A Hamiltonian cycle of a graph is a closed path that visits every vertex once
and only once. It serves as a model of a compact polymer on a lattice. I study
the number of Hamiltonian cycles, or equivalently the entropy of a compact
polymer, on var...
Field theoretic approach to the counting problem of Hamiltonian cycles of graphs
We study the relation between lattice construction and surgery construction
of three-dimensional topological field theories. We show that a class of the
Chung-Fukuma-Shapere theory on the lattice has representation theoretic
reformulation which is...
We derive a minimal set of Feynman rules for the loop amplitudes in unitary
models of closed strings, whose target space is a simply laced (extended)
Dynkin diagram. The string field Feynman graphs are composed of propagators,
vertices (including ...
Large- renormalization group equations for one- and two-matrix models are
derived. The exact renormalization group equation involving infinitely many
induced interactions can be rewritten in a form that has a finite number of
coupling constants...
We investigate the 3d lattice topological field theories defined by Chung,
Fukuma and Shapere. We concentrate on the model defined by taking a deformation of the quantum double of a finite commutative group as the
underlying Hopf algeb...
Progress of theoretical physics. Supplement (114) 53-71 1994
The renormalization group approach is studied for large N models. The approach of Brezin and Zinn-Justin is explained and examined for matrix models. The validity of the approach is clarified by using the vector model as a similar and simpler exam...
An exact renormalization group equation is derived for the free energy of
matrix models. The renormalization group equation turns out to be nonlinear for
matrix models, as opposed to linear for vector models. An algorithm for
determining the criti...
The validity of the renormalization group approach for large is clarified
by using the vector model as an example. An exact difference equation is
obtained which relates free energies for neighboring values of . The
reparametrization freedo...
Point particles as defects in (2+1)-dimensional quantum gravity
Progress of theoretical physics 87(2) 253-268 Feb 1992 [Refereed][Invited]
We investigate possibilities of topology change and nucleation of universes in the (2+1)-dimensional Einstein gravity model with negative cosmological constant. We demonstrate that topology change and nucleation phenomena can occur by quantum tunn...
IEICE technical report. Education technology 11 Oct 2014
We discuss automatic grading of programming assignments with blackbox testing. For programs that involve random algorithms, we propose grading methods based on statistical testing and dependency injection. We also propose a grading method for cont...
