On the calculation of multiplicities for representations of SU(n)

Szczyrba, Igor

doi:10.1007/bf00316681

Cited by 3 publications

(2 citation statements)

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“…The consistency of constraint Equations (4.1) and (4.2) and dynamical Equations (4.3) -(4.6) is ensured by the above-mentioned contracted Bianchi identities. The proof of this fact is similar to that known for the classical Einstein theory [6], [12], [15].…”

Section: S K _ E(a)~(b) ) _ E(a)e(b) Qrq E~s) + E(b)e(a) Qrq E~s) + ~mentioning

confidence: 56%

“…Their method did not enable them to recover (1.2a) from the Hamilton equation. However, for theories of gravity with matter fields [6], [7] and for theories with non-Einstein gravitational Lagrangians [8], [9], [10], [11] Equation (1.2a) is much more complicated and therefore should be treated as parallel to (1.2b). In this paper we solve this problem for the Einstein-Cartan-Sciama-Kibble theory of gravity and show that all the variational equations of the theory can be obtained from the Hamilton equation of type (1.1).…”

Section: Letters In Mathematical Physicsmentioning

confidence: 99%

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A Hamiltonian formulation of the Einstein-Cartan-Sciama-Kibble theory of gravity

Franckiewicz

Szczyrba

1982

Lett Math Phys

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A B S T R ACT. We postulate the energy-momentum function E for the ECSK theory of gravity and formulate the functional Hamiltonian equation in terms of the energy-momentum function E and the symplectic 2-form g2. The system of partial differential equations which follows from the functional Hamilton equation is equivalent to the system of variational equations of the ECSK theory. The Hamiltonian method gives rise to a natural division of these equations into i0 constraint equations and the set of dynamical equations. We discuss the geometric sense of the constraint equations and their relations to the initial value problem.

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Section: S K _ E(a)~(b) ) _ E(a)e(b) Qrq E~s) + E(b)e(a) Qrq E~s) + ~mentioning

confidence: 56%

Section: Letters In Mathematical Physicsmentioning

confidence: 99%

A Hamiltonian formulation of the Einstein-Cartan-Sciama-Kibble theory of gravity

Franckiewicz

Szczyrba

1982

Lett Math Phys

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Weyl group and tensor operators for hadron-type SU(n) representations

Cieciura

Szczyrba

1987

Journal of Mathematical Physics

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Let a particle symmetry be described by a simple Lie algrebra 𝔤 of the type An−1, i.e., 𝔤=sl(n,C) or 𝔤 is a real form of sl(n,C). For 𝔤 representations describing three-particle or particle–antiparticle states, relationships between two actions, the action of 𝔤 and the action of the corresponding Weyl group Sn, on observables are analyzed. It is shown, in particular, how impossible physical relations depend on these two actions. The results enable one to verify quickly if given experimental data can be fitted by means of a 𝔤-symmetry theory.

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