4,474 research outputs found
Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation
The classical dynamics for a charged point particle with intrinsic spin is
governed by a relativistic Hamiltonian for the orbital motion and by the
Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is
natural to ask whether the classical Hamiltonian (with both the orbital and
spin parts) is consistent with that in the relativistic quantum theory for a
spin-1/2 charged particle, which is described by the Dirac equation. In the
low-energy limit, up to terms of the 7th order in ( and
is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation
of the Dirac Hamiltonian in the presence of homogeneous and static
electromagnetic fields and show that it is indeed in agreement with the
classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through
electromagnetic duality, this result can be generalized for a spin-1/2 dyon,
which has both electric and magnetic charges and thus possesses both intrinsic
electric and magnetic dipole moments. Furthermore, the relativistic quantum
theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and
gyroelectric ratios can be described by the Dirac-Pauli equation, which is the
Dirac equation with augmentation for the anomalous electric and anomalous
magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian
is shown, up to the 7th order again, to be also in accord with the classical
Hamiltonian.Comment: 18 page
Massless and Massive Three Dimensional Super Yang-Mills Theory and Mini-Twistor String Theory
We propose various ways of adding mass terms to three-dimensional twistor
string theory. We begin with a review of mini-twistor space--the reduction of
D=4 twistor space to D=3. We adapt the two proposals for twistor string theory,
Witten's and Berkovits's, to D=3 super Yang-Mills theory. In Berkovits's model,
we identify the enhanced R-symmetry. We then construct B-model topological
string theories that, we propose, correspond to D=3 Yang-Mills theory with
massive spinors and massive and massless scalars in the adjoint representation
of the gauge group. We also analyze the counterparts of these constructions in
Berkovits's model. Some of our constructions can be lifted to D=4, where
infinitesimal mass terms correspond to VEVs of certain superconformal gravity
fields.Comment: 69 pages; Typos correcte
On the unitarity of higher-dervative and nonlocal theories
We consider two simple models of higher-derivative and nonlocal quantu
systems.It is shown that, contrary to some claims found in literature, they can
be made unitary.Comment: 8 pages, no figure
Quantum Mechanical Search and Harmonic Perturbation
Perturbation theory in quantum mechanics studies how quantum systems interact
with their environmental perturbations. Harmonic perturbation is a rare special
case of time-dependent perturbations in which exact analysis exists. Some
important technology advances, such as masers, lasers, nuclear magnetic
resonance, etc., originated from it. Here we add quantum computation to this
list with a theoretical demonstration. Based on harmonic perturbation, a
quantum mechanical algorithm is devised to search the ground state of a given
Hamiltonian. The intrinsic complexity of the algorithm is continuous and
parametric in both time T and energy E. More precisely, the probability of
locating a search target of a Hamiltonian in N-dimensional vector space is
shown to be 1/(1+ c N E^{-2} T^{-2}) for some constant c. This result is
optimal. As harmonic perturbation provides a different computation mechanism,
the algorithm may suggest new directions in realizing quantum computers.Comment: 6 pages, 4 figures, revtex
Unimodular Loop Quantum Cosmology
Unimodular gravity is based on a modification of the usual Einstein-Hilbert
action that allows one to recover general relativity with a dynamical
cosmological constant. It also has the interesting property of providing, as
the momentum conjugate to the cosmological constant, an emergent clock
variable. In this paper we investigate the cosmological reduction of unimodular
gravity, and its quantization within the framework of flat homogeneous and
isotropic loop quantum cosmology. It is shown that the unimodular clock can be
used to construct the physical state space, and that the fundamental features
of the previous models featuring scalar field clocks are reproduced. In
particular, the classical singularity is replaced by a quantum bounce, which
takes place in the same condition as obtained previously. We also find that
requirement of semi-classicality demands the expectation value of the
cosmological constant to be small (in Planck units). The relation to spin foam
models is also studied, and we show that the use of the unimodular time
variable leads to a unique vertex expansion.Comment: 26 pages. Revised version taking into account referee's comment
Effective dynamics of the closed loop quantum cosmology
In this paper we study dynamics of the closed FRW model with holonomy
corrections coming from loop quantum cosmology. We consider models with a
scalar field and cosmological constant. In case of the models with cosmological
constant and free scalar field, dynamics reduce to 2D system and analysis of
solutions simplify. If only free scalar field is included then universe
undergoes non-singular oscillations. For the model with cosmological constant,
different behaviours are obtained depending on the value of . If the
value of is sufficiently small, bouncing solutions with asymptotic de
Sitter stages are obtained. However if the value of exceeds critical
value then solutions become oscillatory. Subsequently we study
models with a massive scalar field. We find that this model possess generic
inflationary attractors. In particular field, initially situated in the bottom
of the potential, is driven up during the phase of quantum bounce. This
subsequently leads to the phase of inflation. Finally we find that, comparing
with the flat case, effects of curvature do not change qualitatively dynamics
close to the phase of bounce. Possible effects of inverse volume corrections
are also briefly discussed.Comment: 18 pages, 11 figure
ASTROD, ASTROD I and their gravitational-wave sensitivities
ASTROD (Astrodynamical Space Test of Relativity using Optical Devices) is a
mission concept with three spacecraft -- one near L1/L2 point, one with an
inner solar orbit and one with an outer solar orbit, ranging coherently with
one another using lasers to test relativistic gravity, to measure the solar
system and to detect gravitational waves. ASTROD I with one spacecraft ranging
optically with ground stations is the first step toward the ASTROD mission. In
this paper, we present the ASTROD I payload and accelerometer requirements,
discuss the gravitational-wave sensitivities for ASTROD and ASTROD I, and
compare them with LISA and radio-wave PDoppler-tracking of spacecraft.Comment: presented to the 5th Edoardo Amaldi Conference (July 6-11, 2003) and
submitted to Classical and Quantum Gravit
Dynamics of on-orbit construction process
The topics covered are presented in viewgraph form and include the following: problem definition and motivation; survey of current technology; focus problems; approach; progress/discussion; and future direction and anticipated results
Timeless path integral for relativistic quantum mechanics
Starting from the canonical formalism of relativistic (timeless) quantum
mechanics, the formulation of timeless path integral is rigorously derived. The
transition amplitude is reformulated as the sum, or functional integral, over
all possible paths in the constraint surface specified by the (relativistic)
Hamiltonian constraint, and each path contributes with a phase identical to the
classical action divided by . The timeless path integral manifests the
timeless feature as it is completely independent of the parametrization for
paths. For the special case that the Hamiltonian constraint is a quadratic
polynomial in momenta, the transition amplitude admits the timeless Feynman's
path integral over the (relativistic) configuration space. Meanwhile, the
difference between relativistic quantum mechanics and conventional
nonrelativistic (with time) quantum mechanics is elaborated on in light of
timeless path integral.Comment: 41 pages; more references and comments added; version to appear in
CQ
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