Phonon self-energy to the fourth order: An application to an anharmonic diatomic linear lattice

1992 ◽  
Vol 46 (17) ◽  
pp. 10693-10700 ◽  
Author(s):  
Rajiv Bhandari ◽  
V. K. Jindal
Keyword(s):  
Fourth Order ◽  
Linear Lattice ◽  
Self Energy

Fourth-order self-energy contribution to the Lamb shift

1998 ◽  
Vol 57 (3) ◽  
pp. 1548-1564 ◽  
Author(s):  
S. Mallampalli ◽  
J. Sapirstein
Keyword(s):  
Fourth Order ◽  
Lamb Shift ◽  
Energy Contribution ◽  
Self Energy

On the propagation functions of quantum electrodynamics

1954 ◽  
Vol 225 (1163) ◽  
pp. 535-548 ◽  
Keyword(s):  
Power Series ◽  
Series Expansion ◽  
Fourth Order ◽  
Quantum Electrodynamics ◽  
Power Series Expansion ◽  
Vertex Part ◽  
Self Energy ◽  
One To One ◽  
Renormalization Constants

Schwinger’s equations for the propagation functions of quantum electrodynamics are redefined in a way to give the finite (renormalized) propagation functions without reference to divergent integrals or infinite renormalization constants. This is achieved by incorporating in the equations themselves a limiting process which is an extension of that introduced by Dirac and Heisenberg. The formulation is given independently of the power-series expansion, but the cancellation of singularities is established only in terms of such an expansion. The method is illustrated first by considering the lowest-order approximations. The lowestorder electron self-energy and vertex-part expressions are worked out, and the compensation of the singularities corresponding to the ‘ b ’ divergences is indicated in the fourth order. In the power-series expansion, the prescriptions are in a one-to-one correspondence to those of Dyson. Their formulation independently of this expansion sums up the rules obtained in the different approximations.

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.

Exploring the Fourth Order

2019 ◽  
Vol 2 (1) ◽  
Author(s):  
Barend KLITSIE ◽  
Rebecca PRICE ◽  
Christine DE LILLE
Keyword(s):  
Action Research ◽  
Fourth Order ◽  
Subject Matter ◽  
Action Research Project ◽  
Research Project ◽  
Building Trust ◽  
Current Business

Companies are organised to fulfil two distinctive functions: efficient and resilient exploitation of current business and parallel exploration of new possibilities. For the latter, companies require strong organisational infrastructure such as team compositions and functional structures to ensure exploration remains effective. This paper explores the potential for designing organisational infrastructure to be part of fourth order subject matter. In particular, it explores how organisational infrastructure could be designed in the context of an exploratory unit, operating in a large heritage airline. This paper leverages insights from a long-term action research project and finds that building trust and shared frames are crucial to designing infrastructure that affords the greater explorative agenda of an organisation.

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