By:Farrin Payandeh University of Payame Noor, Tabriz,Iran XVII European Workshop on String Theory...
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By:Farrin Payandeh University of Payame Noor, Tabriz,Iran XVII European Workshop on String Theory 2011 Italy, Padua September 2011
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Transcript of By:Farrin Payandeh University of Payame Noor, Tabriz,Iran XVII European Workshop on String Theory...
By:Farrin PayandehUniversity of Payame
Noor, Tabriz,Iran
XVII European Workshop on String Theory 2011
Italy, Padua
September 2011
Dirac’s equation and the sea of negative energy. Standard quantum field theory leading to the infinites. Renormalization : Sweeping the infinites under the rug. EPR Paradox and Antiparticles. Quantum Mechanics in complex spacetime. The Miracle of creation. Conservation of Angular momentum(a.k.a. “The photon”).
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Neglecting negative Energies:
“At what cost?”
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4
Case Study
P. A. M. Dirac: Bakerian Lecture , Proceedings of the Royal Society A (1941)
Quantization of the minimally coupled scalar field and calculating
the gravitaton two point function in de Sitter spacetime:
Breaking of the covariance.
(a) Appearance of the infrared divergence.
(b) Covariant Quantization adding Negative Frequency States and
Free of divergence graviton field operator in krein Space
Field operator in Krein space: ))x()x((2
1)x( np
Krein QFT calculations in Minkowski spacetimeKrein QFT calculations in Minkowski spacetime
0|)()(|0),( xxTxxiGT
0))((2 0 xxxx
)()(2
)(
2
2log)(2)(
2)!1(!
)1(
2)(
111
11
0
2
1
iziNizJzK
z
zzJzN
z
ss
zzJ
s
ss
Feynman propagator
Two point function in Krein space
02
02
10
2
02
)2()(
8)(
8
1),(Re),(
m
mJmxxGxxG P
FT
0),(Relim,)(8
1
16),(Relim
000
2
0
xxG
mxxG P
FPF
The divergence appears in the imaginary part of this eq. and the real part is convergent :
21
021
0
1
0
1)(lim,
12)(lim,
2
1)(lim
zZ
zK
zz
zN
z
zJzzz
)(2
))(2()(
42
)2()2()(
8)(
8
1
)2(),(
02
02
102
2
02
02
102
10
2
022
).(
4
4
m
mKim
m
miNmJm
imk
ekdxxG
xxikPF
10
Divergent Integrals of QED in Krein Space
2 2( )2 2 0
(1)is k m iids e
k m i
and using integral representation of the causal propagator in momentum space:
General form of divergent integrals of QED is:
we can see that the real part is convergent:
Convergent expressions of vacuum polarization and vertex graphs in krein space will be:
†0 0( , , ) ( , , ) ( , , )p pp q p p q p p q p
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Quantum Field Theory with the N.F.S. , Quantum Field Theory with the N.F.S. , an answer to Feynman reply , “ A an answer to Feynman reply , “ A Nobel prize for sweeping the rushes Nobel prize for sweeping the rushes (infinties) under the rug” ?(infinties) under the rug” ?
Negative-energy modes as a candidate solution to some problems in quantum physics?
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2323
Case Study
P. A. M. Dirac: Bakerian Lecture , Proceedings of the Royal Society A (1941)
GHOSTBUSTING:Reviving quantumtheories that were thoughtto be dead
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Thank you for your
kind attention
