scholarly journals Momentum-space representation of Green’s functions with modified dispersion relations on general backgrounds

2008 ◽  
Vol 78 (2) ◽  
Author(s):  
Massimiliano Rinaldi
Keyword(s):  
Momentum Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Space Representation ◽  
Modified Dispersion Relations

scholarly journals Asymptotic analysis for dispersion relations and travel times in noise cross-correlations: spherically symmetric case

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180382
Author(s):  
Tianshi Liu ◽  
Haiming Zhang
Keyword(s):  
Asymptotic Analysis ◽  
Surface Waves ◽  
Green's Functions ◽  
Green’S Functions ◽  
Dispersion Relations ◽  
Body Waves ◽  
Spherically Symmetric ◽  
Travel Times ◽  
Cross Correlations ◽  
The Cross

The cross-correlations of ambient noise or earthquake codas are massively used in seismic tomography to measure the dispersion curves of surface waves and the travel times of body waves. Such measurements are based on the assumption that these kinematic parameters in the cross-correlations of noise coincide with those in Green's functions. However, the relation between the cross-correlations of noise and Green's functions deserves to be studied more precisely. In this paper, we use the asymptotic analysis to study the dispersion relations of surface waves and the travel times of body waves, and come to the conclusion that for the spherically symmetric Earth model, when the distribution of noise sources is laterally uniform, the dispersion relations of surface waves and the travel times of SH body-wave phases in noise correlations should be exactly the same as those in Green's functions.

scholarly journals Analyticity of off-shell Green’s functions in superstring field theory

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ritabrata Bhattacharya ◽  
Ratul Mahanta
Keyword(s):  
Field Theory ◽  
Momentum Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Lorentz Transformations ◽  
Point Function ◽  
Technical Issue ◽  
Bochner’S Theorem ◽  
Bochner's Theorem

Abstract We consider the off-shell momentum space Green’s functions in closed superstring field theory. Recently in [1], the off-shell Green’s functions — after explicitly removing contributions of massless states — have been shown to be analytic on a domain (to be called the LES domain) in complex external momenta variables. Analyticity of off-shell Green’s functions in local QFTs without massless states in the primitive domain is a well-known result. Using complex Lorentz transformations and Bochner’s theorem allow to extend the LES domain to a larger subset of the primitive domain. For the 2-, 3- and 4-point functions, the full primitive domain is recovered. For the 5-point function, we are not able to obtain the full primitive domain analytically, only a large part of it is recovered. While this problem arises also for higher-point functions, it is expected to be only a technical issue.

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