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Title: A note on semidensities in antisymplectic geometry

Abstract

We revisit Khudaverdian's geometric construction of an odd nilpotent operator {delta}{sub E} that sends semidensities to semidensities on an antisymplectic manifold. We find a local formula for the {delta}{sub E} operator in arbitrary coordinates and we discuss its connection to Batalin-Vilkovisky quantization.

Authors:
 [1]
  1. Institute for Theoretical Physics and Astrophysics, Masaryk University, Kotlarska 2, CZ-611 37 Brno (Czech Republic)
Publication Date:
OSTI Identifier:
20861569
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2352859; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGEBRA; CONSTRUCTION; COORDINATES; GEOMETRY; QUANTIZATION

Citation Formats

Bering, K. A note on semidensities in antisymplectic geometry. United States: N. p., 2006. Web. doi:10.1063/1.2352859.
Bering, K. A note on semidensities in antisymplectic geometry. United States. doi:10.1063/1.2352859.
Bering, K. Fri . "A note on semidensities in antisymplectic geometry". United States. doi:10.1063/1.2352859.
@article{osti_20861569,
title = {A note on semidensities in antisymplectic geometry},
author = {Bering, K.},
abstractNote = {We revisit Khudaverdian's geometric construction of an odd nilpotent operator {delta}{sub E} that sends semidensities to semidensities on an antisymplectic manifold. We find a local formula for the {delta}{sub E} operator in arbitrary coordinates and we discuss its connection to Batalin-Vilkovisky quantization.},
doi = {10.1063/1.2352859},
journal = {Journal of Mathematical Physics},
number = 12,
volume = 47,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2006},
month = {Fri Dec 15 00:00:00 EST 2006}
}
  • A nonlinear complex scalar field with a phi/sup 2d//(d - 2) self-interaction is considered in a flat, (d + 1) -dimensional space-time. Conformal techniques familiar in differential geometry become operative in the construction of exact, ''soliton''-type solutions exhibiting finite energies, but exponential decays.
  • 3-quasi-Sasakian manifolds were recently studied by the authors as a suitable setting unifying 3-Sasakian and 3-cosymplectic geometries. In this paper some geometric properties of this class of almost 3-contact metric manifolds are briefly reviewed, with an emphasis on those more related to physical applications.
  • No abstract prepared.
  • Purpose: To investigate the geometry dependence of the detector response function (DRF) of three commonly used scanning ionization chambers and its impact on a convolution-based method to address the volume averaging effect (VAE). Methods: A convolution-based approach has been proposed recently to address the ionization chamber VAE. It simulates the VAE in the treatment planning system (TPS) by iteratively convolving the calculated beam profiles with the DRF while optimizing the beam model. Since the convolved and the measured profiles are subject to the same VAE, the calculated profiles match the implicit “real” ones when the optimization converges. Three DRFs (Gaussian,more » Lorentzian, and parabolic function) were used for three ionization chambers (CC04, CC13, and SNC125c) in this study. Geometry dependent/independent DRFs were obtained by minimizing the difference between the ionization chamber-measured profiles and the diode-measured profiles convolved with the DRFs. These DRFs were used to obtain eighteen beam models for a commercial TPS. Accuracy of the beam models were evaluated by assessing the 20%–80% penumbra width difference (PWD) between the computed and diode-measured beam profiles. Results: The convolution-based approach was found to be effective for all three ionization chambers with significant improvement for all beam models. Up to 17% geometry dependence of the three DRFs was observed for the studied ionization chambers. With geometry dependent DRFs, the PWD was within 0.80 mm for the parabolic function and CC04 combination and within 0.50 mm for other combinations; with geometry independent DRFs, the PWD was within 1.00 mm for all cases. When using the Gaussian function as the DRF, accounting for geometry dependence led to marginal improvement (PWD < 0.20 mm) for CC04; the improvement ranged from 0.38 to 0.65 mm for CC13; for SNC125c, the improvement was slightly above 0.50 mm. Conclusions: Although all three DRFs were found adequate to represent the response of the studied ionization chambers, the Gaussian function was favored due to its superior overall performance. The geometry dependence of the DRFs can be significant for clinical applications involving small fields such as stereotactic radiotherapy.« less