Perturbative quantum field theory in the framework of the fermionic projector

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Finster, Felix (2013)
  • Related identifiers: doi: 10.1063/1.4871549
  • Subject: Mathematical Physics | High Energy Physics - Theory | 510 Mathematik | ddc:510
    arxiv: Condensed Matter::Quantum Gases | High Energy Physics::Lattice

We give a microscopic derivation of perturbative quantum field theory, taking causal fermion systems and the framework of the fermionic projector as the starting point. The resulting quantum field theory agrees with standard quantum field theory on the tree level and reproduces all bosonic loop diagrams. The fermion loops are described in a different formalism in which no ultraviolet divergences occur.
  • References (35)
    35 references, page 1 of 4

    [1] G.E. Andrews, The Theory of Partitions, Addison-Wesley Publishing Co., Reading, Mass.- London-Amsterdam, 1976, Encyclopedia of Mathematics and its Applications, Vol. 2.

    [2] A.O. Barut, Schr¨odinger's interpretation of ψ as a continuous charge distribution, Ann. Physik Leipzig 45 (1988), no. 1, 31-36.

    [3] A.O. Barut and J. Kraus, Nonperturbative quantum electrodynamics: the Lamb shift, Found. Phys. 13 (1983), no. 2, 189-194.

    [4] A.O. Barut and J.F. Van Huele, Quantum electrodynamics based on self-energy: Lamb shift and spontaneous emission without field quantization, Phys. Rev. A 32 (1985), no. 6, 3187-3195.

    [5] J.D. Bjorken and S.D. Drell, Relativistic Quantum Fields, McGraw-Hill Book Co., New York, 1965.

    [6] T. Br¨ocker and T. tom Dieck, Representations of Compact Lie Groups, Graduate Texts in Mathematics, vol. 98, Springer-Verlag, New York, 1985.

    [7] B. Collins and P. S´niady, Integration with respect to the Haar measure on unitary, orthogonal and symplectic group, arXiv:math-ph/0402073, Comm. Math. Phys. 264 (2006), no. 3, 773-795.

    [8] L. de la Pen˜a and A.M. Cetto, The Quantum Dice, Fundamental Theories of Physics, vol. 75, Kluwer Academic Publishers Group, Dordrecht, 1996.

    [9] D.-A. Deckert, Electrodynamic absorber theory, Dissertation, Ludwig-Maximilians-Universit¨at Mu¨nchen, (2010).

    [10] Finster F., The fermionic projector in an external potential: Non-perturbative construction and the Hadamard property, in preparation.

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