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The Rest-Frame Darwin Potential from the Lienard-Wiechert Solution in the Radiation Gauge | | Horace Crater
; Luca Lusanna
; | | Date: |
10 Dec 1999 | | Journal: | Annals Phys. 289 (2001) 87-177 | | Subject: | High Energy Physics - Theory; Mathematical Physics; Classical Physics | hep-th hep-ph math-ph math.MP nucl-th physics.class-ph | | Affiliation: | Univ. of Tennessee, Tullahoma) and Luca Lusanna (INFN, Firenze | | Abstract: | In the semiclassical approximation in which the electric charges of scalar particles are described by Grassmann variables ($Q_i^2=0, Q_iQ_j
e 0$), it is possible to re-express the Lienard-Wiechert potentials and electric fields in the radiation gauge as phase space functions, because the difference among retarded, advanced, and symmetric Green functions is of order Q_i^2. By working in the rest-frame instant form of dynamics, the elimination of the electromagnetic degrees of freedom by means of suitable second classs contraints leads to the identification of the Lienard-Wiechert reduced phase space containing only N charged particles with mutual action-at-a-distance vector and scalar potentials. A Darboux canonical basis of the reduced phase space is found. This allows one to re-express the potentials for arbitrary N as a unique effective scalar potential containing the Coulomb potential and the complete Darwin one, whose 1/c^2 component agrees for with the known expression. The effective potential gives the classical analogue of all static and non-static effects of the one-photon exchange Feynman diagram of scalar electrodynamics. | | Source: | arXiv, hep-th/0001046 | | Services: | Forum | Review | PDF | Favorites | |
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