Thomas-Fermi Model in the Presence of Natural Cutoffs

It has been revealed, in the context of quantum gravity candidates, that measurement of position cannot be done with arbitrary precision and there is a finite resolution of space-time points. This leads naturally to a minimal measurable length of the order of Planck length. Also, in the context of newly proposed doubly special relativity theories, a test particle’s momentum cannot be arbitrarily imprecise leading nontrivially to a maximal momentum for a test particle. These two natural cutoffs affects most of quantum field theoretic arguments in the spirit of condensed matter physics. Here we focus on the role of these natural cutoffs on Thomas-Fermi theory in condensed matter physics. We show how quantum gravity effects can play important role phenomenologically in many-body interactions of solids

Conformally covariant vector–spinor field in de Sitter space

In this paper, we study conformally invariant field equations for a vector–spinor spin-32 field in the de Sitter space-time. The solutions are also obtained in terms of the de Sitter–Dirac plane waves. The related two-point functions are calculated in both the de Sitter ambient space formalism and intrinsic coordinates. In order to study the conformal invariance, Dirac’s six-cone formalism is utilized in which the field equations are expressed in a manifestly conformal way in 4+2 -dimensional conformal space and then followed by a projection to the de Sitter space

MicroBlack Holes Thermodynamics in the Presence of Quantum Gravity Effects

Black hole thermodynamics is corrected in the presence of quantum gravity effects. Some phenomenological aspects of quantum gravity proposal can be addressed through generalized uncertainty principle (GUP) which provides a perturbation framework to perform required modifications of the black hole quantities. In this paper, we consider the effects of both a minimal measurable length and a maximal momentum on the thermodynamics of TeV-scale black holes. We then extend our study to the case that there are all natural cutoffs as minimal length, minimal momentum, and maximal momentum simultaneously. We also generalize our study to the model universes with large extra dimensions (LED). In this framework existence of black holes remnants as a possible candidate for dark matter is discussed. We study probability of black hole production in the Large Hadronic Collider (LHC) and we show this rate decreasing for sufficiently large values of the GUP parameter

A group theoretical approach to graviton two-point function

Respecting the group theoretical approach, it is debated that the theory of linear conformal gravity should be formulated through a tensor field of rank-3 and mixed symmetry (Binegar et al., Phys Rev D 27: 2249, 1983 ). Pursuing this path, such a field equation was obtained in de Sitter space (Takook et al., J Math Phys 51:032503, 2010 ). In the present work, considering the de Sitter ambient space notation, a proper solution to the physical part of this field equation is obtained. We have also calculated the related two-point function, which is interestingly de Sitter invariant and free of an infrared divergence

Noncommutative Phase Space Schrödinger Equation with Minimal Length

We consider the Schrödinger equation under an external magnetic field in two-dimensional noncommutative phase space with an explicit minimal length relation. The eigenfunctions are reported in terms of the Jacobi polynomials, and the explicit form of energy eigenvalues is reported

Non-linear trans-Planckian corrections of spectra due to the non-trivial initial states

Recent Planck results motivated us to use non-Bunch–Davies vacuum. In this paper, we use the excited-de Sitter mode as non-linear initial states during inflation to calculate the corrected spectra of the initial fluctuations of the scalar field. First, we consider the field in de Sitter space–time as background field and for the non-Bunch–Davies mode, we use the perturbation theory to the second order approximation. Also, unlike conventional renormalization method, we offer de Sitter space–time as the background instead Minkowski space–time. This approach preserve the symmetry of curved space–time and stimulate us to use excited mode. By taking into account this alternative mode and the effects of trans-Planckian physics, we calculate the power spectrum in standard approach and Danielsson argument. The calculated power spectrum with this method is finite, corrections of it is non-linear, and in de Sitter limit corrections reduce to linear form that obtained from several previous conventional methods

Scale-dependent power spectrum from initial excited-de Sitter modes

In this paper, we calculate corrections of scalar perturbations spectra resulting from excited-de Sitter modes as the nontrivial initial states. To obtain these modes, we consider the asymptotic expansion of the Hankel functions up to the higher order of 1 kτ $$\frac{1}{k\tau}$$ . Actually the Planck and WMAP data impose some constrains on the Hankel function index. These observational constraints and back-reaction effects stimulate us to use excited-de Sitter modes. Finally, we nominate these nontrivial general solutions as the fundamental mode functions during inflation and we calculate the corrected form of scale-dependent power spectrum with trans-Planckian corrections, and in de Sitter space-time limit the results reduce to the scale-invariant power spectrum

Coupling constants of bottom (charmed) mesons with the pion from three-point QCD sum rules

In this article, the three-point QCD sum rules are used to compute the strong coupling constants of vertices containing the strange bottomed (charmed) mesons with the pion. The coupling constants are calculated when both the bottom (charm) and the pion states are off-shell. A comparison of the obtained results of the coupling constants with existing predictions is also made

The Krein–Gupta–Bleuler quantization in de Sitter space–time; Casimir energy–momentum tensor for a curved brane

In this paper, vacuum expectation value (VEV) of the energy–momentum tensor for a conformally coupled scalar field in de Sitter space–time is investigated through the Krein–Gupta–Bleuler construction. This construction has already been successfully applied to the de Sitter minimally coupled massless scalar field and massless spin-2 field to obtain a causal and fully covariant quantum field on de Sitter background. We also consider the effects of boundary conditions. In this respect, Casimir energy–momentum tensor induced by Dirichlet boundary condition on a curved brane is evaluated

The semileptonic B¯→Dℓν¯ and B¯s→Dsℓν¯ decays in Isgur–Wise approach

We consider a combination of linear confining and Hulthén potentials in the Hamiltonian and, via the perturbation approach, report the corresponding Isgur–Wise function parameters. Next, we investigate the Isgur–Wise function for B¯→Dℓν¯ and B¯s→Dsℓν¯ semileptonic decays and report the decay width, branching ratio, and |Vcb| CKM matrix element. A comparison with other models and experimental values is included