Covariant amplitude decomposition in relativistic fermion scattering problems
A parameterization of on-mass-shell relativistic fermion scattering amplitudes by a set of 4 covariant amplitudes is proposed, which in the non-relativistic limit turn to coefficients of the matrix amplitude decomposition over the unity and Pauli matrices, and in the ultra-relativistic limit – to sy...
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| Date: | 2007 |
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| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2007
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| Series: | Вопросы атомной науки и техники |
| Subjects: | |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/110941 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Covariant amplitude decomposition in relativistic fermion scattering problems / M.V. Bondarenko // Вопросы атомной науки и техники. — 2007. — № 3. — С. 104-110. — Бібліогр.: 11 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | A parameterization of on-mass-shell relativistic fermion scattering amplitudes by a set of 4 covariant amplitudes is proposed, which in the non-relativistic limit turn to coefficients of the matrix amplitude decomposition over the unity and Pauli matrices, and in the ultra-relativistic limit – to symmetrized helicity amplitudes. In the general rela-tivistic case, the covariant amplitudes express as spurs of the matrix amplitude supplemented by γ-matrix factors not exceeding 3-rd degree. Algebraic computation of such spurs provides a comparatively short and fully covariant approach for calculation of fermion scattering processes, allowing account for all polarization observables. For extension of the method to problems of two-fermion scattering, when permitted are both ways of transition 1→3, 2→4 and 1→4, 2→3, relativistic on-mass-shell Fierz relations interconnecting the two possible definitions of transition amplitudes are derived, under simplifying assumptions of equal fermion masses and scattering elasticity. Eigenfunctions of the on-shell Fierz relations are constructed, and advantages of their use for automatic account for contributions from cross-diagrams are demonstrated with the example of Møller scattering. |
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