The European Physical Journal C

, Volume 50, Issue 4, pp 999–1006 | Cite as

Non-perturbative calculations for the effective potential of the PT symmetric and non-Hermitian (-gφ4) field theoretical model

  • A.M. Shalaby
Regular Article - Theoretical Physics


We investigate the effective potential of the PT symmetric (-gφ4) field theory, perturbatively as well as non-perturbatively. For the perturbative calculations, we first use normal ordering to obtain the first order effective potential, from which the predicted vacuum condensate vanishes exponentially as G→0+, in agreement with previous calculations. For the higher orders, we employ the invariance of the bare parameters under the change of the mass scale t to fix the transformed form totally equivalent to the original theory. The form so obtained up to G3 is new and shows that all the 1PI amplitudes are perturbative for both the \(G\ll1\) and the \(G\gg1\) region. For the intermediate region, we modified the fractal self-similar resummation method to have a unique resummation formula for all G values. This unique formula is necessary, because the effective potential is the generating functional for all the one-particle irreducible (1PI) amplitudes that can be obtained via ∂nE/∂bn, and thus we can obtain an analytic calculation of the 1PI amplitudes. Again, the resummed form of the effective potential is new and interpolates the effective potential between the perturbative regions. Moreover, the resummed effective potential agrees in spirit to a previous calculation concerning bound states.


Effective Potential Vacuum Energy Perturbation Series Vacuum Condensate Lambert Function 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  1. 1.Centre for Theoretical PhysicsThe British University in EgyptEl Sherouk CityEgypt

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