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A method is proposed for constructing infinitesimal gauge transformations for an arbitrary degenerate Lagrangian without restrictions on the constraint algebra. It is thereby shown that in the general case degeneracy of a theory is due to its gauge invariance.

A mechanism of occurrence of higher derivatives of the coordinates in the symmetry transformation law in Noether's second theorem is elucidated. It is shown that the corresponding transformations in the Hamiltonian formalism are canonical in an extended phase space.

The method of QCD analysis of singlet and nonsinglet structure functions, based on their Jacobi polynomial reconstruction from perturbative QCD predictions for the Mellin moments, is described. The accuracy and stability of the method are demonstrated with the help of BCDMS hydrogen data.

The values of the moments of the structure function F μ N 2 ( x , Q 2 ) measured by the BCDMS collaboration at CERN in the interval of Q 2 =30–110 GeV 2 are analysed by means of the perturbative QCD singlet formula. The value of Λ giving the best description of the data is found to be Λ MS≅70MeV.

Dependence of the decay form factor\(F_{\pi ^0 \to e^ + e^ - \gamma } (s)\) on the invariant mass squared of the Dalitz pairs=(p++p−)2 at smalls is calculated with the use of bound-state wave functions-solutions of a covariant single-time equation for a system of two spinor quarks. A quasipotential of one-gluon exchange and an oscillator potential are chosen as quasipotential.

The method is formulated for constructing the generators of gauge transformations in the phase space for a given singular Lagrangian. These generators are used to impose the necessary and sufficient conditions on gauge functions. The results are analyzed for particular examples.

Scaling violations in the nucleon structure function F2(x,Q2) measured with high statistics in deep inelastic scattering of muons on a carbon target are compared to predictions of perturbative QCD. Excellent agreement is observed with numerical solutions of the Altarelli-Parisi evolution equations over the entire x and Q2 range of data. In a next-to-leading order nonsinglet approximation, the QCD mass scale parameter ΛMS is determined to be 230±20(stat.)±60(syst.) MeV. A singlet to the data favours a soft gluon distribution.

A new method of QCD-analysis of singlet and nonsinglet structure functions based on their expansion in orthogonal Jacobi polynomials is proposed. An accuracy of the method is studied and its application is demonstrated using the structure functionF2(x, Q2) obtained by the EMC Collaboration from measurements with an iron target.