938 research outputs found
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 -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 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
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.
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