Analysis and Development of the Locality Principle

We establish the physical origins of chemical transferability from the perspective of the nearsightedness of electronic matter. To do this, we explicitly evaluate the response of electron density to a change in the system, at constant chemical potential, by computing the softness kernel, s(𝐫,𝐫′). The softness kernel is nearsighted, indicating that under constant-chemical-potential conditions like dilute solutions changing the composition of the molecule at 𝐫 has only local effects and does not have any significant impact on the reactivity at positions 𝐫′ far away from point 𝐫. This locality principle elucidates the transferability of functional groups in chemistry.

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On the application of the locality principle in structural dynamics

Acta Mechanica ◽

10.1007/bf01172982 ◽

1990 ◽

Vol 83 (3-4) ◽

pp. 213-222 ◽

Cited By ~ 7

Author(s):

A. K. Belyaev

Keyword(s):

Structural Dynamics ◽

Locality Principle

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Surgery and the relative index in elliptic theory

Abstract and Applied Analysis ◽

10.1155/aaa/2006/98081 ◽

2006 ◽

Vol 2006 ◽

pp. 1-16 ◽

Cited By ~ 3

Author(s):

V. E. Nazaikinskii ◽

B. Yu. Sternin

Keyword(s):

Integral Operators ◽

Fourier Integral ◽

Fourier Integral Operators ◽

Relative Index ◽

Survey Article ◽

General Index ◽

Elliptic Theory ◽

Locality Principle ◽

Index Formulas ◽

Manifolds With Singularities

This is a survey article featuring the general index locality principle introduced by the authors, which can be used to obtain index formulas for elliptic operators and Fourier integral operators in various situations, including operators on stratified manifolds and manifolds with singularities.

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Non-inertial frames in Minkowski space-time, accelerated either mathematical or dynamical observers and comments on non-inertial relativistic quantum mechanics

International Journal of Geometric Methods in Modern Physics ◽

10.1142/s0219887814500868 ◽

2014 ◽

Vol 11 (10) ◽

pp. 1450086 ◽

Cited By ~ 1

Author(s):

Horace W. Crater ◽

Luca Lusanna

Keyword(s):

Quantum Mechanics ◽

Minkowski Space ◽

Relativistic Quantum ◽

Classical Mechanics ◽

Space Time ◽

Relativistic Quantum Mechanics ◽

Minkowski Space Time ◽

Accelerated Observers ◽

Inertial Frames ◽

Locality Principle

After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and how to define Unruh–DeWitt detectors without using mathematical Rindler uniformly accelerated observers. Also some comments are done on the transition from relativistic classical mechanics to relativistic quantum mechanics in non-inertial frames.

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