Relativistic invariance, gauge invariance and Green's function for a dirac particle interacting with a classical plane wave field

2020 ◽  
Vol 95 (8) ◽  
pp. 085217
Author(s):  
H K Ould-Lahoucine
2001 ◽  
Vol 64 (4) ◽  
pp. 285-291 ◽  
Author(s):  
S Zeggari ◽  
T Boudjedaa ◽  
L Chetouani

Author(s):  
A.T Walden ◽  
T Medkour

An ellipse describes the polarized part of a partially polarized quasi-monochromatic plane wave field. Its azimuth angle and aspect ratio are functions of the elements of the covariance matrix associated with the polarized part at a particular time instant. Given an ensemble of K independent samples at that time, the distributions of the estimators of these parameters are derived. The estimation is thus based on a sample ensemble at any time, and does not assume temporal stationarity. Additionally, the azimuth angle estimator has an angular distribution so that non-standard statistical methods are needed when deriving its mean and standard deviation.


Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. S549-S556 ◽  
Author(s):  
Xiongwen Wang ◽  
Xu Ji ◽  
Hongwei Liu ◽  
Yi Luo

Plane-wave reverse time migration (RTM) could potentially provide quick subsurface images by migrating fewer plane-wave gathers than shot gathers. However, the time delay between the first and the last excitation sources in the plane-wave source largely increases the computation cost and decreases the practical value of this method. Although the time delay problem is easily overcome by periodical phase shifting in the frequency domain for one-way wave-equation migration, it remains a challenge for time-domain RTM. We have developed a novel method, referred as to fast plane-wave RTM (FP-RTM), to eliminate unnecessary computation burden and significantly reduce the computational cost. In the proposed FP-RTM, we assume that the Green’s function has finite-length support; thus, the plane-wave source function and its responding data can be wrapped periodically in the time domain. The wrapping length is the assumed total duration length of Green’s function. We also determine that only two period plane-wave source and data after the wrapping process are required for generating the outcome with adequate accuracy. Although the computation time for one plane-wave gather is twice as long as a normal shot gather migration, a large amount of computation cost is saved because the total number of plane-wave gathers to be migrated is usually much less than the total number of shot gathers. Our FP-RTM can be used to rapidly generate RTM images and plane-wave domain common-image gathers for velocity model building. The synthetic and field data examples are evaluated to validate the efficiency and accuracy of our method.


2016 ◽  
Vol 64 (7) ◽  
pp. 3141-3150 ◽  
Author(s):  
Afroza Khatun ◽  
Veli-Matti Kolmonen ◽  
Veikko Hovinen ◽  
Dristy Parveg ◽  
Markus Berg ◽  
...  

1966 ◽  
Vol 145 (4) ◽  
pp. 1035-1040 ◽  
Author(s):  
Joseph H. Eberly ◽  
Howard R. Reiss

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