Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos

The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.

Interesting QFT Problems Tackled in New Fashion

The Dimensional Regularization technique of Bollini and Giambiagi (BG) [Phys. Lett. B 40, 566 (1972);Il Nuovo Cim. B 12, 20 (1972);Phys. Rev. D 53, 5761 (1996)] cannot be employed for all Schwartz Tempered Distributions Explicitly Lorentz Invariant (STDELI) S′L. We lifted such limitation in [J. Phys. Comm. 2 115029 (2018)], which opens new QFT possibilities, centering in the use of STDELI that allows one to obtain a product in a ring with zero divisors. This in turn, overcomes all problems regrading QFT infinities. We provide here three examples of the application of our STDELI-extension to quantum field theory (A) the exact evaluation of an electron’s self energy to one loop, (B) the exact evaluation of QED’s vacuum polarization, and C) the theory for six dimensions, that is non-renormalizable.

One-loop contributions for h→ℓℓγ and e−e+→hγ in the U(1)_(B−L) extension of the standard model

We present one-loop contributions for h→ℓℓγ with ℓ=νe,μ,τ,e,μ and e−e+→hγ in the U(1)_(B−L) extension of the standard model. In the phenomenological results, the signal strengths for h→ℓℓγ at the Large Hadron Collider and for e−e+→hγ at future lepton colliders are analyzed in the physical parameter space for both the vector and chiral B−L models. We found that the contributions from the neutral gauge boson Z′ to the signal strengths are rather small. Consequently, the effects will be difficult to probe at future colliders. However, the impacts of charged Higgs and CP-odd Higgs in the chiral B−L model on the signal strengths are significant and can be measured with the help of the initial polarization beams at future lepton colliders.

THE EXISTENCE OF GLOBAL SOLUTION AND "BLOW UP" PHENOMENON FOR A SYSTEM OF MULTI DIMENSIONAL SYMMETRIC REGULARIZED WAVE EQUATIONS

The existence and uniqueness of the global smooth solution to the initial-boundary valueproblem of a system of multi-dimensions SRWE are proved. The sufficient conditions of 'blowingup' of the solution are given.

Krein regularization of λφ~3 theory

In this paper, the one-loop self energy of λφ3 theory is calculated by using Krein regularization in four and six dimensions and the result, which is finite, is compared with the conventional result of λφ3 theory in Hilbert space. The self energy is calculated in the one-loop approximation and the result is automatically regularized as a result of “Krein Regularization”.

One-loopformulas for H→Zν_(ι)ν_(ι),forιe,μ,τin't Hooft-Veltman gauge

In this paper,we present analytical results for one-loop contributions to the decay processes H-Zvivi(for I=e,μ,T).The calculations are performed within the Standard Model framework in the't Hooft-Veltman gauge.One-loop form factors are then written in terms of scalar one-loop functions in the standard notations of LoopTools.As a result,one-loop decay rates for the decay channels can be evaluated numerically by using the package.Furthermore,we analyze the signals of H→Zvivi via the production processes e-e+→ZH*-Z(H*→Zν_(ι)ν_(ι)),including the initial beam polarizations at future lepton colliders.The Standard Model backgrounds,such as the processes e-e+→ν_(ι)ν_(ι)ZZ,are also examined in this study.Numerical results indicate that one-loop corrections make contributions of approximately 10%to the decay rates.These are sizeable contributions and should be taken into account at future colliders.We show that the signals H-Zν_(ι)ν_(ι)are clearly visible at the center-of-mass energy√s=250 GeV and are difficult to probe in higher-energy regions owing to the dominant backgrounds.

Feynman integrals and hypergeometric functions

We review Davydychev method for calculating Feynman integrals for massive and no massive propagators,by employing Mellin-Barnes transformation and the dimensional regularization scheme,same that lead to hypergeometric functions.In particular,an example is calculated explicitly from such a method.