We continue our study of Horava-Lifshitz type theories using the methods of the spectral geometry. In this work we construct the infrared action of gravity and matter coupled to gravity in the most general way respecting the foliation preserving diffeomorphisms. This is done with the help of the spectral action principle based on some generalized Dirac operator. The gravity part reproduces the infrared limit of the Horava-Lifshitz gravity, while the matter part gives the generalization of the earlier suggested models. Due to the fact that the same Dirac operator is used in the construction of both sectors, the parameters of the gravity and matter parts are related. We expect that this potentially could naturally exclude fine tunings needed to get some desired properties as well as open new possibilities for the experimental tests of the model. * Another, somewhat related, point is the coupling of the gravity based on FPDiff to matter. There are some arguments [10] that in contrary to the gravity part the matter sector should respect the symmetry under full diffeomorphisms (or it should be extremely fine-tuned). Clearly this is very non-natural and one would like to have a more symmetric formulation of the theory where both, gravity and matter sectors, are based on FPDiff or one should give more fundamental reasons why matter should respect much larger symmetry.In this paper, we are advocating the first possibility, i.e. that both sectors have FPDiffs as the fundamental symmetry. This is achieved via the spectral action principle [11]. The main idea is that both sectors are controlled by the same object -some physically relevant Dirac operator. Due to this, both sectors are not independent and the parameters of the gravitational part are related to the parameters of the matter sector. Earlier this strategy was successfully applied to the Standard Model [12]. We are applying this approach to construct the most general infrared (IR) action of the HL gravity coupled to fermionic matter. The action is based on some natural generalization of the standard Dirac operator. In our earlier works [3,13] we used the same type of Dirac operator to analyze the spectral dimension of the HL space-time (which was confirmed to be 2 for an arbitrary curved space-time) and to study the geodesic motion of a test particle in the HL gravity. The main result of the analysis of the geodesic motion was that in the case of the non-minimal coupling it differs from the motion naively calculated from the underlying Riemannian metric. Of course this result was not a big surprise, but what is important that in our approach the deviation from the Riemannian geodesics is controlled by the same Dirac operator that is used in the construction of the HL modification of the Einstein-Hilbert action. Potentially this might lead to some cancellations of the experimentally problematic effects. This urgently requires further studies. In the current work, we take this proposal to the next level and study the most general IR action in both, gravity and matte...

We calculate the closed analytic form of the solution of heat kernel equation for the anisotropic generalizations of flat Laplacian. We consider a UV as well as UV/IR interpolating generalizations. In all cases, the result can be expressed in terms of Fox-Wright psi-functions. We perform different consistency checks, analytically reproducing some of the previous numerical or qualitative results, such as spectral dimension flow. Our study should be considered as a first step towards the construction of a heat kernel for curved Hořava-Lifshitz geometries, which is an essential ingredient in the spectral action approach to the construction of the Hořava-Lifshitz gravity.

The synthesis and characterization of a series of cyclometallated complexes of Pd(ii) incorporating the mixed donor ligand 1-oxa-4,7-dithiacyclononane ([9]aneS2O) are presented in this study.

In this work, we propose an alternative approach to evaluate two-center overlap integrals. It is computationally more efficient than the standard procedure and is based on the deformed exponential function. In the new procedure, the CPU time to calculate each element of the overlap matrix (Sμ,ν) is constant and independent of the number of Gaussian primitives (NG), whereas in the usual procedure this time increases, formally, with NG2. To evaluate the accuracy of the proposed methodology, we computed different molecular properties such as dipole moments, hardness values, atomic charges, multicenter bond indices, group indices, and some thermodynamic properties. In this work, all calculations were performed using a minimal STO-6G basis set and WTBS and the double-ζ Pople split-valence 6-31G basis set on the Hartree–Fock (HF) and post-HF approximations. The integrals were parametrized for the atoms of the first two rows of the periodic table. All calculations were performed in the general ab initio quantum chemistry package GAMESS, where the integrals were implemented.