abstract

Problems of renormalization and dynamic mass formation in a four-fermion model with scalar–scalar, pseudoscalar–pseudoscalar and vector–vector interactions are investigated by the method of functional integration in collective variables. Ward–Takahashi identities and Schwinger–Dyson equations have been obtained for fermion and boson Green’s functions. It is shown that all infinities are absorbed by the finite number of renormalization constants. The matrix elements of the processes of interaction between fermions and their bound states are independent of renormalization constants.

abstract

A careful treatment of closed fermion loops in quantum electrodynamics is developed starting from Schwinger’s gauge invariant formulation of the current, involving a line integral, in an external field problem. The analysis is carried out for multiloop contributions and to all orders of perturbation theory. The derived vanishing property of closed fermion loops when any subset of the external photon momenta are set equal to zero has a very important role in the renormalization program as this does not necessitate the introduction of the unwanted light–light scattering contact term in the Lagrangian. This also permits taking the limit of the photon zero-mass at least for Euclidean nonexceptional external momenta. The functional approach, used in this work, is found to be particularly suited for treating the closed fermion loop problem.

abstract

We compare the dual parton model predictions for \(\pi ^-\pi ^-\to \pi ^{\pm }X\) and \(\pi ^-n\to \pi ^{\pm }X\) with the available experimental data. A good agreement is achieved.

abstract

Continued from a previous paper (Acta Phys. Pol. B13, 321 (1982)), some structural observations are further made on the intrinsic behaviour of the vectorial internal vector \((y)\) associated with each point \((x)\), which is shown to be represented by the base connection of \(y\) (i.e., \(\delta y\)), different from the ordinary absolute differential of \(y\) (i.e., \(Dy\)). Then, corresponding to the difference between \(Dy\) and \(\delta y\), a new Finsler metric such as \(g_{\lambda \kappa }(x,y)=y_{\lambda \kappa }(x)+h_{\lambda \kappa }(x,y)\) is introduced, which is induced by “unifying” the purely Riemannian metric \(\gamma _{\lambda \kappa }(x)\) of the original gravitational field in Einstein’s sense and the internal Finsler metric \(h_{\lambda \kappa }(x,y)\) of the internal space spanned by vectors \(\{y\}\). Some fundamental considerations are also made on the metrical Finsler connections with respect to the metric \(g_{\lambda \kappa }(x,y)\).

abstract

It is shown that in L–R symmetric models with additional horizontal symmetry the one-loop corrections can significantly change the zeroth order predictions of these models.

abstract

Applying Exotic Commutator Method we obtain the mass formula for the meson decouplet composed of an octet and two singlets SU(3). The mesons \(0^+\), \(2^+\), \(1^{++}\) and probably \(4^+\), \(1^{+-}\), \(3^-\) can be classified as decouplets. Almost pure \(s\tilde s\) structure for S\(^*\)(975) can be easily obtained. A possible candidate for the second mixing singlet is gluonium.

abstract

It is shown that existing data are consistent with a constant difference of about 0.2 units between average multiplicities of charged particles in meson–proton and proton–proton collisions for \(p_{\rm LAB} \gtrsim 20\) GeV/\(c\).