International Journal of Modern Physics A

We are emerging from a period of consolidation in particle physics. Its great, historic achievement was to establish the Theory of Matter. This Theory will serve as our description of ordinary matter under ordinary conditions — allowing for an extremely liberal definition of "ordinary" — for the foreseeable future. Yet there are many indications, ranging from the numerical to the semimystical, that a new fertile period lies before us. We will discover compelling evidence for the unification of fundamental forces and for new quantum dimensions (low-energy supersymmetry). We will identify new forms of matter, which dominate the mass density of the Universe. We will achieve much better fundamental understanding of the behavior of matter in extreme astrophysical and cosmological environments. Lying beyond these expectations, we can identify deep questions that seem to call for ideas outside our present grasp. And there is still plenty of room for surprises.

We continue the discussion of our previous paper on writing down gauge-invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space–time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba–Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the free mass shell).

The effects of nonlocal interactions in rare B decays, B→ X_sl⁺l^-, are investigated. We show the correlation between the branching ratio and the forward–backward asymmetry via two coefficients of the nonlocal interactions. This will certainly help us find any deviations from the standard model through the nonlocal interactions.

The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space–time is obtained. The region of validity of the Faddeev–Popov–DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two "equivalent" unconstrained systems: the "dynamic" (with "dynamic" evolution parameter as the metric scale factor) and "geometric" (given by the Levi–Civita type canonical transformation to the action-angle variables where the energy constraint converts into a new momentum).

"Big Bang," the Hubble evolution, and creation of matter fields by the "geometric" vacuum are described by the inverted Levi–Civita transformation of the geomeric system into the dynamic one. The particular case of the Levi–Civita transformations are the Bogoliubov ones of the particle variables (diagonalizing the dynamic Hamiltonian) to the quasiparticles (diagonalizing the equations of motion). The choice of initial conditions for the "Big Bang" in the form of the Bogoliubov (squeezed) vacuum reproduces all stages of the evolution of the Friedmann–Robertson–Walker universe in their conformal (Hoyle–Narlikar) versions.

We investigate the SO(4,1) gauge-invariant theory of the Dirac fermions in the external field of the Kaluza–Klein monopole, pointing out that the quantum modes can be recovered from a Klein–Gordon equation analogous to the Schrödinger equation in the Taub–NUT background. Moreover, we show that there is a large collection of observables that can be directly derived from those of the scalar theory. These offer many possibilities of choosing complete sets of commuting operators which determine the quantum modes. In addition there are some spin-like and Dirac-type operators involving the covariantly constant Killing–Yano tensors of the hyper-Kähler Taub–NUT space. The energy eigenspinors of the central modes in spherical coordinates are completely evaluated in explicit, closed form.

We study the decay width and CP asymmetry of the inclusive process b→sgg (g denotes gluon) in the three and two Higgs doublet models with complex Yukawa couplings. We analyze the dependencies of the differential decay width and CP asymmetry to the s-quark energy E_s and CP violating parameter θ. We observe that there exist a considerable enhancement in the decay width and CP asymmetry is at the order of 10^-2. Further, it is possible to predict the sign of using the CP asymmetry.

The use of the mass term as a gauge fixing term has been studied by Zwanziger, Parrinello and Jona-Lasinio, which is related to the nonlinear gauge of Dirac and Nambu in the large mass limit. We have recently shown that this modified quantization scheme is in fact identical to the conventional local Faddeev–Popov formula without taking the large mass limit, if one takes into account the variation of the gauge field along the entire gauge orbit and if the Gribov complications can be ignored. This suggests that the classical massive vector theory, for example, is interpreted in a more flexible manner either as a gauge invariant theory with a gauge fixing term added, or as a conventional massive nongauge theory. As for massive gauge particles, the Higgs mechanics, where the mass term is gauge-invariant, has a more intrinsic meaning. It is suggested that we extend the notion of quantum gauge symmetry (BRST symmetry) not only to classical gauge theory but also to a wider class of theories whose gauge symmetry is broken by some extra terms in the classical action. We comment on the implications of this extended notion of quantum gauge symmetry.

We study the behavior of quantum field theories defined on a surface S as it tends to a null surface S_n. In the case of a real, free scalar field theory the above limiting procedure reduces the system to one with a finite number of degrees of freedom. This system is shown to admit a one parameter family of inequivalent quantizations. A duality symmetry present in the model can be used to remove the quantum ambiguity at the self-dual point. In the case of the nonlinear σ-model with the Wess–Zumino–Witten term a similar limiting behavior is obtained. The quantization ambiguity in this case however cannot be removed by any means.