Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics PDF
Preview Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics
Springer Theses Recognizing Outstanding Ph.D. Research Peter Millington Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics Springer Theses Recognizing Outstanding Ph.D. Research For furthervolumes: http://www.springer.com/series/8790 Aims and Scope The series ‘‘Springer Theses’’ brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent fieldofresearch.Forgreateraccessibilitytonon-specialists,thepublishedversions includeanextendedintroduction,aswellasaforewordbythestudent’ssupervisor explaining the special relevance of the work for the field. 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Theses are accepted into the series by invited nomination only and must fulfill all of the following criteria • They must be written in good English. • ThetopicshouldfallwithintheconfinesofChemistry,Physics,EarthSciences, Engineering andrelatedinterdisciplinaryfieldssuchasMaterials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • Ifthethesisincludespreviouslypublishedmaterial,permissiontoreproducethis must be gained from the respective copyright holder. • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the signifi- cance of its content. • The theses should have a clearly defined structure including an introduction accessible to scientists not expert in that particular field. Peter Millington Thermal Quantum Field Theory and Perturbative Non-Equilibrium Dynamics Doctoral Thesis accepted by the University of Manchester, UK 123 Author Supervisor Dr. PeterMillington Prof.ApostolosPilaftsis School ofPhysicsand Astronomy School ofPhysicsand Astronomy Universityof Manchester Universityof Manchester Manchester Manchester UK UK ISSN 2190-5053 ISSN 2190-5061 (electronic) ISBN 978-3-319-01185-1 ISBN 978-3-319-01186-8 (eBook) DOI 10.1007/978-3-319-01186-8 SpringerChamHeidelbergNewYorkDordrechtLondon LibraryofCongressControlNumber:2013943465 (cid:2)SpringerInternationalPublishingSwitzerland2014 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpartof the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation,broadcasting,reproductiononmicrofilmsorinanyotherphysicalway,andtransmissionor informationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purposeofbeingenteredandexecutedonacomputersystem,forexclusiveusebythepurchaserofthe work. Duplication of this publication or parts thereof is permitted only under the provisions of theCopyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the CopyrightClearanceCenter.ViolationsareliabletoprosecutionundertherespectiveCopyrightLaw. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexempt fromtherelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. While the advice and information in this book are believed to be true and accurate at the date of publication,neithertheauthorsnortheeditorsnorthepublishercanacceptanylegalresponsibilityfor anyerrorsoromissionsthatmaybemade.Thepublishermakesnowarranty,expressorimplied,with respecttothematerialcontainedherein. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Parts of this thesis have been published in the following journal articles: 1. P. Millington and A. Pilaftsis, ‘‘Perturbative Non-Equilibrium Thermal Field Theory to all Orders inGradient Expansion’’,Phys. Lett. B724, 56–62 (2013); arXiv:1304.7249 2. P. Millington and A. Pilaftsis, ‘‘Thermal field theory to all orders in gradient expansion’’, J. Phys.: Conf. Ser. 447, 012071 (2013); arXiv:1302.6361 3. P. Millington and A. Pilaftsis, ‘‘Perturbative Non-Equilibrium Thermal Field Theory’’, arXiv:1211.3152 (2012) (to appear in Phys. Rev. D) Two roads diverged in a wood, and I— I took the one less travelled by, And that has made all the difference The Road Not Taken Robert Frost (1874–1963) To Alison, Jennifer, Haydn, John, Margo and Ralphie Supervisor’s Foreword Thetheoreticaldescriptionofmacroscopicsystemsofultra-relativisticparticlesat finite temperature and density has applications that span the disciplines of high- energy particle physics, astro-particle physics, cosmology, gravitation, plasma physics, and condensed matter physics. In addition, an understanding of these systems requires us to bring together ideas from across quantum mechanics, rel- ativity, statistical mechanics and thermodynamics. In recent years, there has been increasing interest in the evolution of systems that are out of thermodynamic equilibrium. However, in contrast to the well- established and well-accepted descriptions of equilibrium quantum field theory, it issafetosaythatthereiscurrentlynoconsensusastothe‘correct’formulationof non-equilibrium quantumfield theory. This isnotleastbecauseprevious attempts to describe these phenomena within the usual perturbative paradigm of quantum field theory have run into severe problems. Specifically, these perturbative descriptions are normally found to be plagued by mathematical pathologies, so- called pinch singularities, arising from mathematically ill-defined products of Dirac delta functions. In order to avoid this problem, existing approaches are forced to resort to ad hoc regularizations or effective resummation offinite-width effects.Theresultisaplethoraofcompetingformulations.Furthermore,withouta well-defined canonical framework, the extraction of physically meaningful observables is open to a greater degree of interpretation. Thisthesisdescribesanewperturbativeformulationofnon-equilibriumthermal quantum field theory, which is successfully derived within the perturbative and canonical paradigm of quantum field theory. The resulting framework is able to describetheinteractionoffundamentalparticlesinamacroscopicbackgroundthat isbothout-of-equilibriumandspatiallyinhomogeneous,varyinginbothspaceand time. This newapproach isfreeofthe aforementionedpinch singularities without needing to resort to the ad hoc regularizations or effective resummations men- tioned above. It therefore presents the first viable perturbative formulation of non-equilibrium thermal quantum field theory. This work provides an alternative framework in which to derive master time evolution equations for statistical distribution functions, akin to a quantum-field- theoretic analogue of the Boltzmann equation. In contrast to existing approaches, these evolution equations may be truncated in a perturbative loopwise sense, xi xii Supervisor’sForeword whilst retaining all orders in the time behavior. As a result, its consistent dia- grammatic approach, which is based upon non-homogeneous propagators and manifestly time-dependent Feynman rules, allows the quantitative and analytic study of the transient early-time dynamics of systems out of equilibrium. This promptevolutionisshowntobedominatedbyenergy-violatingeffects,leadingto the non-Markovian evolution of so-called memory effects. Dr.PeterMillingtoncompletedhisPh.D.attheSchoolofPhysicsandAstronomy of University of Manchester in November 2012, under my supervision. The main results of his Ph.D. thesis were communicated in two common scientific articles: (i) ‘‘Perturbative Non-Equilibrium Thermal Field Theory,’’ arXiv:1211.3152 (to appear in Phys. Rev. D); (ii) ‘‘Perturbative Non-Equilibrium Thermal Field Theory to all Orders in Gradient Expansion,’’ Phys. Lett. B724: 56–62, 2013; arXiv:1304.7249. These articles on non-equilibrium thermal field theory are anticipated to become classic references on the subject. The following thesis pro- videsapedagogicalintroductiontothecontentofthesearticles,buildingfromthe basic ideas of classical statistical mechanics and thermodynamics through to an explanationofouroriginalcontributionsandadvancementofthisfield. Manchester, May 2013 Prof. Apostolos Pilaftsis
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