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For a stationary and axisymmetric black hole, there is a natural way to split the fields into a probe sector and a background sector. The equations of motion for the probe sector enjoy a significantly enhanced symmetry on the black hole…
Five fundamental scales of mass follow from holographic limitations, a self-similar law for angular momentum and the basic scaling laws for a fractal universe with dimension 2. The five scales correspond to the observable universe,…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
We consider the loop quantum theory of the spherically symmetric model of gravity coupled to Gaussian dust fields, where the Gaussian dust fields provide a material reference frame of the space and time to deparameterize gravity. This…
Starting with the Heisenberg-Weyl algebra, fundamental to quantum physics, we first show how the ordering of the non-commuting operators intrinsic to that algebra gives rise to generalizations of the classical Stirling Numbers of…
Two-dimensional lattices provide the arena for many physics problems of essential importance, a non-trivial symmetry in such lattices will help to reveal the underlying physics. Whether there is a directional scaling for the 2D lattices is…
We review the development of random-matrix theory (RMT) during the last decade. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the…
If gravity respects quantum mechanics, it is important to identify the essential postulates of a quantum framework capable of incorporating gravitational phenomena. Such a construct likely requires elimination or modification of some of the…
All possible Lie bialgebra structures on the harmonic oscillator algebra are explicitly derived and it is shown that all of them are of the coboundary type. A non-standard quantum oscillator is introduced as a quantization of a triangular…
With the discovery of a particle that seems rather consistent with the minimal Standard Model Higgs boson, attention turns to questions of naturalness, fine-tuning, and what they imply for physics beyond the Standard Model and its discovery…
This paper reveals a categorical equivalence connecting two distinct quantum logic structures. The first is the orthomodular lattice, an algebraic system designed to formalize the properties of quantum systems. The second is a finitary…
A spinning black hole with a much smaller black hole companion forms a fundamental gravitational system, like a colossal classical analog to an atom. In an appealing if imperfect analogy to atomic physics, this gravitational atom can be…
A generalized symmetry of a system of differential equations is an infinitesimal transformation depending locally upon the fields and their derivatives which carries solutions to solutions. We classify all generalized symmetries of the…
In recent years the umbral calculus has emerged from the shadows to provide an elegant correspondence framework that automatically gives systematic solutions of ubiquitous difference equations --- discretized versions of the differential…
We construct regular, asymptotically flat black holes of higher order scalar tensor (DHOST) theories, which are obtained by making use of a generalized Kerr-Schild solution generating method. The solutions depend on a mass integration…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
It is argued that the dynamics of an isolated system, due to the concrete procedure by which it is separated from the environment, has a non-Hamiltonian contribution. By a unified quantum field theoretical treatment of typical subdynamics,…
Dimensionally reduced spherically symmetric gravity and its generalization, generic 2-D dilaton gravity, provide ideal theoretical laboratories for the study of black hole quantum mechanics and thermodynamics. They are sufficiently simple…
We analyze general structure of N-fold supersymmetry which provides a systematic framework to construct weakly quasi-solvable quantum mechanical systems. Main ingredients of our analysis are dimensional analysis and introduction of an…
The extension of the general relativity theory to higher dimensions, so that the field equations for the metric remain of second order, is done through the Lovelock action. This action can also be interpreted as the dimensionally continued…