# Symmetry improvement of 3PI effective actions for O(N) scalar field theory

Brown, Michael J., and Whittingham, Ian B.
(2015)
*Symmetry improvement of 3PI effective actions for O(N) scalar field theory.*
Physical Review D (Particles, Fields, Gravitation and Cosmology), 91 (8).
pp. 1-27.

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## Abstract

N-particle irreducible effective actions (nPIEA) are a powerful tool for extracting nonperturbative and nonequilibrium physics from quantum field theories. Unfortunately, practical truncations of nPIEA can unphysically violate symmetries. Pilaftsis and Teresi (PT) addressed this by introducing a "symmetry improvement" scheme in the context of the 2PIEA for an O (2) scalar theory, ensuring that the Goldstone boson is massless in the broken symmetry phase [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)]. We extend this idea by introducing a symmetry improved 3PIEA for O(N) theories, for which the basic variables are the one-, two- and three-point correlation functions. This requires the imposition of a Ward identity involving the three-point function. We find that the method leads to an infinity of physically distinct schemes, though a field theoretic analogue of d'Alembert's principle is used to single out a unique scheme. The standard equivalence hierarchy of nPIEA no longer holds with symmetry improvement, and we investigate the difference between the symmetry improved 3PIEA and 2PIEA. We present renormalized equations of motion and counterterms for two- and three-loop truncations of the effective action, though we leave their numerical solution to future work. We solve the Hartree-Fock approximation and find that our method achieves a middle ground between the unimproved 2PIEA and PT methods. The phase transition predicted by our method is weakly first order and the Goldstone theorem is satisfied, while the PT method correctly predicts a second-order phase transition. In contrast, the unimproved 2PIEA predicts a strong first-order transition with large violations of the Goldstone theorem. We also show that, in contrast to PT, the two-loop truncation of the symmetry improved 3PIEA does not predict the correct Higgs decay rate, although the three-loop truncation does, at least to leading order. These results suggest that symmetry improvement should not be applied to nPIEA truncated to <n loops. We also show that symmetry improvement schemes are compatible with the Coleman-Mermin-Wagner theorem, giving a check on the consistency of the formalism.

Item ID: | 38293 |
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Item Type: | Article (Research - C1) |

ISSN: | 1551-2368 |

Keywords: | quantum field theory; statistical field theory; effective action; symmetry improvement; nonperturbative methods |

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Additional Information: | A version of this publication was included in the following PhD thesis: Brown, Michael Jonathan (2017) Symmetry improvement techniques for non-perturbative quantum field theory. PhD thesis, James Cook University, which is available Open Access in ResearchOnline@JCU. Please see the Related URLs for access. |

Date Deposited: | 08 Jul 2015 02:10 |

FoR Codes: | 02 PHYSICAL SCIENCES > 0206 Quantum Physics > 020602 Field Theory and String Theory @ 45% 02 PHYSICAL SCIENCES > 0202 Atomic, Molecular, Nuclear, Particle and Plasma Physics > 020203 Particle Physics @ 10% 01 MATHEMATICAL SCIENCES > 0105 Mathematical Physics > 010505 Mathematical Aspects of Quantum and Conformal Field Theory, Quantum Gravity and String Theory @ 45% |

SEO Codes: | 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 50% 97 EXPANDING KNOWLEDGE > 970101 Expanding Knowledge in the Mathematical Sciences @ 50% |

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