QFT in Nontrivil Bcground :Appliction to comology nd blc hol Sng Pyo Kim Kunn Nt l Univ. GC t YITP Dcmbr 8,
Outlin Why i QFT in bcground intrting? Schwingr QED ction Cn tt QFT in bcground? Effctiv ction byond Schwingr Quntum comology QFT in uprpc Thr nontrivil modl in bcground ndu lvl nd ffctiv ction in Bt? Emiion Hwing & Schwingr from RN blc hol Miv clr quntum comology. Summry
Why i QFT in Bcground Intrting?
Pir Production Vcuum fluctution: crtion nd ubqunt nnihiltion of virtul pir vcuum pritnc nd th vcuum polriztion Spontnou pir production: from virtul to rl Schwingr mchnim: xtrnl lctric fild provid th nrgy to prt th virtul chrgd pir Hwing rdition: horizon of blc hol cully prt th pir
Pir Production & Vcuum Polriztion Hwing rdition Quntum Dirc vcuum Horizon KG or Dirc or Mxwll Eq Prmtric intrction On pci of prticl chrgd or unchrgd Vcuum polriztion on-loop ffctiv ction? Schwingr mchnim Quntum Dirc vcuum Elctric fild KG or Dirc Eq Gug intrction Chrgd pir Hinnbrg-Eulr/Schwingr vcuum polriztion
Schwingr QED Action
QED Vcuum Polriztion Sclr QED: Wiopf/Schwingr ffctiv ction pr volum nd pr tim in contnt E-fild c ff E qe d P d m qe in / 6 Spinor QED: Hinbrg-Eulr/Schwingr ffctiv ction pr volum nd pr tim in contnt E-fild p ff E qe d P d m qe co / in /
QED Vcuum Pritnc Spinor QED: Schwingr pir production in contnt E-fild p qe m n qe d Im ff xp 3 ln N 4 n n qe Sclr QED: Schwingr pir production Im N c ff m qe qe 3 8 n n n m β m, m n xp qe β qe / m qe d N ln,
Cn Tt QFT in Bcground?
Currnt Sttu of Strong r Sourc CPA f r Sytm v n r Sytm Tbl-top f CPA lr rg cl n lr PW PUSER JAERI UIRE/OA f OSAKA VUCAN f POARIS UI p OPCPA r Ptwtt N CEA/DAM GSI n MJ NIF P powr TW TW TW ifsa EIA TW OA TW TOKAI Michign JANUSP N TW UI Vulcn CPA Sn Digo TW MBI P GEKKO-XII GEKKO-MII UHI Michign NR, Whington Tridnt Nov Omg I Phébu J UI Nd-gl, n, Europ Nd-gl, n, u. projct Ti-S, f, Europ Nd-gl, f, USA Ti-S, f, USA Nd-gl, n, USA projct Nd-gl, f, Jpn Ti-S, f, Jpn Nd-Gl, f, Europn Nd-Gl, f, Jpn OPCPA, f, u. projct Diod Yb-Gl u. projct Ti-S, f, jpn projct Ti-S, f, uropn projct - - 3 4 5 6 7 Enrgy J Courty of Jongmin, GIST
Sttitic of 4 Pillr of EI Extrm ight Infrtructur [http://www.xtrm-light-infrtructur.u] Country Fcility focu Powr PW Romni Nuclr phyic Pul nrgy J Pul width f x. Rp rt Hz Hungry Attocond phyic / 5/4 5/ /. Czch Rpublic To b dtrmind Scondry bm rdition, high-nrgy prticl High intnity - x /5/x /5/ // //. 3-4 J 5. [Di Pizz, Mullr, Htgortyn, nd Kitl, Extrmly high-intnity lr intrction with fundmntl ytm, Rv. Mod. Phy. 84
EI/IZEST & Schwingr imit [Homm, Hb, Mourou, Ruhl nd Tjim, PTP Suppl. 93 ] Th Schwingr limit criticl trngth for - pir production E B I c c c m.3 m 4.4 Ec.3 8 6 3 9 V G W / cm / cm
Nutron Str nd Mgntr [A. K. Hrding nd D. i, Rp. Prog. Phy. 69 6]
Effctiv Action byond Schwingr
On-oop Effctiv Action Th in-out formlim vi th Schwingr vritionl principl [Schwingr, PNAS 5; DWitt, Phy. Rp. 75, Th Globl Approch to Quntum Fild Thory 3] δ,out iw i,in gd D i,out δs x ff,out,in Th vcuum pritnc twic of th imginry prt nd th mn numbr of producd pir,in,out ImW,in ImW ± VT ln ± N
Bogoliubov Trnformtion & In-Out Formlim Th Bogoliubov trnformtion btwn th in-tt nd th out-tt, quivlnt to th S-mtrix, b,out,out α α,in,in,in,in * β * β,in,in Commuttion rltion from quntiztion rul CTP: Prticl pir production b b,in,in U U b,in,in [ ], p, [, ] δ b b, out p, out { } {, δ p, b, b } δ p,out p,out N β ; α β,out,out p,out p,out U U δ p;
Out-Vcuum from In-Vcuum For boon, th out-vcuum i th multi-prticl tt of but unitry inquivlnt ;out ;in to th in-vcuum: ;out U ;in,in Th out-vcuum for frmion: α n * β α ;out U ;in α,in,in n n, n ; in * β,in, ;in,in, ; in
Out-Vcuum from S-Mtrix Th out-vcuum in trm of th S-mtrix volution oprtor P xp[ iθ,in,in b,inb,in ] U S P, iϕ iϕ S xp[ r,inb,in,inb,in ] α iϑ coh r, β * inh r Th digrmmtic rprnttion for pir production iϑ iϕ iϕ out xp[ r,inb,in,inb,in ] in iϑ iϕ
Effctiv Action t T & T Zro-tmprtur ffctiv ction for clr nd pinor [SKP,, Yoon, PRD 78 8; 8 ; SPK, 84 ] W i ln,out,in ± i finit-tmprtur ffctiv ction for clr nd pinor [SKP,, Yoon, PRD 8 ] lnα * xp[ i d 3 xdt ff ], β,in U, β,in Tr U Tr ρ ρ in in Gmm-function rgulriztion h bn introducd.
QED Action in [KY, PRD 78 8] Th Bogoliubov cofficint nd th ffctiv ction Imginry prt from th mn numbr of pir Ω Ω ln Im 3 3 ff τω τω d /τ ch E t t E [ ] / / 3 3 * / ] [ / / / / τ τ ω ω τ τ ω τω τω α τω τω ω qe qe m qe G d P d i i i i y x z ± Ω Ω Γ Ω Γ Γ Γ ± ± Ω Ω
QED Action in [SPK,, Yoon, PRD 8 ] Th Bogoliubov cofficint nd th ffctiv ction Th imginry prt nd th mn numbr of pir z E z E / ch [ ] 3 3 3 3 3 / / / / 3 * / ] [ / ] [ / / / / qe qe P P qe qe P P m qe P G d P d d i i i i y x ω ω α ω ± ± Ω Ω Γ Ω Γ Γ Γ ± ± ± Ω Ω Ω Ω ln Im 3 ω d d
QED Action in [SPK, PRD 84 ] Sclr/pinor QED in loclizd B-Fild Th invr cttring mtrix nd th ffctiv ction x B x B / ch [ ] / / / / 3 / ] [ / ] [ ~ / / / / qb qb qb qb m qb F d P d d M z y ω ω ± Π Π ± Π Π Ω Π Ω Γ Γ Ω Γ Γ ± ± ± Ω Ω z B z B / ch
Conjctur for Rcontruction of Action from Pir Production Conjctur [Gi, Kim nd Schubrt ] Pir production imginry prt of ffctiv ction follow from th vcuum polriztion rl prt: QED, for intnc, Cuchy thorm ridu for impl pol Cn on find th ffctiv ction from th pir production? invr procdur Pir production in blc hol phyic, xpnding pctim, trong E-fild in QED or trong chromo-e fild in QCD. Mny mthod hv bn dvlopd to comput th pir production. Mittg-fflr thorm/borl nlyi
Quntum Comology QFT in Suprpc
Quntum Comology Th Whlr-DWitt WDW Eqution cond quntizd thory Vribl: mtric on 3-urfc invrint undr diffomorphim gomtrodynmic nd xtrinic curvtur for momnt. WDW qution: th upr-hmiltonin contrint nd/or th upr-momntum contrint vi Dirc quntiztion.
ADM Formlim & WDE EQ H H G H ijl i Arnwitt-Dr-Minr formlim: folit globlly hyprbolic pctim mnifold by pcli 3-urfc i i j d N N N dt N dtdx h dx dx N lp function & N i i hift vctor Th Hmiltonin for grvity nd mttr fild d 3 3 d x' 6m x, x' / h x x[ NH ij j h N P / i ] [ h x h x' h x h x' h x h x' ] T H G i i i ijl, ij x, x' x jl ij il l mp h 6 i x' h / j / ij 3 mp δ x x' 6 ij l 3 δ x x' R Λ T φ,, h ij ij ij K h K K : cond fundmntl form 3 φ ij
Thr Nontrivil Modl in Bcground
Chrgd Boon in Gug Fild nd in Curvd Spctim A globlly hyprbolic pctim mnifold Minowi pctim d g µ ν µν dx dx Th chrgd clr fild Klin-Gordon qution in gug fild nd in curvd pctim µν ν ν i µ qaµ g g i qa g m Φ t, x
Firt Nontrivil Modl A homognou, tim-dpndnt, mgntic fild Bt with th gug fild How to find th ndu lvl nd ffctiv ction? NOT in th firt quntizd thory KG qution BUT in th cond quntizd fild thory! Th rltivitic thory of tim-dpndnt ocilltor coupld to ch othr du to th ngulr momntum. [ ] Φ Φ Π z t m x t p x d H ω ω r t B r t A,
Hwing Rdition v Schwingr Emiion from RN Blc Hol
Evolution of Chrgd Blc Hol [Hicoc, Wm, PRD 4 9] Chrg-lo rt Schwingr formul dq dt 3 q m xp rh qq / rh Totl rt of m lo dm dt 4 T α H Q r H dq dt
Chrgd RN Blc Hol Chrgd RN blc hol Nr horizon nd nr-xtrml blc hol dr dt r Q F dt r Q A d r r Q r M dr dt r Q r M d Ω ε τ ε ερ ρ ρ τ ρ Ω t Q B Q M Q r d Q d B Q d Q B d
Extrml nd Nr-xtrml BH Emittd prticl in xtrml blc hol [Chn t l, PRD 85 ] Emittd prticl in nr-xtrml blc hol / / coh inh l Q m q b qq b b N q Q m b β B Q b b b N ~ ~ coh coh ~ inh inh ω β
Scond Nontrivil Modl Th mtric during th Hwing nd Schwingr miion proc from chrgd blc hol phriclly ymmtric umption d g d i j ij t, r dx dx r Ω Thn QFT in th rducd t-r pln bcom non-trivil bcground problm, imilr in om n to QFT for chrgd prticl in homognou, tim-dpndnt, mgntic fild with th gug potntil A t, r B t r B t A A E t, r t
Quntum Comology
Quntum Univr in th Suprpc Th uprmtric for FRW gomtry nd miniml clr Th Hmiltonin contrint nd th WDW qution A Cuchy initil vlu problm w.r.t. th cl fctor nd prcription for th boundry condition. dφ d d [ ] 4 4 clr fild prt H 6 grvity prt H,,, M G V V V V V H G G G Λ Ψ φ φ φ φ φ φ
Comprion of WDW nd KG Eq Th WDW qution for th FRW univr with miv clr fild Th trnvr motion of chrgd clr in tmporl, homognou, mgntic fild, 6 Ψ φ φ φ m V G, Φ x t m t qb x t qb p t z z /, r t B r t A
Third Quntiztion Th WDW qution cn b drivd from th third quntizd Hmiltonin S ddφ Ψ φ Ψ 4 V φ V Th third quntiztion of ml fild i um of - dpndnt ocilltor [Bn, NPB 39 88; McGuign, PRD 38 88; Gidding, Stromingr, NPB 3 89; Hooy, Moriw, PRD 39 89; Ab, PRD 47 93; SPK, Kim, Soh, NPB 46 93; Horiguchi, 48 93]. Th third quntiztion of miv fild i nlogou to th cond quntizd chrgd KG in tim-dpndnt, homognou, mgntic fild A t, r B t r /. G Ψ
Third Nontrivil Modl Expnd th wv function by th nrgy ignfunction of Hmiltonin for th clr fild to obtin th third quntizd Hmiltonin H ψ / T T Ω ψ vry rly univr: O/ Ω ψ T ψ E ψ lt univr: O 4-p/p Th miv clr quntum comology cn b olvd in th n tht th coupling mtrix Ω nd th nrgyignvlu mtrix E r xplicitly nown.
Summry In-out formlim for th ffctiv ction byond Schwingr. Thr nontrivil modl of QFT in bcground QED in homognou, tim-dpndnt, mgntic fild. Emiion, Hwing or Schwingr, from chrgd blc hol dynmicl proc Quntum comology for miv clr fild in th third quntizd formultion. Anothr chllng byond Schwingr?