A 'differential measure' is used to cast our calculus for the group SU (3) into a form similar to Schwinger's boson operator calculus for the group SU (2). It is then applied to compute (i) the inner product between the basis states and (ii) an algebraic formula for the Clebsch-Gordan coefficients. These were obtained earlier by us using Gaussian integration techniques.

The zero distribution of orthogonal polynomials pn,N , n = 0, 1, . . . generated by recurrence coefficients an,N and bn,N depending on a parameter N has been recently considered by Kuijlaars and Van Assche under the assumption that an,N and bn,N behave like a(n/N) and b(n/N), respectively, where a(·) and b(·) are continuous functions. Here, we extend this result by allowing a(·) and b(·) to be ...

The purpose of this paper is to find out a set of general recurrence formulas for the calculus of the SU(3) Clebsch-Gordan coefficients. The first six sections are introductory, presenting the notations and general group theoretical methods applied to SU(3). The following eight sections are devoted to a detailed treatment of the carrier spaces of the irreducible representations and their direct...

in this paper, we calculate theoretically the relaxation rates of hot, thermal and antinodal quasiparticles by using fermi’s golden rule. the transition probabilities at low temperatures express in terms of bogoliubov coefficients, singlet and triplet scattering amplitudes and dimensionless landau parameters. the values of landau parameters may be determined by comparison with the experimental ...

We identify “spurious” states in meson-baryon scattering, those that appear in QCD for Nc > 3 but decouple for Nc = 3. The key observation is that the relevant flavor SU(3) Clebsch-Gordan coefficients contain factors of 1−3/Nc. We show that this method works even if SU(3) is badly broken. We also observe that resonant scattering poles lying outside naive quark model multiplets are not necessari...

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known res...