International Journal of Modern Physics A

We construct an algebraic representation of the geometrical objects (loop and surface variables) dual to the spins in 2 and 3D Ising models. This algebraic calculus is simpler than dealing with the geometrical objects, in particular when analyzing geometry factors and counting problems. For the 2D case we give the corrected loop expansion of the free energy and the radius of convergence for this series. For the 3D case we give a simple derivation of the geometry factor which prevents overcounting of surfaces in the intrinsic geometry representation of the partition function, and find a classification of the surfaces to be summed over. For 2 and 3D we derive a compact formula for 2n-point functions in loop (surface) representation.

We investigate the implications for the measurability of distances of a covariant dimensionful "κ" deformation of D=4 relativistic symmetries, with quantum time coordinate and modified Heisenberg algebra. We show that the structure of the deformed mass-shell condition has significant implications for measurement procedures relying on light probes, whereas in the case of heavy probes the most sizeable effect is due to the nontrivial commutation relation between three-momenta and quantum time coordinate. We argue that these findings might indicate that κ-Poincaré symmetries capture some aspects of the physics of the quantum-gravity vacuum.

A qqq BSE formalism based on DBχS of an input four-fermion Lagrangian of "current" u, d quarks interacting pairwise via gluon-exchange-propagator in its nonperturbative regime, is employed for the calculation of baryon self-energy via quark-loop integrals. To that end the baryon-qqq vertex function is derived under Covariant Instantaneity Ansatz (CIA), using Green function techniques. This is a three-body extension of an earlier (two-body) result on the exact 3D–4D interconnection for the respective BS wave functions under 3D kernel support. The nonperturbative QCD feature of this approach (vis-a-vis chiral perturbation theory — see text for comparison) is preserved through the gluon exchange propagator in the infrared regime (characterized by two parameters C₀, ω₀), precalibrated to both and qqq spectra plus other observables, together with a DBχ S mechanism to generate the dynamical mass m(p).

The quark-loop integrals for the neutron (n) – proton (p) mass difference receive contributions from two sources: (i) the strong SU(2) effect arising from the d-u mass difference (4 MeV); (ii) the e.m. effect of the respective quark charges. The resultant n-p difference comes dominantly from the d-u effect (+1.71 MeV), which is mildly offset by e.m. effect (-0.44), subject to gauge corrections. For an estimate of the latter a general method for QED gauge corrections to an arbitrary momentum dependent vertex function is outlined (in App. C), and a calculation made for the (two-body) kaon as a test case, indicates an increase by 0.612 MeV in the earlier kaon e.m. value (1.032 MeV). This result is taken as a rough indication of the percentage gauge correction expected for the n-p case. A critical comparison is given with the results from QCD sum rules.

First radial excitations of the scalar and pseudoscalar meson nonets as well as their ground states are described as quark–antiquark bound systems in the framework of a nonlocal chiral quark model of the NJL type. Glueball states and their possible mixing with members of the multiplets are not considered.

Radial excitations are described by means of simple polynomial form factors in the momentum–space which are introduced into the four-quark vertices of the quark Lagrangian. The form factors are chosen in the regime of spontaneous chiral symmetry breaking so that the gap equations do not change their standard form, which provides fulfillment of the low energy theorems. All free parameters of the form factors are fixed by experimentally observed masses of pseudoscalar mesons. All masses of the scalar mesons are predicted.

The local six-quark 't Hooft interaction is introduced to solve the so-called U_A(1)-problem. The (four particle) singlet–octet mixing for the ground and radially excited states of scalar and pseudoscalar mesons is taken into account. The widths of the main strong decays of the first radial excitation of the scalar meson nonet are calculatedin satisfactory agreement with experimental data.

Classification of the considered meson nonets is given. It is shown that the meson states a₀(1450), f₀(1370), f_J(1710) and are the first radial excitations of a₀(980), f₀(400-1200), f₀(980), .

I review the existing theoretical uncertainties in relating the semileptonic decay width in b → u transitions to the underlying Kobayashi–Maskawa mixing element |V_ub|. The theoretical error bars are only a few per cent in |V_ub|, with uncertainties from the impact of the nonperturbative effects nearly negligible.

We find an infinite-dimensional free algebra which lives at large N in any SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural basis of this algebra is a free-algebraic generalization of Chebyshev polynomials and the dual basis is closely related to the planar connected parts. This leads to a number of free-algebraic forms of the master field including an algebraic derivation of the Gopakumar–Gross form. For action theories, these forms of the master field immediately give a number of new free-algebraic packagings of the planar Schwinger–Dyson equations.

The calculation of Dirac brackets (DB) using a symplectic matrix approach but in a Hamiltonian framework is discussed, and the calculation of the DB for the supersymmetric extension of QED (super-QED) is shown. The relation between the zero-mode of the pre-symplectic matrix and the gauge transformations admitted by the model is verified. A general prescription to construct Lagrangians linear in the velocities is also presented.