Systems with Spontaneously Broken Symmetries and Nonperturbative Methods

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In this project, the head investigator Taro Kashiwa studied the validity of the Auxiliary Field Method(AFM) in the cases of 0-and 1-dimensional Bosonic and Fermionic models. In 0-deminional cases, it was found that in the huge range of the coupling constant the 1-loop results fit well with the exact value, and that there arises the caustics, characterized by the vanishing of the second derivative of the action in the exponent under path integrals, in the 0-dimensiona four-fermi model. The 1-dimensional bosnic case (Quantum Mecanical case) with the double well potential needs higher loop corrections in the region where the instantons play an important role, which would be cured by the introduction of additional auxiliary fileds. This is now under investigation.Yasuo Ezawa studied the gravity theories containing higher derivatives; they found the issue, the Hamiltonian in the Buchbinder-Lyakhovich (BL) canonical formalism must be transformed under the general coordinate transformation, is resolved by the combination of BL with Ostrogradski formalism.Yoshiharu Kawamura found the grand unified models in the 5-dimensional spacetime which can explain the origin of the generation and the sum rule for masses of constituent particles in the case of the supersymmetric extension of those models. The results were obtained from the model with 1-dimensional Orbifold as an extra dimemsion.Masahiro Imachi, together with Hiroshi Yoneyama studied the numerical simulation to the theta terms in CP(2) models. The issue is the theta terms is imaginary in the path integration and hard to simulate in the ordinary algorisms. The Maximum Entropy Method (MEM) is a one major tool for this purpose. They found that even under MEM the flattening of the theta data cannot be avoided, the data that the flattening is resoled was just within a statistical error bar.