International Journal of Modern Physics A

By generalizing the Fujikawa approach, we show in the path integral formalism: (1) how the infinitesimal variation of the fermion measure can be integrated to obtain the full anomalous chiral action; (2) how the action derived in this way can be identified as the Chern–Simons term in five dimensions, if the anomaly is consistent; (3) how the regularization can be carried out, so as to lead to the consistent anomaly and not to the covariant anomaly. We consider a massless left-handed fermion interacting with a non-Abelian gauge field. The gauge field also interacts with a set of Goldstone bosons, so that a gauge-invariant configuration of the gauge field exists. We use Schwinger's "proper time" representation of the Green's function and the guage-invariant point-splitting technique, and find that the consistency requirement and the point-splitting technique allow both an anomalous and a nonanomalous action. In the end, the nature of the vacuum determines whether we have an anomalous theory or a nonanomalous theory.

A Yang–Mills theory is presented using the U_q(2) quantum group. Unlike previous works, no assumptions are required — between the quantum gauge parameters and the quantum gauge fields (or curvature) — to get the quantum gauge variations of the different fields. Furthermore, an adequate definition of the quantum trace is presented. Such a definition leads to a quantum metric, which therefore allows us to construct a U_q(2) quantum Yang–Mills Lagrangian. The Weinberg angle θ is found in terms of this q metric to be .

We give a one-dimensional octonionic representation of the different Clifford algebra Cliff(5,5)~Cliff(9,1), Cliff(6,6)~ Cliff(10,2) and lastly Cliff(7,6)~ Cliff(10,3) which can be given by 8×8 real matrices taking into account some suitable manipulation rules.

Two-dimensional random surfaces are studied numerically by the dynamical triangulation method. In order to generate various kinds of random surfaces, two higher derivative terms are added to the action. The structures of surfaces, two higher derivative terms are added to the action. The structures of surfaces in the two-dimensional parameter space are classified into three states: flat surface, crumpled surface and branched polymer. In addition, there exists a special point (pure gravity) corresponding to the universal fractal surface. A new probe to detect branched polymers is proposed by using the analysis of minimum neck baby universe. This method can clearly distinguish the branched polymer phase from others according to the sizes and arrangements of baby universes. The size and arrangement of baby universes change drastically for each state. The phases of surfaces coupled with multi-Ising spins are studied in a similar manner.

We study the gauge dependence of the effective average action Γ_k and Newtonian gravitational constant using the RG equation for Γ_k. Then we truncate the space of action functionals to get a solution of this equation. We solve the truncated evolution equation for the Einstein gravity in the De Sitter background for a general gauge parameter α and obtain a system of equatons for the cosmological and Newtonian constants. Analyaing the running of the gravitational constant we find that the Newtonian constant depends strongly on the gauge parameter. This leads to the appearance of antiscreening and screening behavior of the quantum gravity. The resolution of the gauge dependence problem is suggested. For physical gauges like the Landau–DeWitt gauge the Newtonian constant shows an antiscreening.

A toy model with an infinite number of interacting fermions in four-dimensional space–time is analyzed. We find that the model is finite at any order in perturbation theory. However, perturbation theory is valid only for external momenta smaller than , where λ is the coupling constant.

Using the depths of shower maxima, as measured by Fly's Eye experiment,we study the energy dissipation of hadronic showers resulting from cosmic interactions at energies between 3×10¹⁷ eV and 10¹⁹ eV. We place, based on Fly's Eye data, a set of constraints on the expected depths of shower maxima for proton-initiated showers, disentangling the hadronic interaction features from the cosmic ray composition. It is shown that in the energy region substantially above collider energies, only Monte Carlo simulations using hadronic interaction models characterized by a strong energy dissipation predict the depths of shower maxima that are consistent with this set of constraints. Between the two equally good fitsof the energy dependences of cross-section and multiplicity at collider energies — the power law and log-square law, we find that the cosmic ray data favor the power law above collider energies. The Feynman scaling in the fragmentation region above collider energies is valid only if the cross-section for inelastic hadron–air–nucleus interactions increases much more rapidly than the trend established at accelerator energies. The multiple nucleon interaction picture appears to be plausible for hadron–nucleus interactions.

This paper is the SU(3) extension of the dynamically generated SU(2) linear σ model Lagrangian worked out previously using dimensional regularization. After discussing the quark-level Goldberger–Treiman relations for SU(3) and the related gap equations, we dynamically generate the meson cubic and quartic couplings. This also constrains the meson–quark coupling constant to and determines the SU(3) scalar meson masses in a Nambu–Jona-Lasinio fashion. Finally we dynamically induce the U(3) pseudoscalar and scalar mixing angles in a manner compatible with data.

In this paper, a new approach to quantum gravity is presented in which the de-Broglie–Bohm quantum theory of motion is geometrized. This way of considering quantum gravity leads automatically to the fact that the quantum effects are contained in the conformal degree of freedom of the space–time metric. The present theory is then applied to the maximally symmetric space–time of cosmology, and it is observed that it is possible to avoid the initial singularity, while at large times the correct classical limit emerges.