|Budget Amount *help
¥2,700,000 (Direct Cost : ¥2,700,000)
Fiscal Year 2000 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1999 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1998 : ¥500,000 (Direct Cost : ¥500,000)
Fiscal Year 1997 : ¥1,100,000 (Direct Cost : ¥1,100,000)
String theory is regarded as the most promising candidate to unify all the four forces of the nature. It has been conjectured that all consistent string theory can be derived from a single theory that is called M-theory. It is known that M-theory has a lot of theoretical challenges such as the quantization. In this research, I clarified some aspects of M-theory. It may be classified as (1) examination of the restoration of Lorentz symmetry (2) Quantization of the open membrane as the matrix model (3) Interpretation of string junction from M-theoretical viewpoint (4) extension of the noncommutative space-time which is usually defined through the boundary of the open string to the open membrane situation. In (1), we have carried out only the classical computation and quantized calculus is desirable in the future. In (4), it gives a quantum representation of the volume preserving diffeomorphism, which is related to the many branches of the mathematical physics.
The space-time geometry, which is defined by the string theory, is critically different from the ordinary Riemannian geometry in Einstein gravity. In some limit, it is known that the geometry is simplified to the noncommutative geometry that Connes proposed. Once the space-time becomes noncommutative, there appears a new kind of Soliton configuration, which does not appear in the commutative theory. In this research, I proposed that such Soliton charges might be interpreted as the K-homology of the C-algebra. By applying this proposal, I considered the Soliton configuration defined on the noncommutative torus and indicated that there appears a strange excitation, which is difficult to understand physically at this stage. If open string is defined on such a noncommutative space, we need to introduce the matrix string theory. We give a foundation to such a theory.