Minoru Horibe

On Solutions of Tetrahedron Equations Based on Korepanov Mechanism

We have examined solutions of tetrahedron equations from the elliptic free fermion model by using Korepanov mechanism based on tetrahedral Zamolodchikov algebras. As a byproduct, we have found a new integrable 2-dim. lattice model. We have also studied the relation between tetrahedral Zamolodchikov algebras and tetrahedron equations.

How to Quantize Fields Canonically on Discrete Space-Time

We propose a canonical procedure to quantize fields with interaction on discrete space-time. The time evolution operator that reproduces the field equation is represented by using canonical variables. The generator of the operator is a conserved quantity, but its existence is not obvious. It is possible to calculate the S-matrix perturbatively. Our quantization gives the same results as those given by the path integral quantization.

Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

For the Wigner function of a system in N-dimensional Hilbert space, we propose the condition, which ensures that the Wigner function has correct marginal distributions along tilted lines. Under this condition we get the Wigner function without ambiguity if N is odd. If N is even the Wigner function does not exist.

Wigner functions on a lattice

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also discussed.

The Structure of the Bazhanov-Baxter Model and a New Solution of the Tetrahedron Equation

We clarify the structure of the Bazhanov-Baxter model of the 3-dim N-state integrable model. There are two essential points, i) the cubic symmetries, and ii) the spherical trigonometry parametrization, to understand the structure of this model. We propose two approaches to find a candidate as a solution of the tetrahedron equation, and we find a new solution.We clarify the structure of the Bazhanov-Baxter model of the 3-dim N-state integrable model. There are two essential points, i) the cubic symmetries, and ii) the spherical trigonometry parametrization, to understand the structure of this model. We propose two approaches to find a candidate as a solution of the tetrahedron equation, and we find a new solution.

On Perturbation Expansion of Filed Theory in Accelerated System and the Thermofield Dynamics

We examine the equivalence between the quantum field theory in the Minkowski vacuum observed from the accelerated observer arid the thermodynamics in the two dimensional space· time taking account of self-interactions in the perturbation theory. It is shown that in the case of conformally invariant theory they are equivalent in the physically observable sector.

A Comment on Quantum Fluctuations around Solitons

Mode mixing formalism is applied to the fluctuation modes around soliton configurations for the purpose of looking at possible multiple productions of fluctuation quanta in the soliton collision process. It is shown, however, that mixing among positive and negative frequency parts cannot occur if the theory admits the inverse method of Lax. In that case the soliton scatterings proceed without quantum disturbances.

Quantum Markov Process on a Lattice

Abstract We develop a systematic description of Weyl and Fano operators on a lattice phase space. Introducing the so-called ghost variable even on an odd lattice, odd and even lattices can be treated in a symmetric way. The Wigner function is defined using these operators on the quantum phase space, which can be interpreted as a spin phase space. If we extend the space with a dichotomic variable, a positive distribution function can be defined on the new space. It is shown that there exits a quantum Markov process on the extended space which describes the time evolution of the distribution function.

Can the Wigner function be determined by properties for translation and parity transformation on lattice ‘phase space’?

We show that the Fano operator for a quantum system confined to a line is uniquely determined by assuming reasonable behaviour under translation and parity transformation on phase space. In contrast, for a system on a lattice the same procedure does not work.

Symmetries and the mass ratio of the electron and muon

A model of symmetries and gauge interactions relating the electron and muon is considered. The model is based on the UL(1)⊗UR(1)⊗RL⊗RR group where UL(1)⊗UR(1) denotes the chiral e-μ rotation and RL⊗RR the chiral reflection of the electron field. The invariance under this group is spontaneously broken by the vacuum expectation values of scalar fields. A zeroth-order vacuum is found for which the zeroth-order electron mass vanishes, while one-loop corrections lead to a finite memμ ratio. The decay process μ → e + γ is strictly forbidden in this model.