Spectrality, cluster decomposition and small distance properties in Wightman field theory

1974 ◽  
Vol 15 (10) ◽  
pp. 1680-1685 ◽  
Author(s):  
A. Truman
Keyword(s):  
Field Theory ◽  
Small Distance ◽  
Distance Properties

scholarly journals SHORT DISTANCE PROPERTIES FROM LARGE DISTANCE BEHAVIOR

1998 ◽  
Vol 13 (23) ◽  
pp. 4101-4122 ◽  
Author(s):  
PAUL MANSFIELD ◽  
MARCOS SAMPAIO ◽  
JIANNIS PACHOS
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Scalar Field ◽  
Large Distance ◽  
Short Distance ◽  
Quantum Field ◽  
Scalar Field Theory ◽  
Expansion Coefficients ◽  
Distance Behavior ◽  
Distance Properties

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar field theory in 1+1 dimensions we show that this approach correctly reproduces the short-distance properties as contained in the counterterms. We also describe an approximate simplification that occurs for the sine–Gordon and sinh–Gordon vacuum functionals.

scholarly journals SCALING ALGEBRAS AND SUPERSELECTION SECTORS: STUDY OF A CLASS OF MODELS

2006 ◽  
Vol 18 (05) ◽  
pp. 565-594 ◽  
Author(s):  
CLAUDIO D'ANTONI ◽  
GERARDO MORSELLA
Keyword(s):  
Field Theory ◽  
Short Distance ◽  
Scaling Limit ◽  
Sufficient Conditions ◽  
Irreducible Representations ◽  
Quantum Field ◽  
Compact Lie Group ◽  
General Study ◽  
Closed Normal Subgroup ◽  
Distance Properties

We analyze a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R. Verch). In particular, we show that for each pair (G, N), with G a compact Lie group and N a closed normal subgroup, there is a net of observable algebras which has (a subset of) DHR sectors in 1-1 correspondence with classes of irreducible representations of G, and such that only the sectors corresponding to representations of G/N are preserved in the scaling limit. In the way of achieving this result, we derive sufficient conditions under which the scaling limit of a tensor product theory coincides with the product of the scaling limit theories.

A New Defect in Polyethylene Single Crystals

1973 ◽  
Vol 31 ◽  
pp. 70-71
Author(s):  
E. L. Thomas ◽  
S. L. Sass
Keyword(s):  
Single Crystals ◽  
Screw Dislocation ◽  
Small Distance ◽  
Dipole Model ◽  
Dislocation Dipole ◽  
Chain Folding ◽  
Black And White ◽  
Polymer Crystal ◽  
Different Types

In polyethylene single crystals pairs of black and white lines spaced 700-3,000Å apart, parallel to the [100] and [010] directions, have been identified as microsector boundaries. A microsector is formed when the plane of chain folding changes over a small distance within a polymer crystal. In order for the different types of folds to accommodate at the boundary between the 2 fold domains, a staggering along the chain direction and a rotation of the chains in the plane of the boundary occurs. The black-white contrast from a microsector boundary can be explained in terms of these chain rotations. We demonstrate that microsectors can terminate within the crystal and interpret the observed terminal strain contrast in terms of a screw dislocation dipole model.

Unbiased estimation of particle number and sizes using the new stereological tools: the disector, the fractionator, the selector, and the nucleator — or just point-sampled intercepts

1988 ◽  
Vol 46 ◽  
pp. 428-429
Author(s):  
H.J.G. Gundersen
Keyword(s):  
Particle Number ◽  
Small Distance ◽  
Parallel Plane ◽  
Unbiased Estimation ◽  
Severe Problem ◽  
New Era ◽  
Size And Shape ◽  
Distinct Property ◽  
Sectioned Tissue

Previously, all stereological estimation of particle number and sizes were based on models and notoriously gave biased results, were very inefficient to use and difficult to justify. For all references to old methods and a direct comparison with unbiased methods see recent reviews.The publication in 1984 of the DISECTOR, the first unbiased stereological probe for sampling and counting 3—D objects irrespective of their size and shape, signalled the new era in stereology — and give rise to a number of remarkably simple and efficient techniques based on its distinct property: It is the only known way to obtain an unbiased sample of 3-D objects (cells, organelles, etc). The principle is simple: within a 2-D unbiased frame count or sample only cells which are not hit by a parallel plane at a known, small distance h.The area of the frame and h must be known, which might sometimes in itself be a problem, albeit usually a small one. A more severe problem may arise because these constants are known at the scale of the fixed, embedded and sectioned tissue which is often shrunken considerably.

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