Quantum Field Theory In Curved SpacetimeRVidal).pdf · Birrel and Davies, Quantum Fields in Curved...
Transcript of Quantum Field Theory In Curved SpacetimeRVidal).pdf · Birrel and Davies, Quantum Fields in Curved...
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Quantum Field TheoryIn Curved Spacetime
José Roberto VidalUniversidad Autónoma de Madrid
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Why QFT in curved ST?
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Why QFT in curved ST?
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Why QFT in curved ST?
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Why QFT in curved ST?
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A la Weinberg
Particles vs. fields
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A la Weinberg
The Poincaré group tells the whole story:
● Based on symmetries
Particles vs. fields
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A la Weinberg
We need the Fock space.
And so on...
● Based on symmetries
● Multiparticle states
Particles vs. fields
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A la Weinberg
● Based on symmetries
● Multiparticle states
● Quantum fields are just a tool.
Products of fields
Particles vs. fields
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A la PeskinSchroeder
● We start with a classical system.Classical people:
Poisson, Lagrange, Hamilton...
Particles vs. fields
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A la PeskinSchroeder
● We start with a classical system.
● Canonical quantization.
Diagonalization throughFourier transform:
Particles vs. fields
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A la PeskinSchroeder
● We start with a classical system.
● Canonical quantization.
● A beatiful metaphore.
Particles are quantized excitations of the field
Particles vs. fields
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Part I
QFT in curved ST is like Schwinger effect!
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1+1 FRW universe
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1+1 FRW universe
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In modes
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And so on...No particles in the dinosaurs era
In modes
Complete and normalized basis
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Out modes
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And so on...No particles in the spacecrafts era
Complete too!!
Out modes
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?
?
Particles from nowhere
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Particles from nowhere
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Particles from nowhere
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Particles from nowhere
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Particles from nowhere
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Particles from nowhere
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General formalism● Space plus time
Suitable spacetimes
??Clear separation between space an time
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General formalism● Space plus time
Clear separation between space an time
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General formalism● Space plus time
● Solve field equation
Find a complete and normalized collection of modes.
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General formalism● Space plus time
● Solve field equation
Find a complete and normalized collection of modes.
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General formalism● Space plus time
● Solve field equation
Find a complete and normalized collection of modes.
![Page 31: Quantum Field Theory In Curved SpacetimeRVidal).pdf · Birrel and Davies, Quantum Fields in Curved Space V. Mukhanov, Introduction to Quantum Effects in Gravity R. Wald, Quantum Field](https://reader033.fdocuments.in/reader033/viewer/2022042314/5f0304c47e708231d4072258/html5/thumbnails/31.jpg)
General formalism● Space plus time
● Solve field equation
● Quantize!
We get automatically awell defined field operatorplus a Hilbert space
The
pyramid
once
again
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General formalism● Space plus time
● Solve field equation
● Quantize!
● Ambiguity
Differents sets of modes give rise to differents “particles”.
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General formalism● Space plus time
● Solve field equation
● Quantize!
● Ambiguity
Differents sets of modes give rise to differents “particles”.
Bogoliubov transformations
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General formalism● Space plus time
● Solve field equation
● Quantize!
● Ambiguity
● And much more!
Many other observables
● Expectation values
EM Tensor
● Transition rates
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Part II
QFT in curved ST is not Schwinger effect!
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This is not Schwinger effect!
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What particles?!?
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What particles?!?
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Bonus
Horizons and temperature
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Bonus 1: Minkowski STAccelerated observer
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Bonus 2: de Sitter ST
Time
Horizo
n
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Bonus 3: Black Holes
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Accelerated observer
Unruh effect
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Unruh effect
Rindler ST
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Unruh effect
And of course we already had
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Unruh effect
Final surprise!
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Hawking Radiation
Two kinds of observers/vacua
or
Anyway
when comparing or
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● Birrel and Davies, Quantum Fields in Curved Space
● V. Mukhanov, Introduction to Quantum Effects in Gravity
● R. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics
● S.A. Fulling, Aspects of Quantum Field Theory in Curved SpaceTime
Further reading