Takayuki Hori

Covariant quantization of the superparticle

Abstract The superparticle theory is quantized in a manifestly covariant form. The S -matrix is shown to be equivalent to the non-covariant one obtained by the quantization method developed by Fradkin and Fradkina. In covariant form the Dirac bracket does not appear and the explicit separation of the fermionic constraints into the first and second-class ones is not required.

Moyal Quantization for Constrained System

We study Moyal quantization for a constrained system. One of the purposes of this work is to give a proper definition of the Wigner-Weyl (WW) correspondence, which connects the Weyl symbols with the corresponding quantum operators. A Hamiltonian in terms of the Weyl symbols is different from the classical Hamiltonian for a constrained system. This difference is related to the fact that the naively constructed WW correspondence is no longer one-to-one. In the Moyal quantization, the geometrical meaning of the constraints is clear. In the proposal presented here, the second class constraints are incorporated into the definition of the WW correspondence by limiting the phase space to a hypersurface, while we assume canonical commutation relations for the phase space variables. In the case of linear constraints, we confirm that the Moyal brackets between the Weyl symbols yield the same results as those for the constrained system derived using the Dirac bracket formulation.

The universe as a relativistic ball

Abstract An argument on interpreting the relativistic ball being the universe is given. The intrinsic metric of the ball is shown to have classical solutions without a geometrical singularity. The quantization is discussed in a simple manner.

Relativistic Particle in Complex Spacetime

A modified version of the bilocal particle is presented in terms of complex spacetime. Unusual constraint structure of the model is studied, and a new concept of the physical equivalence is proposed in accordance with Dirac’s conjecture. It is found that in the quantum theory the physical state conditions are compatible with existence of eigenstates of momentum only when the dimension of spacetime is four. An example of scattering amplitude is calculated. Subject Index: 104

Exact Solutions to the Wheeler-DeWitt Equation of Two Dimensional Dilaton Gravity

The two dimensional dilaton gravity with the cosmological term and with an even number of matter fields minimally coupled to the gravity is considered. The exact solutions to the Wheeler-DeWitt equation are obtained in an explicit functional form, which contain an arbitrary holomorphic function of the matter fields

The Problem of Time in the Quantum Theory of Black Holes

We discuss the problem of time in spherically symmetric pure Einstein gravity with the cosmological term by using an exact solution to the Wheeler-DeWitt equation. A positive definite inner product is defined, based on the momentum constraint rather than the hamiltonian constraint. A natural notion of time is introduced via the Heisenberg equation. This notion enables one to reproduce the time-time component of the classical metric. Non-Hermiticity of the hamiltonian is essential in the definition of time.

The Parisi-Sourlas symmetry of the superparticle

Abstract We show that the quantum hamiltonian of the Brink-Schwarz superparticle in D dimensions has OSp(1+ m , 1+ m ∥2+2 m ) symmetry ( m =2 [ D /2]−1 ) which includes the BRST symmetry. The propagatorm in an axial gauge, turns out to have OSp( D + m , 1+ m ∥2+2 m ) or OSp( D −1+ m , 2+ m ∥2+2 m ) symmetry, which unifies the BRST and the space-time supersymmetry through the Parisi-Sourlas mechanism.

Generalization of general relativity to the space of closed strings

Abstract A geometrical string field theory is constructed on the space of bosonic closed strings. Einstein gravity is reproduced in a part of the massless sector at the level of the classical lagrangian.

Quantization via Star Products

We study quantization via star products. We investigate a quantization scheme in which a quantum theory is described entirely in terms of the function space without reference to a Hilbert space, unlike the formulation employing the Wigner functions. The associative law plays an essential role in excluding the unwanted solutions to the stargen-value equation. This is demonstrated explicitly with the D-dimensional harmonic oscillator.