arXiv subjects
Publications and source records attributed to W. S. l'Yi.
A precise form of the time evolution of rolling tachyons corresponding to a brane-antibrane pair is investigated by solving the Hamiltonian equations of motion under the assumption that in a region far away from branes the tachyon vacuum is almost already achieved, even at the beginning of the rolling.
Randall-Sundrum model, which has a scalar field, is used to investigate the domain structure of the extra dimension and to obtain a possible solution of the mass hierarchy problem. It is found that when the domain wall size is comparable to that of domains, domains become unstable. To construct a reliable theory, a region of physical parameter space, where domains are stable, is identified. Analytic forms of field configurations are obtained by perturbative expansions in term of a small parameter that is approximately equal to the relative size of domain wall with respect to domains. By placing a single 3-brane in one of the domain, one can solve the mass hierarchy problem.
General properties of coordinate-space holographic projections of fields in AdS/CFT correspondence, which respect the Ward identity, are investigated. To show the usefulness of this methodology it is applied to the computation of correlators of massive gauge fields.
By solving the equations of motion of massive $p$-form potential in Anti-de-Sitter space and using the $AdS/CFT$ correspondence of Maldacena, the generating functional of two-point correlation functions of the currents is obtained. When the mass parameter vanishes the result agrees with the known massless case.
The generating functional of correlation functions of the currents corresponding to general massless $p$-form potential is calculated in $AdS/CFT$ correspondence of Maldacena. For this we construct the boundary-to-bulk Green's functions of $p$-form potentials. The proportional constant of the current-current correlation function, which is related to the central charge of the operator product expansion, is shown to be $c=(d-p\over 2π^{d/2}) (Γ(d-p) \over Γ({d\over 2}-p)).$ The result agrees with the known cases such as $p=1$ or 2.
Quantum canonical transformations of the second kind and the non-Hermitian realizations of the basic canonical commutation relations are investigated with a special interest in the generalization of the conventional ladder operators. The operator ordering problem is shown to be resolved when the non-Hermitian realizations for the canonical variables which can not be measured simultaneously with the energy are chosen for the canonical quantizations. Another merit of the non-Hermitian representations is that it naturally allows us to introduce the generalized ladder operators with which one can solve eigenvalue problems quite neatly.
The quantum mechanical version of the four kinds of classical canonical transformations is investigated by using non-hermitian operator techniques. To help understand the usefulness of this appoach the eigenvalue problem of a harmonic oscillator is solved in two different types of canonical transformations. The quantum form of the classical Hamiton-Jacobi theory is also employed to solve time dependent Schrödinger wave equations, showing that when one uses the classical action as a generating function of the quantum canonical transformation of time evolutions of state vectors, the corresponding propagator can easily be obtained.