2693 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj-art-dc0f945a233f498b81a824dda00034ee2025-01-10T04:37:16ZengElsevierPhysics Letters B0370-26932025-01-01860139139On geometric bases for quantum A-polynomials of knotsDmitry Galakhov0Alexei Morozov1NRC “Kurchatov Institute”, 123182, Moscow, Russia; IITP RAS, 127051, Moscow, Russia; ITEP, Moscow, Russia; Corresponding author.MIPT, 141701, Dolgoprudny, Russia; NRC “Kurchatov Institute”, 123182, Moscow, Russia; IITP RAS, 127051, Moscow, Russia; ITEP, Moscow, RussiaA simple geometric way is suggested to derive the Ward identities in the Chern-Simons theory, also known as quantum A- and C-polynomials for knots. In quasi-classical limit it is closely related to the well publicized augmentation theory and contact geometry. Quantization allows to present it in much simpler terms, what could make these techniques available to a broader audience. To avoid overloading of the presentation, only the case of the colored Jones polynomial for the trefoil knot is considered, though various generalizations are straightforward. Restriction to solely Jones polynomials (rather than full HOMFLY-PT) is related to a serious simplification, provided by the use of Kauffman calculus. Going beyond looks realistic, however it remains a problem, both challenging and promising.http://www.sciencedirect.com/science/article/pii/S037026932400697X |
| spellingShingle | Dmitry Galakhov Alexei Morozov On geometric bases for quantum A-polynomials of knots Physics Letters B |
| title | On geometric bases for quantum A-polynomials of knots |
| title_full | On geometric bases for quantum A-polynomials of knots |
| title_fullStr | On geometric bases for quantum A-polynomials of knots |
| title_full_unstemmed | On geometric bases for quantum A-polynomials of knots |
| title_short | On geometric bases for quantum A-polynomials of knots |
| title_sort | on geometric bases for quantum a polynomials of knots |
| url | http://www.sciencedirect.com/science/article/pii/S037026932400697X |
| work_keys_str_mv | AT dmitrygalakhov ongeometricbasesforquantumapolynomialsofknots AT alexeimorozov ongeometricbasesforquantumapolynomialsofknots |