Sang Pyo Kim 金相杓 Kunsan Natl Univ amp YITP Kyoto Univ 竹原理論物理硏究會 June 0608 2011 AS amp NCU amp NTHU amp Kinki seminars Outline Introduction ID: 403124
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Slide1
Hawking Radiation and Vacuum Polarization
Sang
Pyo
Kim (
金相杓
)
Kunsan
Nat’l Univ. & YITP, Kyoto Univ.
竹原理論物理硏究會
, June 06-08, 2011
[AS & NCU & NTHU & Kinki seminars]Slide2
Outline
Introduction
Spin Statistics Inversion in QED
Vacuum Polarization and Hawking Radiation
ConclusionSlide3
Introduction
Lectures at YITP
May 24-25, 2011Slide4
QED Vacuum Polarization
Scalar QED:
Weisskopf
/Schwinger effective action per volume and per time in a constant E-field
Spinor
QED: Heisenberg-Euler/Schwinger effective action per volume and per time in a constant E-fieldSlide5
QED Vacuum Persistence
Spinor
QED: Schwinger pair production in a constant E-field
Scalar QED: Schwinger pair productionSlide6
Nonperturbative Aspect of QED &
sQG
[SPK, JHEP11(2007)048]
Slide7
One-Loop Effective Actions
The in-out formalism via the Schwinger
variational
principle [Schwinger, PNAS(‘51); DeWitt, Phys. Rep. (‘75),
The Global Approach to Quantum Field Theory
(‘03)]
The vacuum persistence (twice of the imaginary part ) and the mean number of produced pairsSlide8
Bogoliubov Transformation &
In-Out Formalism
The
Bogoliubov
transformation between the in-state and the out-state, equivalent to the S-matrix,
Commutation relations from quantization rule (CTP):
Particle (pair) productionSlide9
Out-Vacuum from In-Vacuum
For bosons, the out-vacuum is the multi-particle states of but unitary
inequivalent
to the in-vacuum:
The out-vacuum for fermions:Slide10
Out-Vacuum from S-Matrix
The out-vacuum in terms of the S-matrix (evolution operator)
The diagrammatic representation for pair productionSlide11
Effective Actions at T=0 & T
Zero-temperature effective action for scalar and
spinor
[SKP, Lee, Yoon, PRD 78, 105013 (‘08); 82, 025016 (‘10)]
finite-temperature effective action for scalar and
spinor
[SKP, Lee, Yoon, PRD 82, 025016 (‘10)]Slide12
Spin Statistics Inversion in QEDSlide13
Spin Statistics in QFT
The spin statistics theorem
-Bosons: Bose-Einstein distribution and
commutator
-Fermions: Fermi-Dirac distribution and
anticommutator
The vacuum persistence for boson production takes the form of
spinor
QED [Stephens, AP193 (’89)]
The vacuum persistence for
fermion
production takes the form of scalar QEDSlide14
Spin-Statistics Inversion
The vacuum polarization of scalar QED can be written as a spectral function times the Fermi-Dirac distribution and that for
spinor
QED as a spectral function times the Bose-Einstein distribution [Muller, Greiner,
Rafelski
, PLA 63 (‘77)]Slide15
Spin-Statistics Inversion
The vacuum persistence in terms of the transverse energy [Hwang, SPK, PRD 80, 065004(‘09)]
The vacuum persistence in terms of the
instanton
action or the
worldline
instantonSlide16
Vacuum Polarization and Hawking Radiation
SPK & W-Y.
Pauchy
Hwang, “Vacuum Polarization and Persistence on the Black Hole Horizon,” [arXiv:1103.5264]Slide17
Vacuum Persistence for BH
Hawking radiation of bosons and fermions in a charged rotating black hole
Vacuum persistence for zero amplification (R
J
= 0)
2Im(W) as
ln
(Z), the logarithm of the partition function, plus the vacuum energy implies that 2Im(W)/V is the pressure of boson and
fermion
gas [
Ritus
, (‘84), (‘98)]Slide18
Effective Action for Black Hole
Schwarzschild black hole in d-dimensions
Bogoliubov
coefficients for a
massless
boson [DeWitt, Phys.Rep.19 (‘75)]
Effective actionSlide19
Vacuum Polarization for BH
Hawking radiation in a Schwarzschild black hole is effectively two-dimensional one, in the (t-r)
spacetime
Reduced effective action for bosons and fermions
Vacuum polarization as a thermal effective action
Renormalized vacuum polarization for massive emissionSlide20
Vacuum Persistence and Gravitational Anomalies
Vacuum persistence = decay rate of vacuum due to Hawking radiation or Schwinger mechanism
Trace anomalies = Hawking radiation and Schwinger mechanism [Christensen,
Fulling
, PRD 15 (’77);
Dittrich
,
Sieber, JPA 21 (‘88)]Vacuum persistence for bosons and fermions
equals to the total flux of Hawking radiation from gravitational anomalies [Robinson,
Wilczek
, PRL 95 (‘05);
Iso
,
Umetsu
,
Wilczek
, PRL 96 (‘06)].Slide21
Duality between BH and QEDSlide22
Conclusion
The
nonperturbative
effective actions for QED and gravity in the in-/out formalism al a Schwinger
variational
principle.
The effective action for pair production are characterized by two prominent aspects: the vacuum polarization (real part) and persistence (imaginary part)
The effective action for Schwarzschild black hole, modulo number of states, is dual (equivalent) to QED effective action in constant E.Duality of gravity coupling and gauge coupling? (Davies-Unruh temperature)