Minoru Omote

Point canonical transformations and the path integral

Abstract It is shown that the covariance arguments under point canonical transformations serve to remove the ambiguity that is inherent in ordering variables and in choosing an approximate form for the action.

Prolongation structures of nonlinear equations and infinite‐dimensional algebras

Prolongation structures of the sine–Gordon equation, the Ernst equation, and the chiral model are systematically discussed. It is shown that the prolongation structures generate the Kac–Moody algebra for the sine–Gordon equation and another type of infinite‐dimensional algebra for the Ernst equation. This algebra includes the Kac–Moody algebra and the Virasoro algebra as its subalgebra.

Infinite‐dimensional symmetry algebras and an infinite number of conserved quantities of the (2+1)‐dimensional Davey–Stewartson equation

An infinite‐dimensional symmetry algebra of the Davey–Stewartson equation is explicitly presented. It is shown that this algebra is a gauge generalization of the symmetry transformation for the Schrodinger equation, and that the Virasoro algebra appears as the subalgebra. An infinite number of conserved quantities associated with the transformations are also obtained.

Bäcklund transformations for the Ernst equation

Presented is a systematic approach to the transformation theories for the Ernst equation from the viewpoint of the Backlund transformation. It is explicitly shown that the method of Clairin gives a simple derivation of various transformations such as transformations found by Ehlers, Neugebauer, and Harrison.

Superspace formulation of the spectral transform method for the massive thirring model II

Abstract By using the superspace formulation an infinite number of conserved quantities (including the hamiltonian) of the massive Thirring model are shown to be expressed in terms of the “Fermi-like” scattering parameters as well as in terms of the “Bose-like” ones. It is shown that the massive Thirring model in the latter case and the sine-Gordon equation have the same dynamical structures.

Prolongation structures of the supersymmetric sine-Gordon equation and infinite-dimensional superalgebras

Prolongation structures of the supersymmetric sine-Gordon equation are discussed. It is shown that an infinite-dimensional superalgebra is associated with these structures and that a linear representation of the algebra gives the super Lax pairs of the equation.

Gravitational lens effects on the density parameter

The amplification effects by gravitational lensing of local inhomogeneities on the density parameter of the universe are statistically investigated using gravitional lens models of point mass and of spherical opaque lens. We find that the effects reduce the value of the density parameter measured by Loh & Spillar with an assumption of the homogeneous universe. This result shows that the gravitational lens effects of local inhomogeneities in the universe are not negligible in the observational evaluation of cosmological parameters

Gravitational lens effects on the redshift-volume measurement of the density parameter

General formulations are presented for the effects of statistical gravitational amplification effects on the cosmological redshift-volume test. The formulations are used to analyze the data of Loh and Spillar (1986), who measured the number of galaxies with fluxes larger than some threshold flux and the total flux of these galaxies and obtained a value of Omega(0) roughly one. How deeply the amplification affects the resulting values of the cosmological parameters is studied. It is found that the gravitational lens effects on observational cosmology cannot be negligible. 24 refs.

Infinite number of conserved quantities and extended conformal algebra in the Thirring model

It is shown that the Thirring model has an infinite number of local conserved quantities, explicit forms of which are presented. These quantities are shown to be expressed in terms of scattering parameters. It will be shown that in this model there exists an extended symmetry algebra that includes the Virasoro algebra as its subalgebra.

Apparent superluminal motions of images by a gravitational lens

Abstract It is shown that relative motions with superluminal velocities are expected to be observed in the gravitational lens systems. The multiple quasar PG1115+080 may be the most hopeful candidate whihc exhibits interesting but extraordinary phenomena.