# Linear response theory for symmetry improved two particle irreducible effective actions

Brown, Michael, Whittingham, Ian B., and Kosov, Daniel S.
(2016)
*Linear response theory for symmetry improved two particle irreducible effective actions.*
Physical Review D, 93 (10). 105018 . pp. 1-13.

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## Abstract

We investigate the linear response of an O(N) scalar quantum field theory subject to external perturbations using the symmetry-improved two-particle irreducible effective action (SI-2PIEA) formalism [A. Pilaftsis and D. Teresi, Nucl. Phys. B874, 594 (2013)]. Despite satisfactory equilibrium behavior, we find a number of unphysical effects at the linear response level. Goldstone boson field fluctuations are overdetermined, with the only consistent solution being to set the fluctuations and their driving sources to zero, except for momentum modes where the Higgs and Goldstone self-energies obey a particular relationship. Also Higgs field fluctuations propagate masslessly, despite the Higgs propagator having the correct mass. These pathologies are independent of any truncation of the effective action and still exist even if we relax the overdetermining Ward identities, so long as the constraint is formulated O(N) covariantly. We discuss possible reasons for the apparent incompatibility of the constraints and linear response approximation and possible ways forward.

Item ID: | 44119 |
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Item Type: | Article (Research - C1) |

ISSN: | 1089-4918 |

Keywords: | non-equilibrium quantum field theory, effective action, symmetry improvement, linear response theory |

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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: | 27 Jul 2016 04:16 |

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

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

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