An investigation into the use of zeros in some scattering processes

Bowcock, J. E.; Dacunha, N. M. C.; Queen, N.M.

doi:10.1088/0305-4616/11/10/011

Cited by 7 publications

(20 citation statements)

References 9 publications

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“…As we expected, the c-dependent structure constants become more involved rational functions of c. Also one can see that there exist extra terms in the right hand side of (4) which do not appear in the classical version. The classical limit is given by the usual relation between the Poisson bracket and the commutator while c → ∞ [6]. But we also need to take into account nonlinear terms because of nonlinearity of our algebra.…”

Section: Introductionmentioning

confidence: 99%

THE FULL STRUCTURE OF QUANTUM N=2 SUPER-$W_3^{\left( 2 \right)} $ ALGEBRA

Ahn¹,

Krivonos²,

Sorin³

1995

Mod. Phys. Lett. A

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Section: Introductionmentioning

confidence: 99%

THE FULL STRUCTURE OF QUANTUM N=2 SUPER-$W_3^{\left( 2 \right)} $ ALGEBRA

Ahn¹,

Krivonos²,

Sorin³

1995

Mod. Phys. Lett. A

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“…(2.9). On the other hand, in principle the null-state conditions are not necessary conditions for the OPEs (2.9) 3. Remember that one Jacobi-identity produces in general a set of constraints.…”

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confidence: 99%

Classification of structure constants for W-algebras from highest weights

Hornfeck

1994

Nuclear Physics B

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We show that the structure constants of W-algebras can be grouped according to the lowest (bosonic) spin(s) of the algebra. The structure constants in each group are described by a unique formula, depending on a functional parameter h(c) that is characteristic for each algebra. As examples we give the structure constants C 4 33 and C 4 44 for the algebras of type W(2, 3, 4, . . .) (that include the WA n−1 -algebras) and the structure constant C 4 44 for the algebras of type W(2, 4, . . .), especially for all the algebras WD n , WB(0, n), WB n and WC n . It also includes the bosonic projection of the super-Virasoro algebra and a yet unexplained algebra of type W(2, 4, 6) found previously.

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“…Given an extended conformal algebra, we can define the (linearized) vacuum preserving algebra (VPA) by expanding each generator W α (z) of conformal weight h in modes: W α (z) = n W α n z −n−h and considering the finite-dimensional subalgebra which is generated by W α n with |n| ≤ (h − 1) on dropping all quadratic and higher-order terms. This vacuum-preserving algebra is isomorphic to the original Lie algebra G, as explained in [13]. Furthermore, the VPA always contains the subalgebra S, whose generators {M 0 , M ± } correspond precisely to the usual sl(2) subalgebra of the Virasoro algebra with generators {L 0 , L ±1 }.…”

Section: W-algebras and Conformal Field Theorymentioning

confidence: 99%

On the classification of real forms of non-Abelian Toda theories and W-algebras

Evans

Madsen

1998

Nuclear Physics B

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We consider conformal non-Abelian Toda theories obtained by hamiltonian reduction from Wess-Zumino-Witten models based on general real Lie groups. We study in detail the possible choices of reality conditions which can be imposed on the WZW or Toda fields and prove correspondences with sl(2, R) embeddings into real Lie algebras and with the possible real forms of the associated W-algebras. We devise a a method for finding all real embeddings which can be obtained from a given embedding of sl(2, C) into a complex Lie algebra. We then apply this to give a complete classification of real embeddings which are principal in some simple regular subalgebra of a classical Lie algebra. hep-th/9802201US-FT/2-98where the field g(x + , x − ) ∈ G is a function of light-cone coordinates x ± on two-dimensional spacetime; D is some three-dimensional disc whose boundary is spacetime; and 'tr' denotes the usual invariant inner-product on the Lie algebra G. The equations of motion are equivalent to the conservation conditionsfor the Kac-Moody (KM) currents defined bywhich take values in G. The constant k is the level. If we introduce a basis {t a } for G and expand the current J ± on this basis:then the Poisson-brackets of the functions J a ± (x ± ) can be given in the form (suppressing ± indices for convenience) {J a (x), J b (y)} PB = kη ab δ ′ (x − y) + f ab c J c (x)δ(x − y)

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An investigation into the use of zeros in some scattering processes

Cited by 7 publications

References 9 publications

THE FULL STRUCTURE OF QUANTUM N=2 SUPER-$W_3^{\left( 2 \right)} $ ALGEBRA

THE FULL STRUCTURE OF QUANTUM N=2 SUPER-$W_3^{\left( 2 \right)} $ ALGEBRA

Classification of structure constants for W-algebras from highest weights

On the classification of real forms of non-Abelian Toda theories and W-algebras

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