Related papers: Functional integration for Regge gravity
Recent progress in the construction of both electric, coloured and magnetic charges in gauge theories will be presented. The topological properties of the charged sectors will be highlighted as well as the applications of this work to…
Integrally convex functions constitute a fundamental function class in discrete convex analysis, including M-convex functions, L-convex functions, and many others. This paper aims at a rather comprehensive survey of recent results on…
This paper presents the fractional trigonometric functions in complex-valued space and proposes a short outline of local fractional calculus of complex function in fractal spaces.
We give a complete characterization of all real-valued functions on the unit circle $S^1$ that can be represented by integrating the spherical distance on $S^1$ with respect to a signed measure or a probability measure.
We give a short review on the status of research on the theoretical foundations of $f(T)$ gravity theories. We discuss recent results on perturbative and non-perturbative approaches, causality and degrees of freedom, and discuss future…
Quantum gravity is studied in the path integral formulation applying the Regge calculus. Restricting the quadratic link lengths of the originally triangular lattice the path integral can be transformed to the partition function of a spin…
In this paper, we give explicit evaluation for some integrals involving polylogarithm functions of types $\int_{0}^{x}t^{m} Li_{p}(t)\mathrm{d}t$ and $\int_{0}^{x}\log^{m}(t) Li_{p}(t)\mathrm{d}t$. Some more integrals involving the…
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums…
It is found that the induced gravity with conformal couplings requires the conformal invariance in both classical and quantum levels for consistency. This is also true for the induced gravity with an extended conformal coupling interacting…
A formula which expresses logarithmic energy of Borel measures on R^n in terms of the Fourier transforms of the measures is established and some applications are given. In addition, using similar techniques a (known) formula for Riesz…
Functional version for the so-called Furuta parametric relative operator entropy is here investigated. Some related functional inequalities are also discussed. The theoretical results obtained by our functional approach immediately imply…
In this paper, we investigate a novel form of approximate orthogonality that is based on integral orthogonality. Additionally, we establish the fundamental properties of this new approximate orthogonality and examine its capability to…
We consider the maximal function of oscillatory integrals and prove a global estimate for radial test functions which is almost sharp with respect to the Sobolev regularity.
We will present a new proof of the Gromoll-Grove diameter rigidity theorem.
In a talk at the conference {\it Geometrical Foundations of Gravity at Tartu 2017}, it was suggested that the affine spacetime connection could be associated with purely fictitious forces. This leads to gravitation in a flat and smooth…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
An approach to the discrete quantum gravity based on the Regge calculus is discussed which was developed in a number of our papers. Regge calculus is general relativity for the subclass of general Riemannian manifolds called piecewise flat…
We prove some integral inequalities related to Feng Qi's inequality (2000) and obtain a few corollaries.
We shortly review the state of art and perspectives of Extended Theories of Gravity.
We derive the general rules of functional integration in the theories of Schwarzian type, thus completing the elaboration of Schwarzian functional integrals calculus initiated in \cite{(BShExact)}, \cite{(BShCorrel)}. Our approach is…