Sumio Wada

Quantum cosmological perturbations in pure gravity

Abstract We construct the quantum theory of cosmological perturbations as the semiclassical approximation to the linearized canonical quantum gravity. After the elimination of the scalar and vector perturbations of the metric, the harmonic oscillators for the tensor perturbations with background-dependent frequencies are obtained. The semiclassical approximation gives the free field theory of gravitons on the homogeneous isotropic universe in the Schroedinger representation. We discuss the general structure of the theory and present explicit solutions on the de Sitter background. When the background part of the wave function is exponentially increasing in the classically forbidden region, its perturbation part is unique. An interpretation of the solution is given by expanding the wave function into wave packets. In particular, we explain where and how the perturbations are considered to be in the ground state (zero-point oscillation), and where and how they become classical. Back-reactions and their renormalization are also discussed.

Cosmological Perturbations and Quantum Fields in Curved Space

Abstract We identify the quantum theory of cosmological perturbations with the quantum field theory in curved spacetime with emphasis on its field concept. We materialize this idea by using a coherent state as a quantum analogue of a nontrivial classical field configuration. We present analytic results in a de Sitter universe for the massless and massive minimal free scalar fields. Some new features on the spectrum of perturbations are obtained for the massive case. We also show how such quantum field theories can be derived from quantum gravity using the semiclassical approximation. A physical degree of freedom is picked up from three scalar perturbations in the quantum gravity scalar system and its Schrodinger equation is derived. Peculiar features of quantum fields at imaginary time and its possible implications on boundary conditions for the wave function of the universe are also discussed.

De Sitter metric as a self-consistent solution of the back reaction problem

Abstract The de Sitter metric is a solution of the Einstein equation even when quantum effects of matter fields are included. However between the curvature and the cosmological constant Λ changes drastically. For some values of Λ, there are two or three solutions, while there is none in some other cases. There can be even a positive curvature solution for negative Λ. These features depend on mass and spin of matter fields and the matter-curvature coupling.

Deviation from the ideal vector-nonet due to the unitarity correction

Abstract The deviations from the ideal φ - ω mixing and from the nonet mass formulae are evaluated by using the dispersion relation and the unitarity. Assuming a damping form factor (of the Veneziano-type) and the rapid saturation of dispersion integrals, we obtain quantitative agreement with the experimental data.

Twist-four four-quark process in the parton picture

Abstract We present the parton language description of the twist-four four-quark process: (1) the four-quark distribution is defined, (2) its relation to structure functions is given and (3) the differential equation which governs the evolution of the four-quark distribution is derived. As an application we discuss the x → 1 behaviour of the structure functions.

Analyticity of the Kl3 decay form factor in the chiral symmetry breaking parameters

Abstract Langacker and Pagels have shown that the K l 3 decay form factor is renormalized by the term ∼ ϵ82/ϵ0. This expression has a pole at ϵ0 = 0. We recalculate it by considering the phase transition and find that this form factor can be continued to the whole ϵ0−ϵ8 plane not analytically but continuously and is finite everywhere.

Quantitative analysis of the quark-parton distributions

A quantitative and less model-dependent analysis of the quark parton distributions is attempted. Both the valence-sea (symmetric core) model and the deformed core model are compared in detail with the present data. We find that the deformed core model is more reasonable if we assume the almost monotonous behaviour of the ratio of two valence quarks. Some properties of the distributions in the wee region, such as the rate of convergence of Adlers neutrino sum rule, Regge behaviour and J = 0 fixed pole residues, are investigated.