相关论文: Spectral Quadruples
Birkhoff's theorem is a classic result that characterizes locally spherically symmetric solutions of the Einstein equations. In this paper, we illustrate the consequences of its local nature for the cases of vacuum and positive cosmological…
Cosmology might turn out to be the study of fluctuations around a "de Sitter equilibrium" state. In this article I review the basic ideas and the attractive features of this framework, and respond to a number common questions raised about…
This Thesis presents some physically motivated criteria for the existence of particles and infra-particles in a given quantum field theory. It is based on a refined spectral theory of automorphism groups describing the energy-momentum…
The concept of an objective spatial direction in special relativity is investigated and theories assuming light-speed isotropy while accepting the existence of a privileged spatial direction are classified. A natural generalization of the…
We discuss the problem of introducing background spacetimes of the de Sitter type (quintessential backgrounds) in the context of fundamental theories involving supersymmetry. The role of a model presented in 1984, showing that these…
In contemporary applied and computational mathematics, a frequent challenge is to bound the expectation of the spectral norm of a sum of independent random matrices. This quantity is controlled by the norm of the expected square of the…
We describe progress towards constructing a quantum theory of de Sitter space in four dimensions. In particular we indicate how both particle states and Schwarzschild de Sitter black holes can arise as excitations in a theory of a finite…
Spectral triples are defined for C*-algebras associated with hyperbolic dynamical systems known as Smale spaces. The spectral dimension of one of these spectral triples is shown to recover the topological entropy of the Smale space.
This paper reviews work, largely due to W. Simon and the author, on multipole theory of static spacetimes. The main purpose is to make this work, which lies at the interface of potential theory, conformal geometry and general relativity,…
Axiomatic approach to measurement theory is developed. All the possible statistical properties of apparatuses measuring an observable with nondegenerate spectrum allowed in standard quantum mechanics are characterized.
Specutils is an Astropy affiliated package which provides a consistent interface to astronomical spectra (primarily 1D). As Specutils can be adapted to parse spectra in many different formats, Specutils plays a key role at Data Central,…
Embedding theorems have continued to be a topic of interest in the general theory of relativity since these help connect the classical theory to higher-dimensional manifolds. This paper deals with spacetimes of embedding class one, i.e.,…
A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in…
The paper intends to lay out the first steps towards constructing a unified framework to understand the symplectic and spectral theory of finite dimensional integrable Hamiltonian systems. While it is difficult to know what the best…
A new theory of fundamental physics is presented; it predicts that the new dimensions that may be observed by the Large Hadron Collider are timelike.
The quantum break-time of a system is the time-scale after which its true quantum evolution departs from the classical mean field evolution. For capturing it, a quantum resolution of the classical background - e.g., in terms of a coherent…
This is a summary of how the definition of quantum singularity is extended from static space-times to conformally static space-times. Examples are given.
It was recently demonstrated that time-dependent PDE problems can numerically be solved with a fully pseudospectral scheme, i.e. using spectral expansions with respect to both spatial and time directions (Hennig and Ansorg, 2009 [15]). This…
There have been many attempts to construct de Sitter space-times in string theory. While arguably there have been some successes, this has proven challenging, leading to the de Sitter swampland conjecture: quantum theories of gravity do not…
Exact and explicit string solutions in de Sitter spacetime are found. (Here, the string equations reduce to a sinh-Gordon model). A new feature without flat spacetime analogy appears: starting with a single world-sheet, several (here two)…