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The dynamical symmetry breaking in a quasi-(1+1)-dimensional relativisticmodel is investigated. The motions of particles in intrachain are described asa relativistic electron-hole gas, while the interchain hopping term isintroduced as a 0th-component of vector in (1+1)-dimensions, a kind of chemicalpotential of the system. The gauge symmetry of the model is chosen as U(1)suitable for a possible situation of a real substance in condensed matterphysics. We consider the BCS-type contact interactions for the s-wavefermion-pair condensates, while employ the nonlocal interactions of thegeneralized BCS framework to generate the $p$-, $d$- and $f$-wave condensationsin the system. Especially we examine the dynamical generation of a Dirac massterm and superconductivity in the model. The phenomenon is interpreted asmetal-insulator/metal-superconductor phase transitions.

Dynamical Symmetry Breaking of a Relativistic Model in Quasi-(1+1)-Dimensions. I. Formulation