[en] The aim of these lectures is to give a self-contained introduction to nonrelativistic potential models, to their formulation as well as to their possible applications. At the price of some lack of (in a mathematical sense) rigorous derivations, we try to give a feeling and understanding for the simplest conceivable method to extract the explicit form of the forces acting between quarks from the interplay between experimental observations and theoretical considerations. According to this spirit, we demonstrate, in detail, how to obtain the underlying Hamiltonian and how to determine the Lorentz structure of the quark-(anti-)quark interaction potential from well-established experimental facts. (author)

[en] This review scrutinizes the present status of proton decay in grand unified theories. Baryon and lepton number violation in conventional as well as supersymmetric GUTs is discussed with special emphasis being laid on selection rules and model-independent predictions. The theoretical predictions for nucleon lifetimes and branching ratios, when confronted with experiment, inevitably lead to the conclusion that all great desert GUTs, like the minimal SU(5) model, are definitely ruled out by the experimental non-confirmation of proton decay at the expected rate. (Author)

[en] This brief review discusses various aspects of the description of hadrons as bound states of quarks at the simpler example of mesons, which are regarded as composite of a (constituent) quark and antiquark. It is shown how a recently derived relativistic virial theorem may be used in order to cast some light on the interplay between the (semi-)relativistic and (maybe only effective) nonrelativistic treatment of bound states. Furthermore, a new relativistic approach to fermion-antifermion bound states is briefly sketched and applied in order to predict analytically a few selected general features of the meson spectrum. 27 refs.; 2 figs.; 1 tab

[en] Using a phenomenological ansatz for the Lagrangian of baryon- and lepton-number violating interactions the effective baryon-lepton coupling constant is calculated within the framework of a relativistic quark model. Apart from a calculation of B-number violating cross-sections and decays this ansatz allows for a definition of the parity of leptons relative to baryons. (Auth.)

[en] The spinless Salpeter equation may be considered either as a standard approximation to the Bethe-Salpeter formalism, designed for the description of bound states within a relativistic quantum field theory, or as the most simple, to a certain extent relativistic generalization of the customary non relativistic Schroedinger formalism. Because of the presence of the rather difficult-to-handle square-root operator of the relativistic kinetic energy in the corresponding Hamiltonian, very frequently the corresponding (discrete) spectrum of energy eigenvalues cannot be determined analytically. Therefore, we show how to calculate, by some clever choice of basis vectors in the Hilbert space of solutions, for the rather large class of power-law potentials, at least (sometimes excellent) upper bounds on these energy eigenvalues, for the lowest-lying levels this even analytically. (author)

[en] The most spectacular prediction of all Grand Unified Theories - and perhaps the only one to be confronted with experiment - is beyond doubt the instability of the proton. Employing for the decays into pseudoscalar mesons the soft meson technique - which has been developed within the framework of current algebra under the hypothesis of PCAC - and for the decays into vector mesons the assumption of pole dominance, the nucleon decay widths are reduced to a set of effective baryon-lepton transition amplitudes, which provide a very convenient tool for the treatment of the phenomenology of baryon number non-conserving processes. The hadronic matrix elements of the baryon and lepton number violating interactions formulated in terms of quark field operators are evaluated within the Bethe-Salpeter formalism, which guarantees a fully relativistic covariant description of hadrons as bound states of constituent quarks. The resulting branching ratios for the two-body nuclear decays allow for an unambiguous discrimination between the different Grand Unified Models by the experiments dedicated to the investigation of the proton instability. The nucleon lifetime is predicted to some 4.10³⁰ yr in the minimal Grand Unified Model, at the very edge of the experimentally allowed region but still somewhat larger than the values obtained by recent calculations based on different approaches. (Author)

[en] The Comment scrutinizes the present status of proton decay in grand unified theories. Baryon and lepton number violation in conventional as well as supersymmetric GUTs is discussed with special emphasis on selection rules and model-independent predictions. The theoretical predictions for nucleon lifetimes and branching ratios, when confronted with experiment, inevitably lead to the conclusion that all GUTs, like the minimal SU(5) model, are definitely ruled out by the experimental nonconfirmation of proton decay at the expected rate. (author)

[en] Adopting the Bethe-Salpeter formalism for the treatment of hadrons the relative contributions of the two-quark annihilation and three-quark fusion mechanisms to baryon number violating nucleon decay are compared. The former is found to dominate over the latter by a factor of about 3 in amplitude, implying a proton lifetime of 4 x 10₃₀ yr for msub(X)=4.2 x 10₁₄ GeV. (orig.)

[en] Adopting the Bethe-Salpeter formalism for the treatment of hadrons the relative contributions of the two-quark annihilation and three-quark fusion mechanisms to baryon number violating nucleon decay are compared. The former is found to dominate over the latter by a factor of about 3 in amplitude, implying a proton lifetime of 4 x 10₃₀ yr for msub(X) = 4.2 x 10₁₄ GeV. (Author)

[en] Interactions which violate the conservation of baryon and lepton number represent an intrinsic part of all grand unified theories (GUTs) of strong and electroweak interactions. These new interactions - predicted within the framework of GUTs - generate B and L violating four-fermion interactions via the exchange of superheavy particles which cannot be ascribed a well-defined baryon or lepton number. The effective coupling constant of these four-fermion interactions might be large enough to make the proton decay detectable by the present generation of experiments. In this review the basic concepts of conventional as well as supersymmetric GUTs relevant for proton decay are sketched. The baryon number violating sector of grand unified theories is discussed in more detail. Special emphasis is laid on the various selection rules arising as consequences of low-energy gauge invariance and supersymmetry for proton decay. These selection rules already determine the coarse pattern of the resulting decay modes and branching ratios without any reference to or detailed knowledge of the underlying grand unified theory. Finally the numerous theoretical predictions are summarized and confronted with experiment. (author)