scholarly journals Rationality of Conformally Invariant Local Correlation Functions on Compactified Minkowski Space

2001 ◽  
Vol 218 (2) ◽  
pp. 417-436 ◽  
Author(s):  
Nikolay M. Nikolov ◽  
Ivan T. Todorov
Keyword(s):  
Minkowski Space ◽  
Correlation Functions ◽  
Local Correlation ◽  
Conformally Invariant

On Conformally Covariant Spinor Field Equations

1972 ◽  
Vol 50 (18) ◽  
pp. 2100-2104 ◽  
Author(s):  
Mark S. Drew
Keyword(s):  
Minkowski Space ◽  
Invariant Mass ◽  
Spinor Field ◽  
Dimensional Space ◽  
Flat Space ◽  
Field Equations ◽  
First Order ◽  
Conformally Invariant ◽  
Spinor Fields

Conformally covariant equations for free spinor fields are determined uniquely by carrying out a descent to Minkowski space from the most general first-order rotationally covariant spinor equations in a six-dimensional flat space. It is found that the introduction of the concept of the "conformally invariant mass" is not possible for spinor fields even if the fields are defined not only on the null hyperquadric but over the entire manifold of coordinates in six-dimensional space.

scholarly journals QCD Factorization and PDFs from Lattice QCD Calculation

2015 ◽  
Vol 37 ◽  
pp. 1560041 ◽  
Author(s):  
Yan-Qing Ma ◽  
Jian-Wei Qiu
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Lattice Qcd ◽  
Correlation Functions ◽  
Parton Distribution ◽  
Distribution Functions ◽  
Matrix Elements ◽  
Parton Distribution Functions ◽  
Qcd Factorization ◽  
The Matrix

In this talk, we review a QCD factorization based approach to extract parton distribution and correlation functions from lattice QCD calculation of single hadron matrix elements of quark-gluon operators. We argue that although the lattice QCD calculations are done in the Euclidean space, the nonperturbative collinear behavior of the matrix elements are the same as that in the Minkowski space, and could be systematically factorized into parton distribution functions with infrared safe matching coefficients. The matching coefficients can be calculated perturbatively by applying the factorization formalism on to asymptotic partonic states.

FREDHOLM DETERMINANT REPRESENTATION OF QUANTUM CORRELATION FUNCTION FOR SINE-GORDON AT SPECIAL VALUE OF COUPLING CONSTANT

1992 ◽  
Vol 06 (22) ◽  
pp. 1405-1411 ◽  
Author(s):  
H. ITOYAMA ◽  
V. E. KOREPIN ◽  
H. B. THACKER
Keyword(s):  
Correlation Functions ◽  
Fredholm Determinant ◽  
Free Fermion ◽  
Coupling Constant ◽  
Local Correlation ◽  
Determinant Representation ◽  
Special Value ◽  
Quantum Correlation Function ◽  
Sine Gordon Model ◽  
The One

Correlation functions of the Sine-Gordon model (which is equivalent to the Massive-Thirring model) are considered at the free fermion point. We derive a determinant formula for local correlation functions of the Sine-Gordon model, starting from Bethe ansatz wave function. Kernel of integral operator is trigonometric version of the one for Impenetrable Bosons.

CURVATURE VACUUM CORRELATIONS IN FOUR-DERIVATIVE GRAVITY

2001 ◽  
Vol 16 (22) ◽  
pp. 3717-3729
Author(s):  
D. SHAO ◽  
H. NODA ◽  
L. SHAO ◽  
C. G. SHAO
Keyword(s):  
Coordinate System ◽  
Minkowski Space ◽  
Correlation Functions ◽  
Space Time ◽  
Minkowski Space Time ◽  
Graviton Propagator ◽  
Harmonic Coordinate

Under the flat Minkowski space–time background, in the harmonic coordinate system, we calculate the expressions of the leading terms of several two-point curvature vacuum correlation functions in n dimensional four-derivative gravity, resulting in that the two-point curvature vacuum correlation functions are not zero, and discuss the relations between the four-derivative gravity and the R-gravity for the graviton propagator and the curvature correlation functions.

scholarly journals Heterogeneous Correlation Modeling Based on the Wavelet Diagonal Assumption and on the Diffusion Operator

2009 ◽  
Vol 137 (9) ◽  
pp. 2995-3012 ◽  
Author(s):  
Olivier Pannekoucke
Keyword(s):  
Correlation Functions ◽  
Wavelet Transforms ◽  
Length Scale ◽  
Local Correlation ◽  
Background Error ◽  
Correlation Matrices ◽  
Diffusion Operator ◽  
Geographical Variations ◽  
Second Generation Wavelets ◽  
Randomization Method

Abstract This article discusses several models for background error correlation matrices using the wavelet diagonal assumption and the diffusion operator. The most general properties of filtering local correlation functions, with wavelet formulations, are recalled. Two spherical wavelet transforms based on Legendre spectrum and a gridpoint spherical wavelet transform are compared. The latter belongs to the class of second-generation wavelets. In addition, a nonseparable formulation that merges the wavelets and the diffusion operator model is formally proposed. This hybrid formulation is illustrated in a simple two-dimensional framework. These three formulations are tested in a toy experiment on the sphere: a large ensemble of perturbed forecasts is used to simulate a true background error ensemble, which gives a reference. This ensemble is then applied to compute the required parameters for each model. A randomization method is utilized in order to diagnose these different models. In particular, their ability to represent the geographical variations of the local correlation functions is studied by diagnosis of the local length scale. The results from these experiments show that the spectrally based wavelet formulation filters the geographical variations of the local correlation length scale but it is less able to represent the anisotropy. The gridpoint-based wavelet formulation is also able to represent some parts of the geographical variations but it appears that the correlation functions are dependent on the grid. Finally, the formulation based on the diffusion represents quite well the local length scale.

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