Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions.The solution cosmological constant problem

The solution cosmological constant problem.Quantum Field Theory in fractal space-time with negative Hausdorff- Colombeau dimensions and dark matter nature. J. Foukzon Department of mathematics, Israel Institute of Technology, Haifa, Israel E-mail: jaykovfoukzon@list.ru E.Menkova A.Potapov Abstract. The cosmological constant problem arises because the magnitude of vacuum energy density predicted by quantum field theory is about 120 orders of magnitude larger than the value implied by cosmological observations of accelerating cosmic expansion. We pointed out that the fractal nature of the quantum space-time with negative Hausdorff- Colombeau dimensions can resolve this tension. The canonical Quantum Field Theory is widely believed to break down at some fundamental high-energy cutoff

and therefore the quantum fluctuations in the vacuum can be treated classically seriously only up to this high-energy cutoff. In this paper we argue that Quantum Field Theory in fractal space-time with negative Hausdorff-Colombeau dimensions gives high-energy cutoff on natural way.We argue that there exists hidden physical mechanism which cancel divergences in canonical QED4,QCD4,Higher-Derivative-Quantum-Gravity, etc. In fact we argue that corresponding supermassive Pauli-Villars ghost fields really exists.It means that there exist the ghost- driven acceleration of the univers hidden in cosmological constant. In order to obtain desired physical result we apply the canonical Pauli-Villars regularization up to

.This would fit in the observed value of the dark energy needed to explain the accelerated expansion of the universe if we choose highly symmetric masses distribution between standard matter and ghost matter below that scale

,i.e., fs.m

  fg.m

,
 mc,

eff,
effc 

The small value of the cosmological constant explaned by tiny violation of the symmetry between standard matter and ghost matter.Dark matter nature also explaned using a common origin of the dark energy and dark matter phenomena. Content 1.Introduction. 2.1.The formulation of the cosmological constant problem. 2.2. Zel’dovich approach by using Pauli-Villars regularization revisited. 2.3. Dark matter nature. A common origin of the dark energy and dark matter phenomena. 3.Pauli-Villars ghosts as physical dark matter. 3.1.Pauli-Villars renormalization of 4 4.New physical interpretation. 3.2. Pauli–Villars renormalization of QED3.New physical interpretation. 3.2.1.Pauli–Villars renormalization of QED3.What is wrong with Pauli–Villars renormalization of QED3. 3.2.2.New physical interpretation Pauli–Villars ghost fields. 3.3.High covariant derivatives renormalization as Pauli–Villars renormalization of non-Abelian gauge theories.New physical interpretation. 3.4.What is the physical significance of Pauli-Villars renormalization? 4.OFT in a ghost sector via dimensional regularization. 4.1.Dimensional renormalization via Colombeau generalized functions. 4.2.The scalar theory 4 4 in a ghost sector. 4.3.Quantum electrodynamics in a ghost sector. 4.4.Quantum chromodynamics in a ghost sector. 4.5.Quantum chromodynamics in a ghost sector via Colombeau generalized functions. 4.6.The general structure of the R-operation via Colombeau generalized functions. 4.7.Renormalization Group in a ghost sector. 4.8.Dimensional regularization and the MS scheme in a ghost sector. 5.Renormalizability-of-Higher-Derivative-Quantum-Gravity. 6.Hausdorff-Colombeau measure and associated negative Hausdorff-Colombeau dimensions.Fractal spacetime with negative Hausdorff-Colombeau dimension. 6.1. Fractional Integration in negative dimensions. 6.2.Hausdorff measure and associated positive Hausdorff dimension. 6.3.Hausdorff-Colombeau measure and associated negative Hausdorff dimension. 7. Scalar field theory in spacetime with negative Hausdorff-Colombeau dimension. 7.1.Equation of motion and Hamiltonian. 7.2.Propagator in spacetime with negative-dimensions. 7.3.Green’s functions in spacetime with Hausdorff-Colombeau negative dimensions. 7.4.Saddle-Point Evaluation of the Path Integral in negative dimensions. 7.5.Power-counting renormalizability of P
D _scalar field theory in negative dimensions D. 7.6.Power-counting renormalizability of Einstein gravity in negative dimensions. 7.7.Power-counting renormalizability of Horava gravity in negative dimensions. 8.The solution cosmological constant problem. 8.1.Einstein-Gliner-Zel’dovich vacuum with tiny Lorentz invariance violation. 8.2.Zeropoint energy density corresponding to Gliner non-singular cosmology. 8.3. Zeropoint energy density in models with supermassive physical ghost fields. 9. Discussion and conclusions. 10.Conclusion. 1.Introduction 1.1.The cosmological constant problem and Quantum Field Theory in fractal spacetime with negative dimension. One of the greatest challenges in modern physics is to reconcile general relativity and elementary particles physics into a unified theory. Perhaps the most dramatic clash between th

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