By:Farrin Payandeh University 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”). 2

 Neglecting negative Energies: “At what cost?” 3

4 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:

Krein QFT calculations in Minkowski spacetime

Feynman propagator Two point function in Krein space The divergence appears in the imaginary part of this eq. and the real part is convergent :

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Divergent Integrals of QED in Krein Space 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:

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Quantum Field Theory with the N.F.S., an answer to Feynman reply, “ A Nobel prize for sweeping the rushes (infinties) under the rug” ? Negative-energy modes as a candidate solution to some problems in quantum physics?

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23 Case Study P. A. M. Dirac: Bakerian Lecture, Proceedings of the Royal Society A (1941) GHOSTBUSTING: Reviving quantum theories that were thought to be dead

24 Thank you for your kind attention