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Award ID contains: 1707489

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  1. ; ; ; (, Physical Review A)
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  2. ; ; ; ; (, International Conference on Precision Physics and Fundamental Physical Constants - FFK2019)
    We report on progress in the calculation of corrections to positronium energy levels of order $$m \alpha^7$$. Corrections at this level will be needed for the interpretation of the results of upcoming measurements. A procedure for the calculation of high order corrections has been developed based on the Bethe-Salpeter equation of dimensionally regularized NRQED and the method of regions. We demonstrate the effectiveness of this approach by using it to obtain all pure recoil corrections to positronium energies at $$O(m \alpha^6)$$ in a unified manner. 
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  3. (, Journal of Physics: Conference Series)
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  4. (, Physics Letters A)
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  5. (, Indian Journal of Mathematics)
    The tensor product of $$L$$ copies of a single vector, such as $$p_{i_1} \cdots p_{i_L}$$, can be analyzed in terms of angular momentum. When $$p_{i_1} \cdots p_{i_L}$$ is decomposed into a sum of components $$\left ( p_{i_1} \cdots p_{i_L} \right )^L_\ell$$, each characterized by angular momentum $$\ell$$, the components are in general complicated functions of the $$p_i$$ vectors, especially so for large $$\ell$$. We obtain a compact expression for $$\left ( p_{i_1} \cdots p_{i_L} \right )^L_\ell$$ explicitly in terms of the $$p_i$$ valid for all $$L$$ and $$\ell$$. We use this decomposition to perform three-dimensional Fourier transforms of functions like $$p^n \hat p_{i_1} \cdots \hat p_{i_L}$$ that are useful in describing particle interactions. 
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