The algebra of conserved observables of the SO(4, 1) gauge-invariant theory of the Dirac fermions in the external field of the KaluzaKlein monopole is investigated. It is shown that the Dirac conserved operators have physical parts associated with Pauli operators that are also conserved in the sense of the Klein-Gordon theory. In this way one gets simpler methods of analyzing the properties of ...

We introduce the concept of three-dimensional Dirac (Weyl) superconductors (SC), which have protected bulk fourfold (twofold) nodal points and surface Majorana arcs at zero energy. We provide a sufficient criterion for realizing them in centrosymmetric SCs with odd-parity pairing and mirror symmetry. Pairs of Dirac nodes appear in a mirror-invariant plane when the mirror winding number is nontr...

One of the key properties of Dirac operators is the possibility of a degeneracy of zero modes. For the Abelian Dirac operator in three dimensions the question whether such multiple zero modes may exist has remained unanswered until now. Here we prove that the feature of zero mode degeneracy indeed occurs for the Abelian Dirac operator in three dimensions, by explicitly constructing a class of D...

A transformation is devised to convert any chirally non-invariant lattice Dirac fermion operator into Ginsparg-Wilson Dirac fermion operator. For the standard Wilson-Dirac lattice fermion operator, the transformed new operator is local, free of O(a) lattice artifacts, has correct axial anomaly in the vacuum sector, and is not plagued by the notorious problems ( e.g., additive mass renormalizati...

The Schrödinger functional formalism is given as a field theory in a finite volume with a Dirichlet boundary condition in temporal direction. When one tries to construct this formalism with the Ginsparg-Wilson fermion including the overlap Dirac operator and the domain-wall fermion one easily runs into difficulties. The reason is that if the Dirichlet boundary condition is simply imposed on the...