arXiv subjects
Publications and source records attributed to Kazuhiko Odaka.
By using the spherical coordinates in 3+1 dimensions we study the self-adjointness of the Dirac Hamiltonian in an Aharonov-Bohm gauge field of an infinitely thin magnetic flux tube. It is shown that the angular part of the Dirac Hamiltonian requires self-adjoint extensions as well as its radial one. The self-adjoint extensions of the angular part are parametrized by 2x2 unitary matrix.
From the point of view of topology we study the induced representation technique which E. Wigner proposed in 1939. We comment on the gauge structure in the induced representation technique and construc the explicit form of the gauge fields. The topological results ofour study are applied to quantum mechanics on a d-dimensional sphere and its path integral is formulated.
We discuss an extension of the quantization method based on the induced representation of the canonical group.
When the $q$-deformed creation and annihilation operators are used in a second quantization procedure, the algebra satisfied by basis vectors (orthogonal complete set) should be also deformed such as a field operator remains invariant under the coaction of the quantum group. In the 1+1 dimensional quantum field theories we deform the algebra of the basis vectors and study the $q$-deformation in the second quantization procedure.