A complete treatment of the electron propagator through third order

1975 ◽  
Vol 63 (12) ◽  
pp. 5302-5304 ◽  
Author(s):  
Poul Jo/rgensen ◽  
Jack Simons
Keyword(s):  
Third Order ◽  
Electron Propagator ◽  
Complete Treatment

scholarly journals Testing an Inflation Model with Nonminimal Derivative Coupling in the Light of Planck 2015 Data

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Kourosh Nozari ◽  
Narges Rashidi
Keyword(s):  
Weak Coupling ◽  
Weak Coupling Limit ◽  
Inflationary Model ◽  
Third Order ◽  
Derivative Coupling ◽  
Planck Data ◽  
The Third ◽  
Inflation Model ◽  
Complete Treatment ◽  
Point Correlation

We study the dynamics of a generalized inflationary model in which both the scalar field and its derivatives are coupled with the gravity. We consider a general form of the nonminimal derivative coupling in order to have a complete treatment of the model. By expanding the action up to the second order in perturbation, we study the spectrum of the primordial modes of the perturbations. Also, by expanding the action up to the third order and considering the three-point correlation functions, the amplitude of the non-Gaussianity of the primordial perturbations is studied in both equilateral and orthogonal configurations. Finally, by adopting some sort of potentials, we compare the model in hand with the Planck 2015 released observational data and obtain some constraints on the model’s parameters space. As an important result, we show that the nonminimal couplings help to make models of chaotic inflation that would otherwise be in tension with Planck data, in better agreement with the data. This model is consistent with observation at weak coupling limit.

Application and Testing of Diagonal, Partial Third-Order Electron Propagator Approximations

2005 ◽  
pp. 131-160 ◽  
Author(s):  
Antonio M. Ferreira ◽  
Gustavo Seabra ◽  
O. Dolgounitcheva ◽  
V. G. Zakrzewski ◽  
J. V. Ortiz
Keyword(s):  
Third Order ◽  
Electron Propagator

A fresh look at the photoelectron spectrum of bromobenzene: A third-order non-Dyson electron propagator study

2015 ◽  
Vol 143 (14) ◽  
pp. 144103 ◽  
Author(s):  
M. Schneider ◽  
D. Yu. Soshnikov ◽  
D. M. P. Holland ◽  
I. Powis ◽  
E. Antonsson ◽  
...  
Keyword(s):  
Photoelectron Spectrum ◽  
Third Order ◽  
Electron Propagator

Probe size and 5th-order aberration

1987 ◽  
Vol 45 ◽  
pp. 134-135 ◽  
Author(s):  
Zhifeng Shao
Keyword(s):  
Electron Probe ◽  
Spherical Aberration ◽  
Wave Length ◽  
Cylindrical Symmetry ◽  
Electron Wave ◽  
Third Order ◽  
The Third ◽  
Probe Radius ◽  
Small Probe ◽  
Probe Size

A small electron probe has many applications in many fields and in the case of the STEM, the probe size essentially determines the ultimate resolution. However, there are many difficulties in obtaining a very small probe.Spherical aberration is one of them and all existing probe forming systems have non-zero spherical aberration. The ultimate probe radius is given byδ = 0.43Csl/4ƛ3/4where ƛ is the electron wave length and it is apparent that δ decreases only slowly with decreasing Cs. Scherzer pointed out that the third order aberration coefficient always has the same sign regardless of the field distribution, provided only that the fields have cylindrical symmetry, are independent of time and no space charge is present. To overcome this problem, he proposed a corrector consisting of octupoles and quadrupoles.

Children’s Recall of Approximations to English

1973 ◽  
Vol 16 (2) ◽  
pp. 201-212 ◽  
Author(s):  
Elizabeth Carrow ◽  
Michael Mauldin
Keyword(s):  
Language Development ◽  
Fourth Order ◽  
Third Order ◽  
Memory Processes ◽  
The Third ◽  
General Index ◽  
General Linguistic

As a general index of language development, the recall of first through fourth order approximations to English was examined in four, five, six, and seven year olds and adults. Data suggested that recall improved with age, and increases in approximation to English were accompanied by increases in recall for six and seven year olds and adults. Recall improved for four and five year olds through the third order but declined at the fourth. The latter finding was attributed to deficits in semantic structures and memory processes in four and five year olds. The former finding was interpreted as an index of the development of general linguistic processes.

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