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The canonical formalism for quantizing theories with constraints (Dirac formalism) is presented. The method is extended to superspace and equivalence with action principle quantization is shown.

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The stability of the Schwarzschild instanton in a Euclidean background metric is discussed as an introduction. The method is applied to the magnetic monopole solution in 5 dimensions and it is indicated that the classical solution is unstable against small perturbations of the metric.

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The pseudo-rapidity of pion jets which were measured for 50 GeV and 150 GeV incident pions and protons on carbon, copper, and lead targets are analyzed. The shape of the rapidity distribution for a “fireball” which emits particles isotropically in its center of mass is a cosh\(^{-2}y\) distribution. It is possible to unfold all measured distributions into three groups which correspond to a low rapidity originating from the target fragmentation, a middle group which is a function of the center of mass of the projectile and target rapidity and a fast group which is due to the projectile.

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We discuss problems of the lattice regularization of the quantum chromodynamics. We derive on the two-loop level a finite relation between the coupling constants of two versions of the lattice action: Wilson and mixed fundamental-adjoint. This relation maps onto each other the weak coupling predictions of theories built with these actions. We discuss also finite size effects, and in particular the role played by the zero-momentum sector of the lattice gauge theory. We derive a form of the leading-order contribution to the averages of Wilson loops coming from this sector valid for \(d = 4\) and the SU(\(N\)) group with \(N \geq 3\).

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The problem of axial anomaly is analyzed within the framework of analytic regularization scheme. The form of triangle anomaly is obtained.

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It is shown that the theories of spin 2, equivalent in the massive case, are not equivalent in the \(m^2 = 0\) limit. While the massless theory of Pauli and Fierz describes the helicities \(\pm 2\), the one based on the 3-rd rank tensor has no physical content (a pure gauge theory), and the one based on the 4-th rank tensor describes the helicity 0 (a scalar “notivarg” theory).

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Deuteron stripping nuclear reactions are reconsidered as a three-body problem. The Coulomb effects between the proton and the target nucleus are investigated. The mathematical formalism introduces three-body integral equations which can be exactly calculated for such simple models. These coupled integral equations suitably include the Coulomb effects due to repulsive or attractive Coulomb potentials. Numerical calculations of the differential cross-sections of the reactions \(^{28}\)Si(d,p)\(^{29}\)Si and \(^{40}\)Ca(d,p)\(^{41}\)Ca are carried out, showing the importance of the Coulomb effects. The angular distributions of these reactions are theoretically calculated and fitted to the experimental data. From this fitting, reasonable spectroscopic factors are obtained. Inclusion of Coulomb force in three-body model are found to improve the results by about 6.826% as an average value corresponding to the different reactions considered.

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Energy of the lowest collective states and the electromagnetic transitions between them are studied theoretically for even–even nuclei in the radium region. Quadrupole- and octupole-transition probabilities \(B\)(E2) and \(B\)(E3) are considered. The energy as well as the probabilities are found to be sensitive functions of the shape of the collective potential energy of a nucleus.