Geometrical Approach to Quantum Gravity and Super-String Theory

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(1) Proposal of a new indeterminacy principle as a possible basis for the unified string theory :We have proposed to interpret the short-distance properties of the string theory by assuming a new indeterminacy principle which demands that there two dual measures DELTAA and DELTAB of the length scale obeying the relation DELTAADELTAB=lambda^2 with lambda being the Planck length. This naturally explains the decrease of the degrees of the freedom in the high-energy behavior of the string amplitudes.(2) Proposal of a new action principle describing the structure of the non-perturbative string theory in less-than one dimension :We have constructed a general mathematical framework in which non-perturbative string theory derived as the double scaling limit from the matrix model is described in a unified and universal way based on the KP hierarchy. In particular, we have proposed an action principle from which the whole structure of the theory, especially, its symmetry property, can be underst … More ood. It can be regarded as a new canonical formalism for 2D quantum gravity replacing the Hamiltonian formalism of the ordinary field theory.(3) Investigation of effective low-energy theory for the unified string theory :We have investigated the effect of the dilaton field, which is a characteristic of the effective field theory for strings, on the classical solutions of the black-hole type, and found new solutions in a coupled Einstein-Maxwell-Yang Mills system.(4) Investigation of quantum cosmology :We have discussed the interpretation of quantum cosmolosy, in particular, the generation of the notion of macroscopic time from the viewpoint of the Van-Hove theory in statistical mechanics.(5) Investigation of the role of scalar fields in general relativity and cosmology :We have investigated the effects of scalar fields, in particular, its possible manifestation as the so-called fifth force. We have proposed a scenario which explains the smallness of the cosmological constant as a result of the natural time-dependent dynamics of coupled scalar-gravitational systems. Less