| 研究実績の概要 |
Research carried out during the last fiscal year has focused on two topics: one regarded the deformation of the quantum vacuum in nonlinear sigma models at finite density. For these theories we have shown that the ground state, usually believed to be homogeneous, it becomes inhomogeneous above a critical density. We have further shown that at high density, the ground state becomes homogeneous as for small density. This behavior indicates a sharp similarity between nonlinear sigma models and their fermion cousins, the Gross-Neveu models which manifest a similar behavior. A paper about this has been submitted to the journal of high energy physics for publication and is currently under revision, and a second paper is preparation. The second research line that we have conducted has focused on analyzing the implication of the Mermin-Wagner theorem for the Casimir effect. With this work we have shown that the Casimir effect manifests anomalous features. Furthermore we have generalized certain consideration regarding the mass gap for nonlinear sigma models to high dimensionality, settling a recently debated topic. A paper about is currently in preparation.
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