Related papers: Dilatation Operator and Space-time Geometry
The paper shortly presents the role of Stochastic Processes Theory in the present day Quantum Theory, and the relation to Operational Quantum Physics. The dynamics of an open quantum system is studied on a usual example from Quantum Optics,…
It is shown that the renormalisation group (RG) equation can be viewed as an equation for Lie transport of physical amplitudes along the integral curves generated by the $\beta$-functions of a quantum field theory. The anomalous dimensions…
Various results for higher-order perturbative calculations in the gradient-flow formalism are reviewed, including the gradient-flow beta function and the small-flow-time expansion of the hadronic vacuum polarization and the energy-momentum…
We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-operator, the six-vertex transfer matrix and fusion matrices are…
Paul Halmos' work in dilation theory began with a question and its answer: Which operators on a Hilbert space can be extended to normal operators on a larger Hilbert space? The answer is interesting and subtle. The idea of representing…
We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.
This article develops a variational formulation of relativistic nature applicable to the quantum mechanics context. The main results are obtained through basic concepts on Riemannian geometry. Standards definitions such as vector fields and…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In this series of lectures directed towards a mainly mathematically oriented audience I try to motivate the use of operator algebra methods in quantum field theory. Therefore a title as ``why mathematicians are/should be interested in…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…
We discuss physics-informed renormalisation group flows (PIRGs) for general operators. We show that operator PIRGs provide a comprehensive access to all correlation functions of the quantum field theory under investigation. The operator…
The problem of equivalency for linear differential operators of the first order is discussed.
A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki modular…
Motivated by the existence of cyclic phenomena in which some characteristics are mapped into corresponding ones over more than one phase, we introduce the $r$-cyclic operators with respect to a covering of a metric space and investigate…
Two-dimensional matterless dilaton gravity with arbitrary dilatonic potential can be discussed in a unitary way, both in the Lagrangian and canonical frameworks, by introducing suitable field redefinitions. The new fields are directly…
We discuss how to use the recent progress in understanding of the $x$-$y$ duality and symplectic duality in the theory of topological recursion and its generalizations in order to efficiently compute the quantum spectral curve operators for…
In a previous paper we have introduced a class of multiplications of distributions in one dimension. Here we furnish different generalizations of the original definition and we discuss some applications of these procedures to the…
We consider the radiation field operators in a cavity with varying dielectric medium in terms of solutions of Heisenberg's equations of motion for the most general one-dimensional quadratic Hamiltonian. Explicit solutions of these equations…
We argue that String Theory and Loop Quantum Gravity can be thought of as describing different regimes of a single unified theory of quantum gravity. LQG can be thought of as providing the pre-geometric exoskeleton out of which macroscopic…
We study a class of perturbative scalar quantum field theories where dynamics is characterized by Lorentz-invariant or Lorentz-breaking non-local operators of fractional order and the underlying spacetime has a varying spectral dimension.…