Invariant Operators vs Heisenberg Operators for Time-Dependent Generalized Oscillators

We investigate the relation between the invariant operators satisfying the quantum Liouville-von Neumann and the Heisenberg operators satisfying the Heisenberg equation. For time-dependent generalized oscillators we find the invariant operators, known as the Ermakov-Lewis invariants, in terms of a complex classical solution, from which the evolution operator is derived, and obtain the Heisenberg position and momentum operators. Physical quantities such as correlation functions are calculated using both the invariant operators and Heisenberg operators.Comment: RevTex 5page

Third Quantization and Quantum Universes

We study the third quantization of the Friedmann-Robertson-Walker cosmology with $N$-minimal massless fields. The third quantized Hamiltonian for the WDW equation in the minisuperspace consists of infinite number of intrinsic time-dependent, decoupled oscillators. The Hamiltonian has a pair of invariant operators for each universe with conserved momenta of the fields that play a role of the annihilation and the creation operators and that construct various quantum states for the universe. The closed universe exhibits an interesting feature of transitions from stable states to tachyonic states depending on the conserved momenta of the fields. In the classical forbidden unstable regime, the quantum states have googolplex growing position and conjugate momentum dispersions, which defy any measurements of the position of the universe.Comment: LaTex 8 pages, no figure; 9th CosPA (Cosmology and Particle Astrophysics) Proceeding

Liouville-Neumann Approach to the Nonperturbative Quantum Field Theory

We present a nonperturbative field theoretic method based on the Liouville-Neumann (LN) equation. The LN approach provides a unified formulation of nonperturbative quantum fields and also nonequilibrium quantum fields, which makes use of mean-field type equations and whose results at the lowest level are identically the same as those of the Gaussian effective potential approach and the mean-field approach. The great advantageous point of this formulation is its readiness of applicability to time-dependent quantum systems and to finite temperature field theory, and its possibility to go beyond the Gaussian approximation.Comment: To appear in the proceedings to be published by World Scientific of APCTP-ICTP Joint International Conference '97 on 'Recent Developments in Nonperturbative Quantum Field Theory', May 26-30, 1997, Seoul, Some typos corrected, ReVTeX, 12 Pages, No Figur

Method for Solving the Bloch Equation from the Connection with Time-Dependent Oscillator

We introduce a novel method to find exact density operators for a spin-1/2 particle in time-dependent magnetic fields by using the one-mode bosonic representation of $su(2)$ and the connection with a time-dependent oscillator. As illustrative examples, we apply the method to find the density operators for constant and/or oscillating magnetic fields, which turn out to be time-dependent in general.Comment: RevTex, 14 pages, no figur

QED Effective Actions in Space-Dependent Gauge and Electromagnetic Duality

We develop the in-out formalism for one-loop effective actions in electromagnetic fields in the space-dependent gauge. We further advance a method using the inverse scattering matrix to calculate the effective actions in pure magnetic fields, find the effective actions in a constant magnetic field and a localized Sauter-type magnetic field and apply the uniform semiclassical approximation to the effective action in a general magnetic field. In the in-out formalism we show that the one-loop effective actions in constant fields and Sauter-type fields exhibit the electromagnetic duality.Comment: RevTex 19 pages; drastically revised by reformulating the second quantized field theory for barrier tunneling and adding reference

Quantum Cosmology for Tunneling Universes

In a quantum cosmological model consisting of a Euclidean region and a Lorentzian region, Hartle-Hawking's no-bounary wave function, and Linde's wave function and Vilenkin's tunneling wave function are briefly described and compared with each other. We put a particular emphasis on semiclassical gravity from quantum cosmology and compare it with the conventional quantum field theory in curved spacetimes. Finally, we discuss the recent debate on catastrophic particle production in the tunneling universe between Rubakov and Vilenkin within the semiclassical gravity.Comment: RevTex4; invited talk at VI APCTP International Conference of Gravitation and Astrophysics (ICGA6), Seoul, Oct. 6-9, 200

Problem of Unitarity and Quantum Corrections in Semiclassical Quantum Gravity

Using both the Born-Oppenheimer idea and the de Broglie-Bohm interpretation of wavefunction we represent in a different way the semiclassical quantum gravity from the Wheeler-DeWitt equation in an oscillating regime which can preserve completely the unitary quantum evolution of a matter field at the expense of a nonlinear gravitational field equation, but has the same asymptotic limit as the others. We apply the de Broglie-Bohm interpretation to the nonlinear gravitational field equation to develop a perturbation method to find the quantum corrections of a matter field to the gravity. The semiclassical Einstein equation with the quantum corrections is found for a minimal quantum FRW cosmological model.Comment: Replaced with the version published in PR

Time-dependent Displaced and Squeezed Number States

We generalize the wave functions of the displaced and squeezed number states, found by Nieto, to a time-dependent harmonic oscillator with variable mass and frequency. These time-dependent displaced and squeezed number states are obtained by first squeezing and then displacing the exact number states and are exact solutions of the Schr\"{o}dinger equation. Further, these wave functions are the time-dependent squeezed harmonic-oscillator wave functions centered at classical trajectories.Comment: RevTex4, 9pages, no figure; to be published in J. Korean Phys. So

Spontaneous Emission of Charged Bosons from Supercritical Point Charges

We study the spontaneous emission of charged bosons from supercritical Coulomb potentials and charged black holes. We find the exact emission rate from the Bogoliubov transformation by applying the tunneling boundary condition on the Jost functions at the asymptotic boundaries. The emission rate for charged bosons in the supercritical Coulomb potential increases as the charge $Z\alpha > 1/2$ of the superatom and the energy of the bosons increase but is suppressed for large angular momenta. We discuss physical implications of the emission of charged bosons from superatoms and charged black holes.Comment: RevTex 5 pages, 5 figures, Proceedings of the 13th Italian-Korean Symposium on Relativistic Astrophysics, Seoul, July 15-19, 201

Geometric Origin of Stokes Phenomenon for de Sitter Radiation

We propose a geometric interpretation for the Stokes phenomenon in de Sitter spacetime that particles are produced in even dimensions but not in odd dimensions. The scattering amplitude for a quantum field between the in-vacuum and the transported one along a closed path in the complex-time plane gives the particle-production rate that explains not only the Boltzmann factor from the simple pole at infinity, corresponding to the cosmological horizon, but also the sinusoidal behavior from simple poles at the north and south poles of the Euclidean geometry. The Stokes phenomenon is a consequence of interference among four independent closed paths in the complex plane.Comment: RevTex 6 pages, 3 figures; replaced by the version to be published in Phys. Rev.