Abstract:
Parity-violating asymmetries in polarized electron scattering have been interpreted as the asymmetries between opposite helicities of incoming fermion based on the approximation of the spin polarization operator. Here exact calculations of cross sections for parity-violating asymmetries in SLAC E158 and SLD have been performed using spin projection operators. And the parity-violating factor incorporating with spin polarization and momentum has been identified and shown that its sign depends on the spin polarization of incoming particle and the relative velocity of incoming and target particles. Therefore, I suggest a new concept of relative spin polarization to interpret the parity-violating asymmetry as contributed by the antisymmetric nature of the weak interactions depending on whether the spin direction of the incoming electron is inward or outward relative to the target electron.

Abstract:
This volume spans musical traditions as ostensibly disparate as Japanese court music, fourteenth-century French court song, contemporary Korean p’ungmul (folk drumming), and Native American song. In juxtaposing these musics, points of convergence emerge, particularly in the common temporal processes experienced by performers and audience within a cultural context. Detailed analysis highlights both the individuality of a piece as well as similarities to other musics.

Abstract:
We propose a 4-dimensional Kaluza-Klein approach to general relativity in the (2,2)-splitting of space-time using the double null gauge. The associated Lagrangian is equivalent to the Einstein-Hilbert Lagrangian, since it yields the same field equations as the E-H Lagrangian does. It is describable as a (1+1)-dimensional Yang-Mills type gauge theory coupled to (1+1)-dimensional matter fields, where the minimal coupling associated with the diffeomorphism group of the 2-dimensional spacelike fibre space automatically appears. Written in the first-order formalism, our Lagrangian density directly yields a non-zero local Hamiltonian density, where the associated time function is the retarded time. From this Hamiltonian density, we obtain a positive-definite local gravitational energy density. In the asymptotically flat space-times, the volume integrals of the proposed local gravitational energy density over suitable 3-dimensional hypersurfaces correctly reproduce the Bondi and the ADM surface integral, at null and spatial infinity, respectively, supporting our proposal. We also obtain the Bondi mass-loss formula as a negative-definite flux integral of a bilinear in the gravitational currents at null infinity.

Abstract:
We propose a Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-splitting of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. In this Kaluza-Klein formalism we find that general relativity of 4-dimensional spacetimes can be interpreted in a natural way as a (1+1)-dimensional gauge theory. In a gauge where the (1+1)-dimensional metric can be written as the Polyakov metric, the action is describable as a (1+1)-dimensional Yang-Mills type gauge theory action coupled to a (1+1)-dimensional non-linear sigma field and a scalar field, subject to the constraint equations associated with the diffeomorphism invariance of the (1+1)-dimensional base manifold. Diffeomorphisms along the fibre directions show up as the Yang-Mills type gauge symmetries, giving rise to the Gauss-law constraints. We also present the Einstein's equations in the Polyakov gauge and discuss them from the (1+1)-dimensional gauge theory point of view. Finally we show that this Kaluza-Klein formalism is closely related to the null hypersurface formalism of general relativity.

Abstract:
We present the (1+1)-dimensional description of the algebraically special class of space-times of 4-dimensions. It is described by the (1+1)-dimensional Yang-Mills action interacting with matter fields, with diffeomorphisms of 2-surface as the gauge symmetry. Parts of the constraints are identified as the gauge fixing condition. We also show that the representations of $w_{\infty}$-gravity appear naturally as special cases of this description, and discuss the geometry of $w_{\infty}$-gravity in term of the fibre bundle.

Abstract:
This is an article contributed to the Brill Festschrift, in honor of the 60th birthday of Prof. D.R. Brill, which will appear in the Vol.2 of the Proceedings of the International Symposia on Directions in General Relativity. In this article we present the (1+1)-dimensional method for studying general relativity of 4-dimensions. We first discuss the general formalism, and subsequently draw attention to the algebraically special class of space-times, following the Petrov classification. It is shown that this class of space-times can be described by the (1+1)-dimensional Yang-Mills action interacting with matter fields, with the spacial diffeomorphisms of the 2-surface as the gauge symmetry. The constraint appears polynomial in part, whereas the non-polynomial part is a non-linear sigma model type in (1+1)-dimensions. It is also shown that the representations of $w_{\infty}$-gravity appear naturally as special cases of this description, and we discuss briefly the $w_{\infty}$-geometry in term of the fibre bundle.

Abstract:
I describe the Kaluza-Klein approach to general relativity of 4-dimensional spacetimes. This approach is based on the (2,2)-fibration of a generic 4-dimensional spacetime, which is viewed as a local product of a (1+1)-dimensional base manifold and a 2-dimensional fibre space. It is shown that the metric coefficients can be decomposed into sets of fields, which transform as a tensor field, gauge fields, and scalar fields with respect to the infinite dimensional group of the diffeomorphisms of the 2-dimensional fibre space. I discuss a few applications of this formalism.

Abstract:
I discuss the (2,2)-formalism of general relativity based on the (2,2)-fibration of a generic 4-dimensional spacetime of the Lorentzian signature. In this formalism general relativity is describable as a Yang-Mills gauge theory defined on the (1+1)-dimensional base manifold, whose local gauge symmetry is the group of the diffeomorphisms of the 2-dimensional fibre manifold. After presenting the Einstein's field equations in this formalism, I solve them for spherically symmetric case to obtain the Schwarzschild solution. Then I discuss possible applications of this formalism.

Abstract:
A set of exact quasi-local conservation equations is derived from the Einstein's equations using the first-order Kaluza-Klein formalism of general relativity in the (2,2)-splitting of 4-dimensional spacetime. These equations are interpreted as quasi-local energy, momentum, and angular momentum conservation equations. In the asymptotic region of asymptotically flat spacetimes, it is shown that the quasi-local energy and energy-flux integral reduce to the Bondi energy and energy-flux, respectively. In spherically symmetric spacetimes, the quasi-local energy becomes the Misner-Sharp energy. Moreover, on the event horizon of a general dynamical black hole, the quasi-local energy conservation equation coincides with the conservation equation studied by Thorne {\it et al}. We discuss the remaining quasi-local conservation equations briefly.

Abstract:
Certain types of asymmetries in neutral meson physics have not been treated properly, ignoring the difference of normalization factors with an assumption of the equality of total decay width. Since the corrected asymmetries in $B^0$ meson are different from known asymmetries by a shift in the first order of CP- and CPT-violation parameters, experimental data should be analyzed with the consideration of this effect as in $K^0$ meson physics.