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Complexity in quantum field theory and physics beyond the standard model

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  • Goldfain, Ervin

Abstract

Complex quantum field theory (abbreviated c-QFT) is introduced in this paper as an alternative framework for the description of physics beyond the energy range of the standard model. The mathematics of c-QFT is based on fractal differential operators that generalize the momentum operators of conventional quantum field theory (QFT). The underlying premise of our approach is that c-QFT contains the right analytical tools for dealing with the asymptotic regime of QFT. Canonical quantization of c-QFT leads to the following findings: (i) the Fock space of c-QFT includes fractional numbers of particles and antiparticles per state, (ii) c-QFT represents a generalization of topological field theory and (iii) classical limit of c-QFT is equivalent to field theory in curved space–time. The first finding provides a field-theoretic motivation for the transfinite discretization approach of El-Naschie’s ε(∞) theory. The second and third findings suggest the dynamic unification of boson and fermion fields as particles with fractional spin, as well as the close connection between spin and space-time topology beyond the conventional physics of the standard model.

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  • Goldfain, Ervin, 2006. "Complexity in quantum field theory and physics beyond the standard model," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 913-922.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:4:p:913-922
    DOI: 10.1016/j.chaos.2005.09.012
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    Cited by:

    1. Korabel, Nickolay & Zaslavsky, George M., 2007. "Transition to chaos in discrete nonlinear Schrödinger equation with long-range interaction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 223-237.
    2. Rami, El-Nabulsi Ahmad, 2009. "On the fractional minimal length Heisenberg–Weyl uncertainty relation from fractional Riccati generalized momentum operator," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 84-88.
    3. Morales-Delgado, V.F. & Gómez-Aguilar, J.F. & Escobar-Jiménez, R.F. & Taneco-Hernández, M.A., 2018. "Fractional conformable derivatives of Liouville–Caputo type with low-fractionality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 424-438.
    4. Herrmann, Richard, 2010. "Common aspects of q-deformed Lie algebras and fractional calculus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4613-4622.
    5. El-Nabulsi, Rami Ahmad, 2009. "Fractional Dirac operators and deformed field theory on Clifford algebra," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2614-2622.
    6. EL-Nabulsi, Ahmad Rami, 2009. "Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 52-61.
    7. Rami, El-Nabulsi Ahmad, 2009. "Fractional illusion theory of space: Fractional gravitational field with fractional extra-dimensions," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 377-384.
    8. El-Nabulsi, Ahmad Rami, 2009. "Complexified quantum field theory and “mass without mass” from multidimensional fractional actionlike variational approach with dynamical fractional exponents," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2384-2398.

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