Related papers: Nonperturbative late time asymptotics for heat ker…
A new noncommutative spacetime of structure $ {\cal M}^4 \times Z_2 \times Z_2$ is proposed. The generalized Hilbert-Einstein action contains gravity, all known interactions and Higgs field. This theory can also provide a unified geometric…
We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part $-\N^\mu\N_\mu$. Our…
Anomalous heat transport observed in low dimensional classical systems is associated to super-diffusive spreading of space-time correlation of the conserved fields in the system. This leads to non-local linear response relation between the…
We show how a nonlocal gravitational interaction can circumvent the Weinberg no-go theorem on cosmological constant, which forbids the existence of any solution to the cosmological constant problem within the context of local field theories…
We consider a multiplicatively renormalizable higher-derivative scalar theory which is used as an effective theory for quantum gravity at large distances (infrared phase of quantum gravity). The asymptotic regimes (in particular, the…
Using the heat kernel method, we compute nonrelativistic trace anomalies for Schr\"odinger theories in flat spacetime, with a generic background gauge field for the particle number symmetry, both for a free scalar and a free fermion. The…
The aim of this paper is threefold. First, we obtain the precise bounds for the heat kernel on isotropic Heisenberg groups by using well-known results in the three dimensional case. Second, we study the asymptotic estimates at infinity for…
We deepen the analysis of the cosmological acceleration produced by quantum gravity dynamics in the formalism of group field theory condensate cosmology, treated at the coarse-grained level via a phenomenological model, in the language of…
In quantum gravity perturbation theory in Newton's constant G is known to be badly divergent, and as a result not very useful. Nevertheless some of the most interesting phenomena in physics are often associated with non-analytic behavior in…
The aim of our paper is twofold. First, we present new mathematical developments on the analysis of de Gennes' hypothesis on the short-time asymptotics of the heat content for bounded domains with smooth boundary and with fractal boundary.…
Let $G$ be a simple, finite graph and let $p_t(x,y)$ denote the heat kernel on $G$. The purpose of this short note is to show that for $t \rightarrow 0^+$ $$ p_t(x,y) = \# \left\{\mbox{paths of…
We have recently constructed a manifestly local formulation of a nonlocal approach to the cosmological constant problem which can treat with quantum effects from both matter and gravitational fields. In this formulation, it has been…
In this paper, we employ probabilistic techniques to derive sharp, explicit two-sided estimates for the heat kernel of the nonlocal kinetic operator $$ \Delta^{\alpha/2}_v + v \cdot \nabla_x, \quad \alpha \in (0, 2),\ (x,v)\in {\mathbb…
We have constructed a non-relativistic theory of quantum mechanics based on local modulus symmetry. The resulting connection in the covariant derivative is identified as the escape velocity of the gravitational field. A new real and…
The noncommutative spectral action extends our familiar notion of commutative spaces, using the data encoded in a spectral triple on an almost commutative space. Varying a rather simple action, one can derive all of the standard model of…
We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…
The aim of this note is twofold. The first one is to find conditions on the asymptotic sequence which ensures differentiation of a general asymptotic expansion with respect to it. Our method results from the classical one but generalizes…
We clarify the relations between certain new coherent states for loop quantum gravity and the analytically continued heat kernel coherent states, highlighting the underlying general construction, the presence of a modified heat equation as…
A common tool in Casimir physics (and many other areas) is the asymptotic (high-frequency) expansion of eigenvalue densities, employed as either input or output of calculations of the asymptotic behavior of various Green functions. Here we…
In this work the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically…