International Journal of Modern Physics A

It is a pleasure and an honor for me to give this lecture in honor of Oscar Klein who made major contributions to field theory, quantum electrodynamics and particle physics, including weak interactions. He was the first one to observe that the μ decay and the β decay could be described by the same interaction with the same coupling constant; this led to the discovery of the Universal Fermi Interaction.

Perhaps I should begin my discussion of the history of weak interactions by separating it into three periods:

(1) Classical Period, 1898–1949.

(2) Transition Period, 1949–1956.

(3) Modern Period, 1956–.

We construct explicitly the open descendants of some exceptional automorphism invariants of U(2N) orbifolds. We focus on the case N = p₁ × p₂, p₁ and p₂ prime, and on the automorphisms of the diagonal and charge conjugation invariants that exist for these values of N. These correspond to orbifolds of the circle with radius R² = 2p₁/p₂. For each automorphism invariant we find two consistent Klein bottles, and for each Klein bottle we find a complete (and probably unique) set of boundary states. The two Klein bottles are in each case related to each other by simple currents, but surprisingly for the automorphism of the charge conjugation invariant neither of the Klein bottle choices is the canonical (symmetric) one.

Analytical and numerical results, for the orbital and spin content carried by different quark flavors in the baryons, are given in the chiral quark model with symmetry breaking. The reduction of the quark spin, due to the spin dilution in the chiral splitting processes, is transferred into the orbital motion of quarks and antiquarks. The orbital angular momentum for each quark flavor in the proton as a function of the partition factor κ and the chiral splitting probability a is shown. The cancellation between the spin and orbital contributions in the spin sum rule and in the baryon magnetic moments is discussed.

We have used a two-dimensional analog of the Hadamard state-condition to study the local constraints on the two-point function of a linear quantum field conformally coupled to a two-dimensional gravitational background. We develop a dynamical model in which the determination of the state of the quantum field is essentially related to the determination of a conformal frame. A particular conformal frame is then introduced in which a two-dimensional gravitational equation is established.

The aim of the present paper is to analyze some globally pathologic properties in worlds described by a class of static planary symmetric exact solutions with g₄₄ = -cosh²(αz), pointing out some unusual (pathological) features such as cosmic-time traps, non-spacelike imprisonments of test particle trajectories and structures very much like the ones of a BTZ black hole. Finally, we deal with the exactly solvable analytical behavior of the magnetostatic fields, stressing the significant difference from the Minkowskian case, namely a nonsingular, almost total, confinement of the field in a finite spacelike region, which we termed as a gravitomagnetic resonance, entirely due to the large scale pathology of such a Universe.

Under the flat Minkowski space–time background, in the harmonic coordinate system, we calculate the expressions of the leading terms of several two-point curvature vacuum correlation functions in n dimensional four-derivative gravity, resulting in that the two-point curvature vacuum correlation functions are not zero, and discuss the relations between the four-derivative gravity and the R-gravity for the graviton propagator and the curvature correlation functions.

We study the two-point function for the gauge boson in the axial-type gauges. We use the exact treatment of the axial gauges recently proposed that is intrinsically compatible with the Lorentz-type gauges in the path-integral formulation and has been arrived at from this connection and which is a "one-vector" treatment. We find that in this treatment, we can evaluate the two-point functions without imposing any additional interpretation on the axial gauge 1/(η·q)^q type poles. The calculations are as easy as the other treatments based on other known prescriptions. Unlike the "uniform-prescription"/LM prescription, we note, here, the absence of any nonlocal divergences in the two-point proper vertex. We correlate our calculation with that for the Cauchy Principal Value prescription and find from this comparison that the two-point proper vertex differs from the CPV calculation only by finite terms. For simplicity of treatment, the divergences have been calculated here with η² > 0 and these have a smooth light cone limit.

It is pointed out that the retardation terms given in the original Fermi–Breit potential vanish in the center-of-mass frame. The retarded one-gluon exchange potential is rederived in this paper from the three-dimensional one-gluon exchange kernel which appears in the exact three-dimensional relativistic equation for quark–antiquark bound states. The retardation part of the potential given in the approximation of order p²/m² is shown to be different from those derived in the previous literature. This part is off-shell and no longer vanishes in the center-of-mass frame.

We study the regularization and renormalization of the Yang–Mills theory in the framework of the manifestly invariant formalism, which consists of a higher covariant derivative with an infinitely many Pauli–Villars fields. Unphysical logarithmic divergence, which is the problematic point on the Slavnov method, does not appear in our scheme, and the well-known value of the renormalization group functions are derived. The cancellation mechanism of the quadratic divergence is also demonstrated by calculating the vacuum polarization tensor of the order of Λ⁰ and Λ^-4. These results are the evidence that our method is valid for intrinsically divergent theories and is expected to be available for the theory which contains the quantity depending on the space–time dimensions, like supersymmetric gauge theories.