International Journal of Modern Physics A

The additive quark model is one of the simplest and oldest models for the description of soft processes at high energies, and it still works. We present here a review of this model and verify the rules of quark combinatorics following from it in hadronic Z⁰ decays.

The asymmetry, between electric (E) and magnetic (H) fields of Maxwell's equation is here analyzed by using the concept of chirality. The chiral spinorial approach sets the stage for the construction of a more general theory of spin-1 particles than usual electrodynamics. Chiral components of a rank-2 spinor field are taken as the dynamic variables of the theory. A rank-2 spinor accommodates another particle (the magnetic photon). This new particle emerges naturally from chiral invariance arguments. The nonexistence, in nature, of such a particle is the reason for the nonexistence of monopoles and the asymmetry in Maxwell's equation. The existence of magnetic monopoles would restore the symmetry of Maxwell's equation. We establish, in this way, at a very formal level, the connection between magnetic monopoles and chiral asymmetry.

For the noncommutative torus , in the case of the noncommutative parameter , we construct the basis of Hilbert space ℋ_n in terms of θ functions of the positions z_i of n solitons. The wrapping around the torus generates the algebra , which is the Z_n × Z_n Heisenberg group on θ functions. We find the generators g of a local elliptic su(n), which transform covariantly by the global gauge transformation of . By acting on ℋ_n we establish the isomorphism of and g. We embed this g into the L-matrix of the elliptic Gaudin and Calogero–Moser models to give the dynamics. The moment map of this twisted cotangent bundle is matched to the D-equation with the Fayet–Illiopoulos source term, so the dynamics of the noncommutative solitons become that of the brane. The geometric configuration (k, u) of the spectral curve det|L(u) - k| = 0 describes the brane configuration, with the dynamical variables z_i of the noncommutative solitons as the moduli T^{⊗ n}/S_n. Furthermore, in the noncommutative Chern–Simons theory for the quantum Hall effect, the constrain equation with quasiparticle source is identified also with the moment map equation of the noncommutative cotangent bundle with marked points. The eigenfunction of the Gaudin differential L-operators as the Laughlin wave function is solved by Bethe ansatz.

While it is clear that in some kinematic regime QCD can be described by an effective (as opposed to fundamental) string theory, it is not at all clear how this string theory should be. The "natural" candidate, the bosonic string, leads to amplitudes with the usual problems related to the existence of the tachyon, the absence of the adequate Adler zero, and massless vector particles, not to mention the conformal anomaly. The supersymmetric version does not really solve most of these problems. For a long time it has been believed that the solution of at least some of these difficulties is associated to a proper identification of the vacuum, but this program has remained elusive. We show in this work how the first three problems can be avoided, by using a sigma model approach where excitations above the correct (chirally noninvariant) QCD vacuum are identified. At the leading order in a derivative expansion we recover the nonlinear sigma model of pion interactions. At the next-to-leading order the O(p⁴) Lagrangian of Gasser and Leutwyler is obtained, with values for the coefficients that match the observed values. We also discuss some issues related to the conformal anomaly.

A procedure, allowing us to calculate the coefficients of the SW prepotential in the framework of the instanton calculus is presented. As a demonstration explicit calculations for 2, 3 and 4-instanton contributions are carried out.