| 1. |
- Alcock-Zeilinger, Judith, et al.
(författare)
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Wigner 6 j symbols for SU(N) : Symbols with at least two quark-lines
- 2023
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 64:2
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Tidskriftsartikel (refereegranskat)abstract
- We study a class of SU(N) Wigner 6j symbols involving two fundamental representations and derive explicit formulas for all 6j symbols in this class. Our formulas express the 6j symbols in terms of the dimensions of the involved representations, and they are thereby functions of N. We view these explicit formulas as a first step toward efficiently decomposing SU(N) color structures in terms of group invariants.
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| 2. |
- Guhr, Thomas, et al.
(författare)
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Semiclassical limits for the QCD Dirac operator
- 2007
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Ingår i: Annals of Physics. - : Elsevier BV. - 0003-4916. ; 322:2, s. 287-314
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Tidskriftsartikel (refereegranskat)abstract
- We identify three semiclassical parameters in the QCD Dirac operator. Mutual coupling of the different types of degrees of freedom (translational, colour and spin) depends on how the semiclassical limit is taken. We discuss various semiclassical limits and their potential to describe spectrum and spectral statistics of the QCD Dirac operator close to zero virtuality. (c) 2006 Elsevier Inc. All rights reserved.
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| 3. |
- Keppeler, Stefan, et al.
(författare)
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Hermitian Young operators
- 2014
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 55:2
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Tidskriftsartikel (refereegranskat)abstract
- Starting from conventional Young operators, we construct Hermitian operators which project orthogonally onto irreducible representations of the (special) unitary group. (C) 2014 AIP Publishing LLC.
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| 4. |
- Keppeler, Stefan, et al.
(författare)
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Orthogonal multiplet bases in SU(N-c) color space
- 2012
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Ingår i: Journal of High Energy Physics. - 1029-8479. ; :9
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Tidskriftsartikel (refereegranskat)abstract
- We develop a general recipe for constructing orthogonal bases for the calculation of color structures appearing in QCD for any number of partons and arbitrary N-c. The bases are constructed using hermitian gluon projectors onto irreducible subspaces invariant under SU(N-c). Thus, each basis vector is associated with an irreducible representation of SU(N-c). The resulting multiplet bases are not only orthogonal, but also minimal for finite N-c. As a consequence, for calculations involving many colored particles, the number of basis vectors is reduced significantly compared to standard approaches employing overcomplete bases. We exemplify the method by constructing multiplet bases for all processes involving a total of 6 external colored partons.
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| 5. |
- Keppeler, Stefan
(författare)
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Semiclassical quantisation rules for the Dirac and Pauli equations
- 2003
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Ingår i: Annals of Physics. - 0003-4916. ; 304:1, s. 40-71
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Tidskriftsartikel (refereegranskat)abstract
- We derive explicit semiclassical quantisation conditions for the Dirac and Pauli equations. We show that the spin degree of freedom yields a contribution which is of the same order of magnitude as the Maslov correction in Einstein-Brillouin-Keller quantisation. In order to obtain this result a generalisation of the notion of integrability for a certain skew product flow of classical translational dynamics and classical spin precession has to be derived. Among the examples discussed is the relativistic Kepler problem with Thomas precession, whose treatment sheds some light on the amazing success of Sommerfeld's theory of fine structure [Ann. Phys. (Leipzig) 51 (1916) 1]. (C) 2003 Elsevier Science (USA). All rights reserved.
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| 6. |
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| 7. |
- Keppeler, Stefan, et al.
(författare)
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Wigner 6j symbols with gluon lines : completing the set of 6j symbols required for color decomposition
- 2024
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Ingår i: Journal of High Energy Physics. - 1029-8479. ; 2024:5
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Tidskriftsartikel (refereegranskat)abstract
- We construct a set of Wigner 6j symbols with gluon lines (adjoint representations) in closed form, expressed in terms of similar 6j symbols with quark lines (fundamental representations). Together with these Wigner 6j symbols with quark lines, this gives a set of 6j symbols sufficient for treating QCD color structure for any number of external particles, in or beyond perturbation theory. This facilitates a complete treatment of QCD color structure in terms of orthogonal multiplet bases, without the need of ever explicitly constructing the corresponding bases. We thereby open up for a completely representation theory based treatment of SU(N) color structure, with the potential of significantly speeding up the color structure treatment.
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