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A new resummation scheme in scalar field theories

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Abstract

A new resummation scheme in scalar field theories is proposed by combining parquet resummation techniques and flow equations, which is characterized by a hierarchy structure of the Bethe–Salpeter (BS) equations. The new resummation scheme greatly improves on the approximations for the BS kernel. Resummation of the BS kernel in the t and u channels to infinite order is equivalent to truncate the effective action to infinite order. Our approximation approaches ensure that the theory can be renormalized, which is very important for numerical calculations. Two-point function can also be obtained from the four-point one through flow evolution equations resulting from the functional renormalization group. BS equations of different hierarchies and the flow evolution equation for the propagator constitute a closed self-consistent system, which can be solved completely.

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Acknowledgements

I am indebted to M.E. Carrington for useful discussions. This work was supported by the National Natural Science Foundation of China under Contracts No. 11005138.

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Authors and Affiliations

  1. Department of Physics, Brandon University, Brandon, Manitoba, R7A 6A9, Canada

    Wei-jie Fu

  2. Winnipeg Institute for Theoretical Physics, Winnipeg, Manitoba, Canada

    Wei-jie Fu

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  1. Wei-jie Fu
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Correspondence to Wei-jie Fu.

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Fu, Wj. A new resummation scheme in scalar field theories. Eur. Phys. J. C 73, 2411 (2013). https://doi.org/10.1140/epjc/s10052-013-2411-0

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