相关论文: Canonical General Relativity and Emergent Geometry
Building on the results of previous work, we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
Using the methods of symplectic geometry, we establish the existence of a canonical transformation from potential model Hamiltonians of standard form in a Euclidean space to an equivalent geometrical form on a manifold, where the…
We explore the possibility of emergent cosmology using the effective potential formalism. We discover new models of emergent cosmology which satisfy the constraints posed by the cosmic microwave background (CMB). We demonstrate that, within…
Determining properties of ground states of spin Hamiltonians remains a topic of central relevance connecting disciplines of mathematical, theoretical and applied physics. In the last few decades, ground state properties of physical systems…
We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing…
The phenomenon of emergent physics in condensed-matter many-body systems has become the paradigm of modern physics, and can probably also be applied to high-energy physics and cosmology. This encouraging fact comes from the universal…
We review the recent construction \cite{brower2024isingmodelmathbbs2} of the 2d Ising model on a triangulated sphere $\mathbb{S}^2$. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach…
We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity…
We consider a simpler geometrical formulation of General Relativity based on non-metricity, known as Coincident General Relativity. We study the ADM formulation of the theory and perform a detailed Hamiltonian analysis. We explicitly show…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
Einstein's general relativity with both metric and vielbein treated as independent fields is considered, demonstrating the existence of a consistent variational principle and deriving a Hamiltonian formalism that treats the spatial metric…
We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a…
In this thesis, the implications of a new cosmological model are studied, which has features similar to that of decaying vacuum cosmologies. Decaying vacuum (or cosmological constant \Lambda) models are the results of attempts to resolve…
The Covariant Canonical Gauge theory of Gravity is generalized by including at the Lagrangian level all possible quadratic curvature invariants. In this approach, the covariant Hamiltonian principle and the canonical transformation…
We systematically derive an action for a nonrelativistic spinning partile in flat background and discuss its canonical formulation in both Lagrangian and Hamiltonian approaches. This action is taken as the starting point for deriving the…
Using the formalism of differential equations, we introduce a new method to continuously deform the $s$-embeddings associated with a family of Ising models as their coupling constants vary. This provides a geometric interpretation of the…
Hadron properties and interactions are emergent from QCD. Atomic and condensed matter physics are emergent from QED. Could the local gauge symmetries of particle physics also be emergent? We give an introduction to this question and recent…
We discuss the reconstruction of generic 3+1-dimensional space-time geometries from covariant quantum spaces as backgrounds in the IKKT matrix model. An explicit recipe to realize generic classical geometries is provided. Even though this…
Inspired by the prospect of having discretized spaces emerge from random graphs, we construct a collection of simple and explicit exponential random graph models that enjoy, in an appropriate parameter regime, a roughly constant vertex…