Related papers: Construction and Properties of the Ground State of…
Given a reflexive Banach space $X$, we consider a class of functionals $\Phi \in C^1(X,\Re)$ that do not behave in a uniform way, in the sense that the map $t \mapsto \Phi(tu)$, $t>0$, does not have a uniform geometry with respect to $u\in…
Let $\alpha : {\mathbb R} \to Aut(G)$ define a continuous ${\mathbb R}$-action on the topological group $G$. A unitary representation $\pi^\flat$ of the extended group $G^\flat := G \rtimes_\alpha {\mathbb R}$ is called a ground state…
Quantum state wave functionals are constructed in exact form for the graviton-like field theory obtained by breaking down the topological symmetry of the string action related with the Euler characteristic of the world-surface; their…
The physical, observable spectrum in gauge theories is made up from gauge-invariant states. The Fr\"ohlich-Morchio-Strocchi mechanism allows in the standard model to map these states to the gauge-dependent elementary $W$, $Z$ and Higgs…
We consider a continuous dynamical system $f:X\to X$ on a compact metric space $X$ equipped with an $m$-dimensional continuous potential $\Phi=(\phi_1,\cdots,\phi_m):X\to \bR^m$. We study the set of ground states $ GS(\alpha)$ of the…
We present a broad class of spherical thin shells of matter in F(R) gravity. We show that the corresponding junction conditions determine the equation of state between the energy density and the pressure/tension at the surface. We analyze…
In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…
Given a category C acted on by the loop group G((t)), we define its Whittaker model Whit(C) as C^{N((t)),\chi}, where \chi is a non-degenerate character. We study the properties of this construction. When C is the category of sheaves on the…
The flatness of an accelerating universe model (characterized by a dark energy scalar field $\chi$) is mimicked from a curved model that is filled with, apart from the cold dark matter component, a quintessencelike scalar field $Q$. In this…
Let $G$ be a finite group and $Ch_i(G)$ some quantitative sets. In this paper we study the influence of $Ch_i(G)$ to the structure of $G$. We present a survey of author and his colleagues' recent works.
An important but little-studied property of spin glasses is the stability of their ground states to changes in one or a finite number of couplings. It was shown in earlier work that, if multiple ground states are assumed to exist, then…
In this paper we develop a theory of stability for $G$-categories (presheaf of categories on the orbit category of $G$), where $G$ is a finite group. We give a description of Mackey functors as $G$-commutative monoids exploit it to…
By introducing a phase field and solving the eigen-functional equation of particles, we obtain the exact expressions of the ground state energy as a functional of the particle density for interacting electron/boson systems, and a…
In this article, we provide a Stein type characterization for $G$-normal distributions: Let $\mathcal{N}[\varphi]=\max_{\mu\in\Theta}\mu[\varphi],\ \varphi\in C_{b,Lip}(\mathbb{R}),$ be a sublinear expectation. $\mathcal{N}$ is $G$-normal…
We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and…
We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $\eta G^{\mu\nu}\phi_{,\mu}\phi_{,\nu}$, where $\eta$ is an arbitrary coupling parameter, and…
In this paper we discuss the categorical properties of $\mathbb{Z}$-graded manifolds. We start by describing the local model paying special attention to the differences in comparison to the $\mathbb{N}$-graded case. In particular we explain…
We study Chern numbers to characterize the ground state of strongly interacting systems on a lattice. This method allows us to perform a numerical characterization of bosonic fractional quantum Hall (FQH) states on a lattice where…
We prove that the category $\textbf{G-Cat}$ of small categories with $G$-action forms a model of unstable $G$-global homotopy theory for every discrete group $G$, generalizing Schwede's global model structure on $\textbf{Cat}$. As a…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…