# Soft symmetry improvement of two particle irreducible effective actions

Brown, Michael J., and Whittingham, Ian B.
(2017)
*Soft symmetry improvement of two particle irreducible effective actions.*
Physical Review D, 95 (2). 025018. pp. 1-18.

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## Abstract

Two particle irreducible effective actions (2PIEAs) are valuable nonperturbative techniques in quantum field theory; however, finite truncations of them violate the Ward identities (WIs) of theories with spontaneously broken symmetries. The symmetry improvement (SI) method of Pilaftsis and Teresi attempts to overcome this by imposing the WIs as constraints on the solution; however, the method suffers from the nonexistence of solutions in linear response theory and in certain truncations in equilibrium. Motivated by this, we introduce a new method called soft-symmetry improvement (SSI) which relaxes the constraint. Violations of WIs are allowed but punished in a least-squares implementation of the symmetry improvement idea. A new parameter ξ controls the strength of the constraint. The method interpolates between the unimproved (ξ→∞) and SI (ξ→0) cases, and the hope is that practically useful solutions can be found for finite ξ. We study the SSI 2PIEA for a scalar O(N) model in the Hartree-Fock approximation. We find that the method is IR sensitive; the system must be formulated in finite volume V and temperature T=β^{−1}, and the Vβ→∞ limit must be taken carefully. Three distinct limits exist. Two are equivalent to the unimproved 2PIEA and SI 2PIEA respectively, and the third is a new limit where the WI is satisfied but the phase transition is strongly first order and solutions can fail to exist depending on ξ. Further, these limits are disconnected from each other; there is no smooth way to interpolate from one to another. These results suggest that any potential advantages of SSI methods, and indeed any application of (S)SI methods out of equilibrium, must occur in finite volume.

Item ID: | 46944 |
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Item Type: | Article (Research - C1) |

ISSN: | 2470-0029 |

Keywords: | quantum field theory, effective action, symmetry improvement, soft symmetry improvement |

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Additional Information: | Unrestricted preprint available on the arxiv. Please see Related URLs for access. 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: | 27 Jan 2017 00:40 |

FoR Codes: | 51 PHYSICAL SCIENCES > 5107 Particle and high energy physics > 510702 Field theory and string theory @ 50% 49 MATHEMATICAL SCIENCES > 4902 Mathematical physics > 490205 Mathematical aspects of quantum and conformal field theory, quantum gravity and string theory @ 50% |

SEO Codes: | 97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 100% |

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