arXiv subjects

Dae-Yup Song

Publications and source records attributed to Dae-Yup Song.

23 records · Page 2Linked to original sources

arXiv1998

Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schrödinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.

quant-ph↗

arXiv1997

Restrictions on negative energy density in a curved spacetime

Recently a restriction ("quantum inequality-type relation") on the (renormalized) energy density measured by a static observer in a "globally static" (ultrastatic) spacetime has been formulated by Pfenning and Ford for the minimally coupled scalar field, in the extension of quantum inequality-type relation on flat spacetime of Ford and Roman. They found negative lower bounds for the line integrals of energy density multiplied by a sampling (weighting) function, and explicitly evaluate them for some specific spacetimes. In this paper, we study the lower bound on spacetimes whose spacelike hypersurfaces are compact and without boundary. In the short "sampling time" limit, the bound has asymptotic expansion. Although the expansion can not be represented by locally invariant quantities in general due to the nonlocal nature of the integral, we explicitly evaluate the dominant terms in the limit in terms of the invariant quantities. We also make an estimate for the bound in the long sampling time limit.

gr-qc↗

arXiv1995

Critical curvature of large-$N$ nonlinear $O(N)$ sigma model on $S^2$

We study the nonlinear $O(N)$ sigma model on $S^2$ with the gravitational coupling term, by evaluating the effective potential in the large-$N$ limit. It is shown that there is a critical curvature $R_c$ of $S^2$ for any positive gravitational coupling constant $ξ$, and the dynamical mass generation takes place only when $R 0)$, which leads us to define a function looking like a natural generalization of Euler-Mascheroni constant.

hep-th↗

arXiv1995

Phase transition by curvature in three dimensional $O(N)$ sigma model

Using the effective potential, the large-$N$ nonlinear $O(N)$ sigma model with the curvature coupled term is studied on $S^2\times R^1$. We show that, for the conformally coupled case, the dynamical mass generation of the model in the strong-coupled regime on $R^3$ takes place for any finite scalar curvature (or radius of the $S^2$). If the coupling constant is larger than that of the conformally coupled case, there exist a critical curvature (radius) above (below) which the dynamical mass generation does not take place even in the strong-coupled regime. Below the critical curvature, the mass generation occurs as in the model on $R^3$.

hep-th↗

arXiv1994

S matrix of collective field theory

By applying the Lehmann-Symanzik-Zimmermann (LSZ) reduction formalism, we study the S matrix of collective field theory in which fermi energy is larger than the height of potential. We consider the spatially symmetric and antisymmetric boundary conditions. The difference is that S matrices are proportional to momenta of external particles in antisymmetric boundary condition, while they are proportional to energies in symmetric boundary condition. To the order of $g_{st}^2$, we find simple formulas for the S matrix of general potential. As an application, we calculate the S matrix of a case which has been conjectured to describe a "naked singularity".

hep-th↗