Related papers: General Formulation of Topos Many-Node Theory
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
This letter describes a novel derivation of general relativity by considering the (non)self-consistency of theories whose Hamiltonians are constraints. The constraints, from Hamilton's equations, generate the evolution, while the evolution,…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
"Quantum Topology" deals with the general quantum theory as the theory of the functional quantum space; space time and energy momentum forms form a connected manifold; a functional quantum space on the quantum level. The general quantum…
We develop the Hamiltonian theory of axial perturbations around a general time-dependent spherical background spacetime. Using the fact that the linearized constraints are gauge generators, we isolate the physical and unconstrained axial…
We generalise Langlois' Hamiltonian treatment of gauge-invariant linear cosmological perturbations to a cosmological setting with multiple scalar fields minimally coupled to gravity. We review the Hamilton-Jacobi-like technique for a…
Concise, accurate descriptions of physical systems through their conserved quantities abound in the natural sciences. In data science, however, current research often focuses on regression problems, without routinely incorporating…
A variety of local index formulas is constructed for quantum Hamiltonians with periodic boundary conditions. All dimensions of physical space as well as many symmetry constraints are covered, notably one-dimensional systems in Class DIII as…
The intrinsic non-linearities of the spin dynamics in condensed matter systems give rise to a rich phenomenology that can be strongly affected by topology. Here we study formation of magnonic solitons in the topologically nontrivial bandgap…
The main purpose of this paper is to give a topological and symplectic classification of completely integrable Hamiltonian systems in terms of characteristic classes and other local and global invariants.
Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization…
The system of N particles moving on a circle and interacting via a global repulsive cosine interaction is well known to display spatially inhomogeneous structures of extraordinary stability starting from certain low energy initial…
Preparing general relativity for quantization in the Hamiltonian approach leads to the `problem of time,' rendering the world fundamentally timeless. One proposed solution is the `thermal time hypothesis,' which defines time in terms of…
Random matrix theory yields valuable insights into the universal features of quantum many-body chaotic systems. Although all-to-all interactions are traditionally studied, many interesting dynamical questions, such as transport of a…
Classical field theory is considered as a theory of unparametrized surfaces embedded in a configuration space, which accommodates, in a symmetric way, spacetime positions and field values. Dynamics is defined via the (Hamiltonian)…
Topological defects and smooth excitations determine the properties of systems showing collective order. We introduce a generic non-singular field theory that comprehensively describes defects and excitations in systems with $O(n)$ broken…
Microscopically conserving reduced models of many-body systems have a long, highly successful history. Established theories of this type are the random-phase approximation for Coulomb fluids and the particle-particle ladder model for…
Graphs are topological spaces that include broader objects than discretized manifolds, making them interesting playgrounds for the study of quantum phases not realized by symmetry breaking. In particular they are known to support anyons of…
We extend random matrix theory to consider randomly interacting spin systems with spatial locality. We develop several methods by which arbitrary correlators may be systematically evaluated in a limit where the local Hilbert space dimension…
Gravity, and the puzzle regarding its energy, can be understood from a gauge theory perspective. Gravity, i.e., dynamical spacetime geometry, can be considered as a local gauge theory of the symmetry group of Minkowski spacetime: the…