Meson mass formula in broken SUN symmetry and its applications

Hayashi, Hirotsugu; Ishiwata, I.; Iwao, S.; Shako, M.; Takeshita, Shoji

doi:10.1016/0003-4916(76)90017-8

Cited by 14 publications

(8 citation statements)

References 31 publications

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“…which reproduce the su(3) expressions when only the (1,2 and 5)-labelled quantities are retained. Our choice of signs in (49) depends upon the signs of the structure constants for su(5) -our choice of lambda-matrices was made above to yield agreement with the tables given in [22], upon our wish of avoiding constant terms in the definitions (52) and upon our desire of having all entries in (57) below equal to +1. We define the highest weight state of any irrep of su(5) by taking first the highest Z 4 eigenvalue, then the highest Z 3 eigenvalue that can arise for that Z 4 eigenvalue.…”

Section: Basic Definitions For Su(5)mentioning

confidence: 99%

“…The relevant f abc are in the tables of [22] and we used data from MAPLE, which agreed with these tables.…”

Section: Su(5) Fermionic Operatorsmentioning

confidence: 99%

“…We use an explicit and essentially standard (cf. [22]) set of Gell-Mann lambda matrices for su (5). For the diagonal matrices λ (p 2 −1) , (p = 2, 3, 4, 5), we have…”

Section: Basic Definitions For Su(5)mentioning

confidence: 99%

“…The index pairs (1, 2), (4, 5), (6, 7), (9,10), (11,12), (13,14), (16,17), (18,19), (20,21), (22,23) , (47) are associated with the remaining λ's in a way that can be inferred from the following array:…”

Section: Basic Definitions For Su(5)mentioning

confidence: 99%

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Fermionic realisations of simple Lie algebras and their invariant fermionic operators

Azcárraga

Macfarlane

2000

Nuclear Physics B

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We study the representation D of a simple compact Lie algebra g of rank l constructed with the aid of the hermitian Dirac matrices of a (dim g)-dimensional euclidean space. The irreducible representations of g contained in D are found by providing a general construction on suitable fermionic Fock spaces. We give full details not only for the simplest odd and even cases, namely su(2) and su (3), but also for the next (dim g)-even case of su(5). Our results are far reaching: they apply to any g-invariant quantum mechanical system containing dim g fermions. Another reason for undertaking this study is to examine the role of the g-invariant fermionic operators that naturally arise. These are given in terms of products of an odd number of gamma matrices, and include, besides a cubic operator, (l − 1) fermionic scalars of higher order. The latter are constructed from the Lie algebra cohomology cocycles, and must be considered to be of theoretical significance similar to the cubic operator. In the (dim g)-even case, the product of all l operators turns out to be the chirality operator γ q , q = (dim g + 1).

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Section: Basic Definitions For Su(5)mentioning

confidence: 99%

“…The relevant f abc are in the tables of [22] and we used data from MAPLE, which agreed with these tables.…”

Section: Su(5) Fermionic Operatorsmentioning

confidence: 99%

“…We use an explicit and essentially standard (cf. [22]) set of Gell-Mann lambda matrices for su (5). For the diagonal matrices λ (p 2 −1) , (p = 2, 3, 4, 5), we have…”

Section: Basic Definitions For Su(5)mentioning

confidence: 99%

Section: Basic Definitions For Su(5)mentioning

confidence: 99%

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Fermionic realisations of simple Lie algebras and their invariant fermionic operators

Azcárraga

Macfarlane

2000

Nuclear Physics B

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“…To discuss this and other examples involving G = SU(4), it is most convenient to generalise the Gell-Mann λ-matrices from SU(3) to SU(4) in a fashion different from that in [3,14] and to use the d and f tensors that follow from this new set. Thus, set…”

Section: B) (Symmetric Cosets)mentioning

confidence: 99%