45,129 research outputs found
Quantum field theory as eigenvalue problem
A mathematically well-defined, manifestly covariant theory of classical and
quantum field is given, based on Euclidean Poisson algebras and a
generalization of the Ehrenfest equation, which implies the stationary action
principle. The theory opens a constructive spectral approach to finding
physical states both in relativistic quantum field theories and for flexible
phenomenological few-particle approximations.
In particular, we obtain a Lorentz-covariant phenomenological multiparticle
quantum dynamics for electromagnetic and gravitational interaction which
provides a representation of the Poincare group without negative energy states.
The dynamics reduces in the nonrelativistic limit to the traditional
Hamiltonian multiparticle description with standard Newton and Coulomb forces.
The key that allows us to overcome the traditional problems in canonical
quantization is the fact that we use the algebra of linear operators on a space
of wave functions slightly bigger than traditional Fock spaces.Comment: 32 page
Quantum state diffusion, localization and computation
Numerical simulation of individual open quantum systems has proven advantages
over density operator computations. Quantum state diffusion with a moving basis
(MQSD) provides a practical numerical simulation method which takes full
advantage of the localization of quantum states into wave packets occupying
small regions of classical phase space. Following and extending the original
proposal of Percival, Alber and Steimle, we show that MQSD can provide a
further gain over ordinary QSD and other quantum trajectory methods of many
orders of magnitude in computational space and time. Because of these gains, it
is even possible to calculate an open quantum system trajectory when the
corresponding isolated system is intractable. MQSD is particularly advantageous
where classical or semiclassical dynamics provides an adequate qualitative
picture but is numerically inaccurate because of significant quantum effects.
The principles are illustrated by computations for the quantum Duffing
oscillator and for second harmonic generation in quantum optics. Potential
applications in atomic and molecular dynamics, quantum circuits and quantum
computation are suggested.Comment: 16 pages in LaTeX, 2 uuencoded postscript figures, submitted to J.
Phys.
Large N Gauge Theory -- Expansions and Transitions
We use solvable two-dimensional gauge theories to illustrate the issues in
relating large N gauge theory to string theory. We also give an introduction to
recent mathematical work which allows constructing master fields for higher
dimensional large N theories. We illustrate this with a new derivation of the
Hopf equation governing the evolution of the spectral density in matrix quantum
mechanics. Based on lectures given at the 1994 Trieste Spring School on String
Theory, Gauge Theory and Quantum Gravity.Comment: RU-94-72 (LaTeX with espcrc2.sty and epsf.sty, 26 pp., 6 figures.
References added and other improvements.
Generalizations of entanglement based on coherent states and convex sets
Unentangled pure states on a bipartite system are exactly the coherent states
with respect to the group of local transformations. What aspects of the study
of entanglement are applicable to generalized coherent states? Conversely, what
can be learned about entanglement from the well-studied theory of coherent
states? With these questions in mind, we characterize unentangled pure states
as extremal states when considered as linear functionals on the local Lie
algebra. As a result, a relativized notion of purity emerges, showing that
there is a close relationship between purity, coherence and (non-)entanglement.
To a large extent, these concepts can be defined and studied in the even more
general setting of convex cones of states. Based on the idea that entanglement
is relative, we suggest considering these notions in the context of partially
ordered families of Lie algebras or convex cones, such as those that arise
naturally for multipartite systems. The study of entanglement includes notions
of local operations and, for information-theoretic purposes, entanglement
measures and ways of scaling systems to enable asymptotic developments. We
propose ways in which these may be generalized to the Lie-algebraic setting,
and to a lesser extent to the convex-cones setting. One of our original
motivations for this program is to understand the role of entanglement-like
concepts in condensed matter. We discuss how our work provides tools for
analyzing the correlations involved in quantum phase transitions and other
aspects of condensed-matter systems.Comment: 37 page
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