Quantum Field Theory  

In General > s.a. Second Quantization.
* Idea: A physical theory of particles and their interactions, based on the connection between properties of quantum fields and particles, incorporating special relativity and quantum mechanics; 0+1-dimensional quantum field theory is equivalent to quantum mechanics.
* Motivation: Believed to be the correct fundamental description of all interactions, since there are "adequate" (renormalizable, phenomenologically reasonable) quantum field theories for all of them but gravity; No evidence against it yet; Also, relativistic effects imply that 1-particle wave functions don't have consistent probabilistic interpretations.
* Allowed fields: Given by linear representations of the Lorentz group, labelled by m and s.
* Classical picture: Interactions in terms of forces and potentials are recovered in the static limit; > s.a. interaction.
* Issues: The no-interaction result proved in Haag's theorem; The need for renormalization.
blue bullet Specific aspects: see approaches; formalism and techniques; phenomenology and effects; types of quantum field theories.

References > s.a. astrophysics [applications]; quantum gauge theories; relativistic quantum mechanics; teaching.
@ General: Schwinger PR(51); Heisenberg RMP(57); Schroer ht/06 [existence of interacting quantum field theory].
@ Intros, reviews: Crewther ht/95; Buchholz & Haag JMP(00)ht/99; Dine hp/00-conf [applications]; Fredenhagen et al LNP(07)ht/06 [status].
@ Mathematical: Edwards IJTP(81); Federbush BAMS(87)mar [survey]; Araki 99; Ticciati 99; Borcherds & Barnard mp/02-ln; Abdesselam m.CO/02; Zeidler 06; Chen a0803 [and differential geometry]; Dimock 11; Dereziński & Gérard 13 [r CP(14)#2]; Rinehart a1505 [foundations, Hamiltonian formulation].
@ II: Mandl 59; Mandl & Shaw 93; Han 04 [esp quarks and leptons]; Walecka 10; Ohlsson 11; Klauber 13 [student-friendly]; Setlur 13 [and classical fields]; Lancaster & Blundell 14 [for the gifted amateur]; Becchi & Ridolfi 14 [and the standard model]; Ilisie 16; Redmount a1908 [at the introductory level].
@ III: Wentzel 49; Schweber 61; Bjorken & Drell 64, 65; Jost 65; Dirac 66; Berezin 66; Sakurai 67; Ziman 69; Beresteski et al 71; Lifshitz & Pitaevskii 71; Coleman ln(76)-a1110 [Physics 253a lecture notes]; Nash 78; Bogoliubov & Shirkov 80; Itzykson & Zuber 80; Lee 81; Bogoliubov & Shirkov 83; DeWit & Smith 86; Chang 90; Greiner 90; Brown 92; Gross 93; Kaku 93; Sterman 93; Peskin & Schroeder 95; Weinberg 95-96; Greiner & Reinhardt 96; Elbaz 98; Huang 98; Siegel ht/99-text; Stone 00; Capri 02; Bytsenko et al 03 [techniques]; DeWitt 03; Zee 03; Srednicki ht/04, ht/04 [textbook, parts 1+2]; Lahiri & Pal 05; Maggiore 05; Nair 05; Álvarez-Gaumé & Vázquez-Mozo ht/05-ln, 12; Srednicki 07; Das 08; Banks 08; Flory et al a1201-ln [stop worrying about the mathematical shape of the theory]; in Scheck 13; van Baal 13; Shchesnovich a1308-ln [second-quantization method]; Coleman 16 [lectures]; D'Auria & Trigiante 16; Manoukian 16; Padmanabhan 16; Baulieu et al 17; Casalbuoni 17; Pauchy Hwang & Wu 18; Gelis 19; Năstase 19; Cline a2005-ln [with problems].
@ Texts, axiomatic: Bogoliubov, Logunov & Todorov 75; Strocchi 93.
@ Texts, topological methods: Ryder 85; Nash 91; Huang 92; Schwartz 93; Bandyopadhyay 03; > s.a. topology in physics.
@ Texts, condensed matter: Abrikosov et al 75; Wen 04 [and many-body]; Schakel 08 [effective theories]; Altland & Simons 10; Mudry 14; Shankar 17; > s.a. condensed matter.
@ Texts, particle physics: Hatfield 92 [including strings]; Shifman 12 [monopoles, instantons, supersymmetry, etc, r CP(12)#5]; Kleinert 16; Schwartz 13, Han 14 [and the standard model].
@ Texts, other emphasis: Prykarpatsky et al 02 [and non-linear optics]; Grensing 13 [and non-commutative geometry]; Lam 15 [techniques].
@ Problems: Atkinson & Johnson 04; Radovanović 06.
@ Collections: Batalin et al ed-87.
> Online resources: see Sidney Coleman lectures.

Interpretations and Other Conceptual Aspects > s.a. cellular automata; formalism and techniques; klein-gordon fields; particle models.
@ Conceptual: Dirac PRS(42); Auyang 95; de Souza ht/96 [and classical field theory]; Jackiw ht/96 [effectiveness and reservations]; Tian 96; news PT(96)jun [evidence]; Cao 99; Jackiw ht/97; Schnitzer phy/97; Wilczek RMP(99)ht/98; Huggett BJPS(00); Haag ht/00; Ruetsche PhSc(02)jun [Hilbert space and algebraic]; Zeh PLA(03)qp/02 [fields and particles]; Strocchi FP(04)ht-in [issues]; Hollands & Wald GRG(04)gq-GRF [not just quantum mechanics of low-energy degrees of freedom]; Hättich 04 [Whiteheadian interpretation]; Krekora et al PRA(06) [difficulties]; Baker BJPS(09) [against field interpretations]; Fraser PhSc(09)oct; D'Ariano AIP-a1001 [and quantum computation]; Schroer EPJH(13)-a1101 [fluctuations and the Einstein-Jordan conundrum], SHPMP-a1107 [localization]; Sassoli de Bianchi AJP(13)-a1202 [quantum "fields" are not fields]; Zeh ZfN-a1304; Egg et al a1701 [on the Fraser-Wallace debate]; Cao 19; Pavšič 20 [misconceptions]; Skullerud a2011-MS.
@ Ontology: Kuhlmann et al ed-02; Deckert et al a1608 [based on the Dirac sea]; Durham a1807; Lazarovici EJPS(18)-a1809 [against fields, superiority of a pure particle ontology].
@ Historical: Schroer FP(10)-a0905 [importance of crossing property]; Close 11; > s.a. history of quantum theory.
@ Philosophical: Brown & Harré ed-88; Teller PhSc(90)dec, p95; Huggett & Weingard PhSc(94)sep; Weinberg ht/97; Smeenk & Myrvold SHPMP(11); Öttinger a1509-book, 18.
@ Pilot-wave interpretation: Bell PRP(86); Vigier FP(91) [non-linear solitons piloted by solutions of linear equations]; in Bohm & Hiley 93; Holland PRP(93); Pinto-Neto & Santini GRG(02)gq/00; Horton et al FP(02) [Klein-Gordon theory]; Potel et al PLA(02)qp [random noise]; Nikolić FPL(04)qp/02 [bosonic quantum field theory]; Nikolić FPL(05)qp/03 [fermions], PLA(06)ht/05 [and multi-fingered time], EPJC(05)ht/04, IJMPD(06)ht [and covariance]; Dürr et al JPA(03) [trajectories, creation/annihilation], PRL(04)qp/03; Horton & Dewdney JPA(04) [Klein-Gordon, covariant]; Struyve & Westman in(06)qp, PRS(07)-a0707 [beables for bosonic degrees of freedom, QED]; Tumulka JPA(07)qp/06; Colin & Struyve JPA(07)qp [using Dirac sea]; Struyve RPP(10)-a0707 [beables]; Schmelzer FP(10)-a0904 [difficulty from non-significant overlaps]; Nikolić IJMPA(10)-a0904; Struyve JPCS(11)-a1101 [overview]; > s.a. dirac fields.
@ Hidden variables, other: Khrennikov NCB(06)ht-in.
@ Classical statistical models: Wetterich a1111 [for fermions]; Khrennikov JRLR-a1412 [probabilities of photon detection from classical Brownian motion].
@ Interpretations, other: Huggett & Weingard PhSc(96)jun [re Teller 95]; Tommasini JHEP(02)ht [local, causal, statistical]; Colin PLA(03)qp [realistic, deterministic, fermions]; Larsson ht/07 [alternative, quantum jet theory]; Ruetsche 11; Oldofredi & Öttinger a2011 [dissipative approach]; > s.a. approaches; interpretations of quantum mechanics [modal]; quantum gravity; Relational Blockworld; wave-function collapse.
@ Related topics: Todorov BulgJP-a1311 [remarks]; Linde EJP(17)-a1907 [visualizing quantum fields].

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