Fréchet derivative for light-like Wilson loops
We address the equations of motion for the light-like QCD Wilson exponentials defined in the generalized loop space. We attribute an important class of the infinitesimal shape variations of the rectangular light-like Wilson loops to the Fréchet derivative associated to a diffeomorphism in loop space...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2015-02-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269314009009 |
| _version_ | 1811299021474496512 |
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| author | I.O. Cherednikov T. Mertens |
| author_facet | I.O. Cherednikov T. Mertens |
| author_sort | I.O. Cherednikov |
| collection | DOAJ |
| description | We address the equations of motion for the light-like QCD Wilson exponentials defined in the generalized loop space. We attribute an important class of the infinitesimal shape variations of the rectangular light-like Wilson loops to the Fréchet derivative associated to a diffeomorphism in loop space what enables the derivation of the law of the classically conformal-invariant shape variations. We show explicitly that the Fréchet derivative coincides (at least in the leading perturbative order) with the area differential operator introduced in the previous works. We discuss interesting implications of this result which will allow one to relate the rapidity evolution and ultra-violet evolution of phenomenologically important quantum correlation functions (such as 3-dimensional parton distribution functions) and geometrical properties of the light-like cusped Wilson loops. |
| first_indexed | 2024-04-13T06:29:01Z |
| format | Article |
| id | doaj.art-299cf99357de45c1994658b554157196 |
| institution | Directory Open Access Journal |
| issn | 0370-2693 |
| language | English |
| last_indexed | 2024-04-13T06:29:01Z |
| publishDate | 2015-02-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-299cf99357de45c1994658b5541571962022-12-22T02:58:14ZengElsevierPhysics Letters B0370-26932015-02-017417176Fréchet derivative for light-like Wilson loopsI.O. Cherednikov0T. Mertens1EDF, Departement Fysica, Universiteit Antwerpen, B-2020 Antwerpen, BelgiumCorresponding author.; EDF, Departement Fysica, Universiteit Antwerpen, B-2020 Antwerpen, BelgiumWe address the equations of motion for the light-like QCD Wilson exponentials defined in the generalized loop space. We attribute an important class of the infinitesimal shape variations of the rectangular light-like Wilson loops to the Fréchet derivative associated to a diffeomorphism in loop space what enables the derivation of the law of the classically conformal-invariant shape variations. We show explicitly that the Fréchet derivative coincides (at least in the leading perturbative order) with the area differential operator introduced in the previous works. We discuss interesting implications of this result which will allow one to relate the rapidity evolution and ultra-violet evolution of phenomenologically important quantum correlation functions (such as 3-dimensional parton distribution functions) and geometrical properties of the light-like cusped Wilson loops.http://www.sciencedirect.com/science/article/pii/S0370269314009009 |
| spellingShingle | I.O. Cherednikov T. Mertens Fréchet derivative for light-like Wilson loops Physics Letters B |
| title | Fréchet derivative for light-like Wilson loops |
| title_full | Fréchet derivative for light-like Wilson loops |
| title_fullStr | Fréchet derivative for light-like Wilson loops |
| title_full_unstemmed | Fréchet derivative for light-like Wilson loops |
| title_short | Fréchet derivative for light-like Wilson loops |
| title_sort | frechet derivative for light like wilson loops |
| url | http://www.sciencedirect.com/science/article/pii/S0370269314009009 |
| work_keys_str_mv | AT iocherednikov frechetderivativeforlightlikewilsonloops AT tmertens frechetderivativeforlightlikewilsonloops |