Related papers: The Spectral Analysis Inner Product for Quantum Gr…
We investigate tensor products of Hilbert complexes, in particular the (essential) spectrum of their Laplacians. It is shown that the essential spectrum of the Laplacian associated to the tensor product complex is computable in terms of the…
In this note, we present a generalization of some results concerning the spectral properties of a certain class of block matrices. As applications, we study some of its implications on nonnegative matrices, doubly stochastic matrices and…
Superconducting high kinetic inductance elements constitute a valuable resource for quantum circuit design and millimeter-wave detection. Granular aluminum (GrAl) in the superconducting regime is a particularly interesting material since it…
We study the dynamics of gravitons in a squeezed vacuum state under a thermal radiation background. Unlike traditional treatments that rely on the Boltzmann equation, we employ the Heisenberg equation and average it over general quantum…
We study the power spectral density of time delay fluctuations in an interferometer as a potential low-energy quantum gravitational observable. We derive a general expression for the spectrum in terms of the Wightman function of linear…
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
Indentation test is used with growing popularity for the characterization of various materials on different scales. Developed methods are combining the test with computer simulation and inverse analyses to assess material parameters…
Hilbert spaces in theories of gravity are notoriously subtle due to the Hamiltonian constraints, particularly regarding the inner product. To demystify this subject, we review and extend a collection of ideas in canonical gravity, and…
In this paper, we aim to explore the interplay between neutrinos and quantum gravity, illustrating some proposals about the use of these particles as probes for the supposed quantized structure of spacetime. The residual signatures of a…
In order to find the correct theory of quantum gravity, one has to look for observational effects in any candidate theory. Here, we focus on canonical quantum gravity and calculate the quantum-gravitational contributions to the anisotropy…
Integral invariants obtained from Principal Component Analysis on a small kernel domain of a submanifold encode important geometric information classically defined in differential-geometric terms. We generalize to hypersurfaces in any…
Quantum-gravity effects are expected to be suppressed by the Planck mass. For experimental progress it is therefore important to identify potential signatures from Planck-scale physics that are amenable to ultrahigh-precision tests. It is…
We reconstruct the quantum enveloping superalgebra ${\bf U}(\mathfrak{gl}_{m|n})$ over $\mathbb Q(v)$ via (finite dimensional) quantum Schur superalgebras. In particular, we obtain a new basis containing the standard generators of ${\bf…
We present a new model of quantum gravity as a theory of random geometries given explicitly in terms of a multitrace matrix model. This is a generalization of the usual discretized random surfaces of 2D quantum gravity which works away from…
The main purpose of this paper is to generalize and develop a few basic properties of the innerproduct space on a hypervector space. On this hypervector space we define the norm. Also we establish a important relation between normed…
A new inequality between angles in inner product spaces is formulated and proved. It leads directly to a concise statement and proof of the generalized Wielandt inequality, including a simple description of all cases of equality. As a…
In this paper, spectral Barron spaces are defined in the framework of quantum harmonic analysis. Their fundamental properties are studied. These include, among others, their completeness structure and some continuous embedding results. As…
Motivated by the dark energy issue, the minisuperspace approach for general relativistic cosmological theories is outlined.
Lisi, Marrone, and Montanino have recently proposed a test for quantum gravity induced decoherence effects in neutrino oscillations observed at Super-Kamiokande. We comment here that their equations have the same qualitative form as the…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…