Green function formulation of the Dirac field in curved space

1966 ◽  
Vol 294 (1439) ◽  
pp. 437-448 ◽  
Keyword(s):  
Green Function ◽  
Dirac Field ◽  
Green Functions ◽  
Field Equations ◽  
Curved Space ◽  
Particle Field ◽  
Function Formulation ◽  
Essential Idea ◽  
Mass Field

A Green function formulation of the Dirac field in curved space is considered in the cases where the mass is constant and where it is regarded as a direct particle field in the manner of Hoyle & Narlikar (1964 c ). This description is equivalent to, and in some ways more satisfactory than, that given in terms of a suitable Lagrangian, in which the Dirac or the mass field is regarded as independent of the geometry. The essential idea is to define the Dirac or the mass field in terms of certain Green functions and sources so that the field equations are satisfied identically, and then to obtain the contribution of these fields to the metric field equations from the variation of a suitable action that is defined in terms of the Green functions and sources.

Green function formulation of interactions of arbitrary fields

1969 ◽  
Vol 65 (3) ◽  
pp. 759-771
Author(s):  
Jamal N. Islam
Keyword(s):  
Gravitational Field ◽  
Green Function ◽  
Arbitrary Spin ◽  
Green Functions ◽  
Function Formulation

AbstractA Green function formulation of a system that describes the interaction of fields of arbitrary spin with the gravitational field andparticles is given. The Lagrangian considered is essentially the most general that admits of a description through Green functions.

Population Field Theory with Applications to Tag Analysis and Fishery Modeling: the Empirical Green Function

1993 ◽  
Vol 50 (11) ◽  
pp. 2491-2512 ◽  
Author(s):  
Carlos A. M. Salvadó
Keyword(s):  
Green Function ◽  
Transition Probability ◽  
Space Time ◽  
Point Sources ◽  
Closed Form Expression ◽  
Model Parameters ◽  
Green Functions ◽  
Field Equations ◽  
Empirical Green Function ◽  
The Green Function

A theoretical framework is proposed for analyzing fish movement and modeling the associated dynamics using tagging data. When tagged fish are released in an area small compared with the domain of the fish population and over a period short compared with the time they take to disperse throughout their domain, the pattern of movement approximates a point-source solution of the underlying population dynamics. A method of point sources (Green functions) is invoked for representing the solution of the tagged and untagged fish field equations (partial differential equations) in terms of integral equations. As an approximate representation of a tagging experiment, the Green function is interpreted as the probability density of survival and movement from point to point in space–time. The Green functions are constructed empirically using one parameter, catchability, as the ratio of population density of tagged fish divided by the number of tagged fish released. The number of tagging experiments necessary to characterize the population is dictated by the dependence of catchability on space–time. The moments of the Green function are used to calculate model parameters and lead to the identification of a closed form expression for the transition probability densities of the model assumed.

On modified Green functions in exterior problems for the Helmholtz equation

1982 ◽  
Vol 383 (1785) ◽  
pp. 313-332 ◽  
Keyword(s):  
Integral Equation ◽  
Green Function ◽  
Helmholtz Equation ◽  
Least Squares ◽  
Present Note ◽  
Boundary Integral ◽  
Green Functions ◽  
Exterior Problems ◽  
The Green Function ◽  
Definition Of

The question of non-uniqueness in boundary integral equation formu­lations of exterior problems for the Helmholtz equation has recently been resolved with the use of additional radiating multipoles in the definition of the Green function. The present note shows how this modification may be included in a rigorous formalism and presents an explicit choice of co­efficients of the added terms that is optimal in the sense of minimizing the least-squares difference between the modified and exact Green functions.

The g factor of an electron in hydrogenlike carbon and the precision determination of the electron mass

2019 ◽  
Vol 34 (28) ◽  
pp. 1941001
Author(s):  
Jonathan Sapirstein
Keyword(s):  
Synchrotron Radiation ◽  
Green Function ◽  
Green Functions ◽  
Electron Mass ◽  
Precision Determination ◽  
High Precision Determination ◽  
Bound Electron ◽  
Modern Form

The role of the bound electron Green function in the recent high precision determination of the electron mass is discussed. Emphasis is placed on the connection to Schwinger’s use of such Green functions in his early work establishing the modern form of QED, his calculation of leading binding corrections, and his work on synchrotron radiation.

Free Surface Green Function Research Based on Cloud Computing for Ship Movement on the Water

2013 ◽  
Vol 344 ◽  
pp. 27-30
Author(s):  
Cong Zhang ◽  
Xin Wang ◽  
Jie Zhao ◽  
She Sheng Zhang
Keyword(s):  
Cloud Computing ◽  
Free Surface ◽  
Green Function ◽  
Point Source ◽  
Calculation Procedure ◽  
Green Functions ◽  
Two Dimensional ◽  
Surface Green Function ◽  
Cloud Computation ◽  
Control Equation

In order to easy use Green function on cloud computation, the author consider control equation of point source with free surface, and discuss the representation of Green function on cloud computation, and then propose the discrete calculation expression as well as the calculation procedure. Finally, the two-dimensional graphics of the Green functions real and imaginary parts are plotted.

scholarly journals Theory of Nonlocal Point Transformations in General Relativity

2016 ◽  
Vol 2016 ◽  
pp. 1-32 ◽  
Author(s):  
Massimo Tessarotto ◽  
Claudio Cremaschini
Keyword(s):  
General Relativity ◽  
Field Equations ◽  
Traditional Concept ◽  
Curved Space ◽  
Point Transformations ◽  
Functional Setting ◽  
Mathematical Foundations ◽  
The Relationship ◽  
Metric Tensors

A discussion of the functional setting customarily adopted in General Relativity (GR) is proposed. This is based on the introduction of the notion of nonlocal point transformations (NLPTs). While allowing the extension of the traditional concept of GR-reference frame, NLPTs are important because they permit the explicit determination of the map between intrinsically different and generally curved space-times expressed in arbitrary coordinate systems. For this purpose in the paper the mathematical foundations of NLPT-theory are laid down and basic physical implications are considered. In particular, explicit applications of the theory are proposed, which concern(1)a solution to the so-called Einstein teleparallel problem in the framework of NLPT-theory;(2)the determination of the tensor transformation laws holding for the acceleration 4-tensor with respect to the group of NLPTs and the identification of NLPT-acceleration effects, namely, the relationship established via general NLPT between particle 4-acceleration tensors existing in different curved space-times;(3)the construction of the nonlocal transformation law connecting different diagonal metric tensors solution to the Einstein field equations; and(4)the diagonalization of nondiagonal metric tensors.

scholarly journals A generally relativistic gauge classification of the Dirac fields

2016 ◽  
Vol 13 (06) ◽  
pp. 1650078 ◽  
Author(s):  
Luca Fabbri
Keyword(s):  
Axial Vector ◽  
Supplementary Information ◽  
Dirac Field ◽  
Field Equations ◽  
Momentum Vector ◽  
Nonrelativistic Approximation ◽  
Gauge Transformations ◽  
Dirac Fields

We consider generally relativistic gauge transformations for the spinorial fields finding two mutually exclusive but together exhaustive classes in which fermions are placed adding supplementary information to the results obtained by Lounesto, and identifying quantities analogous to the momentum vector and the Pauli–Lubanski axial vector. We discuss how our results are similar to those obtained by Wigner by taking into account the system of Dirac field equations. We will investigate the consequences for the dynamics and in particular we shall address the problem of getting the nonrelativistic approximation in a consistent way. We are going to comment on extensions.

scholarly journals LIMITS OF MULTIPOLE PLURICOMPLEX GREEN FUNCTIONS

2012 ◽  
Vol 23 (06) ◽  
pp. 1250065 ◽  
Author(s):  
JÓN I. MAGNÚSSON ◽  
ALEXANDER RASHKOVSKII ◽  
RAGNAR SIGURDSSON ◽  
PASCAL J. THOMAS
Keyword(s):  
Green Function ◽  
Uniform Convergence ◽  
Complete Intersection ◽  
Green Functions ◽  
Ideal Formula ◽  
Vanishing Ideal ◽  
Pluricomplex Green Function ◽  
Samuel Multiplicity ◽  
Hyperconvex Domain ◽  
Local Uniform Convergence

Let Ω be a bounded hyperconvex domain in ℂn, 0 ∈ Ω, and Sε a family of N poles in Ω, all tending to 0 as ε tends to 0. To each Sε we associate its vanishing ideal [Formula: see text] and pluricomplex Green function [Formula: see text]. Suppose that, as ε tends to 0, [Formula: see text] converges to [Formula: see text] (local uniform convergence), and that (Gε)ε converges to G, locally uniformly away from 0; then [Formula: see text]. If the Hilbert–Samuel multiplicity of [Formula: see text] is strictly larger than its length (codimension, equal to N here), then (Gε)ε cannot converge to [Formula: see text]. Conversely, if [Formula: see text] is a complete intersection ideal, then (Gε)ε converges to [Formula: see text]. We work out the case of three poles.

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