On the Euler angles for SU(N)

Bertini, S.; Cacciatori, Sergio L.; Cerchiai, Bianca L.

doi:10.1063/1.2190898

Cited by 40 publications

(56 citation statements)

References 8 publications

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“…Below we will find some particular cases of H. We define the Lie algebra valued variables q i , y a through A −1Ȧ = i {q i E α i +ẏ a H a } in the generalized Gell-Mann representation [26]. In terms of these variables the action (3.2), for a diagonal mass matrix such that D ij = δ ij , takes the form…”

Section: Semi-classical Quantization and The Gsg Ansatzmentioning

confidence: 99%

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

Blas

2007

J. High Energy Phys.

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The solitons and kinks of the SU (3) generalized sine-Gordon model (GSG) are shown to describe the baryonic spectrum of two-dimensional quantum chromodynamics (QCD 2 ). The GSG model arises in the low-energy effective action of bosonized QCD 2 with unequal quark mass parameters. The GSG potential for N f = 3 flavors resembles the potential of the effective chiral lagrangian proposed by Witten to describe low-energy behavior of four dimensional QCD. Among the attractive features of the GSG model are the variety of soliton and kink type solutions for QCD 2 unequal quark mass parameters [JHEP(0701)(2007)(027)]. Exotic baryons in QCD 2 [J. Ellis et al JHEP0508(2005)081] are discussed in the context of the GSG model. Various semi-classical computations are performed improving the results of this reference and clarifying the role of unequal quark masses. The remarkable double sine Gordon model also arises as a reduced GSG model bearing a kink(K) type solution describing a multi-baryon; so, the description of some resonances in QCD 2 may take advantage of the properties of the KK system.

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Section: Semi-classical Quantization and The Gsg Ansatzmentioning

confidence: 99%

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

Blas

2007

J. High Energy Phys.

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“…where Rp p p is a root system, R + p p p is a choice of corresponding positive roots, 10) and k is a Weyl invariant function over Rp p p whose values kα have positive real part. For example, the multiplicities mα select such a function.…”

Section: Further Connections With the Generalized Dyson Integralsmentioning

confidence: 99%

“…A simple procedure to parameterize compact simple Lie groups is provided by the generalized Euler parameterization [4,5,6,7,8,9,10,26,27]. The role of Lie groups both in mathematics and in physics is very important and well known.…”

Section: Introductionmentioning

confidence: 99%

“…In [7,9], in studying the case of G 2 , a more general strategy (later reviewed in [8]), which was expected to be applicable case by case to all compact simply connected simple Lie groups, has been developed. Indeed, it has been first applied to the SU (N ) case in [10], showing the drastic simplification with respect to [26,27], and successively to the exceptional Lie groups F 4 , E 6 and E 7 in [6,5,4] respectively. It is only after these several years experience that we realized that the success of our method was due to the deep geometrical structure of the compact connected simple Lie groups, and, in fact, of all compact connected Lie groups.…”

Section: Introductionmentioning

confidence: 99%

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Compact Lie groups: Euler constructions and generalized Dyson conjecture

Cacciatori

Piazza

Scotti

2017

Trans. Amer. Math. Soc.

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Abstract. A generalized Euler parameterization of a compact Lie group is a way for parameterizing the group starting from a maximal Lie subgroup, which allows a simple characterization of the range of parameters. In the present paper we consider the class of all compact connected Lie groups. We present a general method for realizing their generalized Euler parameterization starting from any symmetrically embedded Lie group. Our construction is based on a detailed analysis of the geometry of these groups. As a byproduct this gives rise to an interesting connection with certain Dyson integrals. In particular, we obtain a geometry based proof of a Macdonald conjecture regarding the Dyson integrals correspondent to the root systems associated to all irreducible symmetric spaces. As an application of our general method we explicitly parameterize all groups of the class of simple, simply connected compact Lie groups. We provide a table giving all necessary ingredients for all such Euler parameterizations.

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“…Essentially this has restricted attention to groups directly related to the rotation group and its covering, SU(2). However, recently there has been much progress in finding suitable parameterisations for the higher dimensional unitary groups [4,5,6,7] and particularly for the group SU(3) [8,9]. These advances open the door to detailed investigations of dynamics on spaces such as the five-sphere, S 5 , now viewed as the reduction from SU (3) to SU(3)/SU (2).…”

Section: Introductionmentioning

confidence: 99%

On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2)

Gerdt

Horan

Khvedelidze

et al. 2006

Journal of Mathematical Physics

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The reduced Hamiltonian system on T * (SU(3)/SU(2)) is derived from a Riemannian geodesic motion on the SU(3) group manifold parameterised by the generalised Euler angles and endowed with a bi-invariant metric. Our calculations show that the metric defined by the derived reduced Hamiltonian flow on the orbit space SU(3)/SU(2) ≃ S 5 is not isometric or even geodesically equivalent to the standard Riemannian metric on the five-sphere S 5 embedded into R 6 .

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On the Euler angles for SU(N)

Cited by 40 publications

References 8 publications

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

Exotic baryons in two-dimensional QCD and the generalized sine-Gordon solitons

Compact Lie groups: Euler constructions and generalized Dyson conjecture

On the Hamiltonian reduction of geodesic motion on SU(3) to SU(3)/SU(2)

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