We derive a dual theory of the four-dimensional anomalous U(1) gauge theory with a Wess-Zumino (WZ) term and with a Stückelberg type mass term by means of a duality transformation at each of the classical and quantum levels. It is shown that in the dual anomalous U(1) gauge theory, the BF term with a rank-two antisymmetric tensor field plays the roles of the WZ term as well as the mass term of the U(1) gauge field. Similar anomalous U(1) gauge theory with BF term is considered in six-dimensions by introducing a rank-four antisymmetric tensor field. In addition to this theory, we propose a six-dimensional anomalous U(1) gauge theory including an extended BF term with a rank-two antisymmetric tensor field, discussing a difference between the two theories. We also consider a four-dimensional anomalous SU(2)×U(1) gauge theory with BF term and recognize a crucial role of the BF term in cancelling the non-abelian chiral anomaly.
We show software tools to intuitively create a virtual environment (VE) system based on a soft computing technique. The proposed tools use Interactive Evolutionary Computation (IEC) to easily perform 3D authoring tasks such as creating aesthetically pleasing 3D computer graphics (3DCG) models, adding realistic touch sensations to the models, and configuring an effective VE system. Because the tools require no special knowledge and programming skills of users except for sensitivity, we apply the tools to high school IT education. The high school students can make virtual contents by rating the candidate 3DCG models generated and displayed by the system.Then the system evolves the models based on the rates. In this paper, we describe two IEC-based tools for designing the 3DCG model and adding the touch sensation. An ongoing experiment letting the high school students to make a collaborative VE by using the proposed tools is also mentioned.
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