3,922,537 research outputs found
Fundamentals of Quantum Gravity
The outline of a recent approach to quantum gravity is presented. Novel
ingredients include: (1) Affine kinematical variables; (2) Affine coherent
states; (3) Projection operator approach toward quantum constraints; (4)
Continuous-time regularized functional integral representation without/with
constraints; and (5) Hard core picture of nonrenormalizability. The ``diagonal
representation'' for operator representations, introduced by Sudarshan into
quantum optics, arises naturally within this program.Comment: 15 pages, conference proceeding
The Affine Quantum Gravity Program
The central principle of affine quantum gravity is securing and maintaining
the strict positivity of the matrix \{\hg_{ab}(x)\} composed of the spatial
components of the local metric operator. On spectral grounds, canonical
commutation relations are incompatible with this principle, and they must be
replaced by noncanonical, affine commutation relations. Due to the partial
second-class nature of the quantum gravitational constraints, it is
advantageous to use the recently developed projection operator method, which
treats all quantum constraints on an equal footing. Using this method,
enforcement of regularized versions of the gravitational operator constraints
is formulated quite naturally by means of a novel and relatively well-defined
functional integral involving only the same set of variables that appears in
the usual classical formulation. It is anticipated that skills and insight to
study this formulation can be developed by studying special, reduced-variable
models that still retain some basic characteristics of gravity, specifically a
partial second-class constraint operator structure. Although perturbatively
nonrenormalizable, gravity may possibly be understood nonperturbatively from a
hard-core perspective that has proved valuable for specialized models. Finally,
developing a procedure to pass to the genuine physical Hilbert space involves
several interconnected steps that require careful coordination.Comment: 16 pages, LaTeX, no figure
The challenge of the chiral Potts model
The chiral Potts model continues to pose particular challenges in statistical
mechanics: it is ``exactly solvable'' in the sense that it satisfies the
Yang-Baxter relation, but actually obtaining the solution is not easy. Its free
energy was calculated in 1988 and the order parameter was conjectured in full
generality a year later.
However, a derivation of that conjecture had to wait until 2005. Here we
discuss that derivation.Comment: 22 pages, 3 figures, 29 reference
The structure of the C4 cluster radical
The first infrared spectrum of gas phase, jet-cooled C4 has been measured by high resolution diode laser absorption spectroscopy. Twelve rovibrational transitions are assigned to the nu3(sigmau) antisymmetric stretch of linear 3Sigma - g C4. No evidence is observed for the bent structure of triplet C4 recently observed in a matrix study by Cheung and Graham [J. Chem. Phys. 91, 6664 (1989)]. Indeed, the measured band origin (1548.9368(21) cm^–1) and effective ground state C–C bond length [1.304 31(21)A] are consistent with several ab initio predictions of a rigid, linear, cumulenic structure for this cluster radical
On the role of coherent states in quantum foundations
Coherent states, and the Hilbert space representations they generate, provide
ideal tools to discuss classical/quantum relationships. In this paper we
analyze three separate classical/quantum problems using coherent states, and
show that useful connections arise among them. The topics discussed are: (1) a
truly natural formulation of phase space path integrals; (2) how this analysis
implies that the usual classical formalism is ``simply a subset'' of the
quantum formalism, and thus demonstrates a universal coexistence of both the
classical and quantum formalisms; and (3) how these two insights lead to a
complete analytic solution of a formerly insoluble family of nonlinear quantum
field theory models.Comment: ICQOQI'2010, Kiev, Ukraine, May-June 2010, Conference Proceedings (9
pages
The Utility of Coherent States and other Mathematical Methods in the Foundations of Affine Quantum Gravity
Affine quantum gravity involves (i) affine commutation relations to ensure
metric positivity, (ii) a regularized projection operator procedure to
accomodate first- and second-class quantum constraints, and (iii) a hard-core
interpretation of nonlinear interactions to understand and potentially overcome
nonrenormalizability. In this program, some of the less traditional
mathematical methods employed are (i) coherent state representations, (ii)
reproducing kernel Hilbert spaces, and (iii) functional integral
representations involving a continuous-time regularization. Of special
importance is the profoundly different integration measure used for the
Lagrange multiplier (shift and lapse) functions. These various concepts are
first introduced on elementary systems to help motivate their application to
affine quantum gravity.Comment: 15 pages, Presented at the X-International Conference on Symmetry
Methods in Physic
The C9 cluster: Structure and infrared frequencies
The high resolution infrared spectrum of the C9 cluster has been measured in direct absorption by infrared diode laser spectroscopy of a pulsed supersonic carbon cluster jet. Fifty-one rovibrational transitions have been assigned to the nu6 (sigmau ) antisymmetric stretch fundamental of the 1Sigma + 9 linear ground state of C9. The measured rotational constant [429.30(50) MHz] is in good agreement with ab initio calculations and indicates an effective bond length of 1.278 68(75) Ă…, consistent with cumulenic bonding in this cluster. Several perturbations are observed in the upper state, and the upper- and lower-state centrifugal distortion constants are observed to be anomolously large, evidencing a high degree of Coriolis mixing of the normal modes
Derivation of the order parameter of the chiral Potts model
We derive the order parameter of the chiral Potts model, using the method of
Jimbo et al. The result agrees with previous conjectures.Comment: Version 2 submitted 21 Feb 2005. It has 7 pages, 2 figures. The
introduction has been expanded and a significant typographical error in eqn
23 has been correcte
A pseudo random-access synchronous meteorological satellite system
Communications satellite system uses pseudo-random time frequency multiplexing technique for extracting real-time meteorological data from great number of isolated weather stations /data collection platforms/ situated randomly throughout the world
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