Related papers: The QCD theta-parameter in canonical quantization
Manifestly non-Hermitian quantum graphs with real spectra are introduced and shown tractable as a new class of phenomenological models with several appealing descriptive properties. For illustrative purposes, just equilateral star-graphs…
We construct toral Chern-Simons theory with gauge group $\mathbb T=\mathfrak t/\Lambda\cong U(1)^n$ from an even, integral, nondegenerate symmetric bilinear form $K:\Lambda\times\Lambda\to\mathbb Z$ by geometric quantization via real…
We propose a grading protocol which assigns global symmetry associated phases to states in the Hilbert space. Without modifying the Hilbert space, this changes the state sum, a process that we call quantum distillation. We describe the…
A new set of gauge invariant variables is defined to describe the physical Hilbert space of $d = 3 + 1$ $SU(2)$ Yang-Mills theory in the fixed-time canonical formalism. A natural geometric interpretation arises due to the $GL(3)$ covariance…
One-dimensional unitary scattering controlled by non-Hermitian (typically, ${\cal PT}$-symmetric) quantum Hamiltonians $H\neq H^\dagger$ is considered. Treating these operators via Runge-Kutta approximation, our three-Hilbert-space…
For particles constrained on a curved surface, how to perform quantization within Dirac's canonical quantization scheme is a long-standing problem. On one hand, Dirac stressed that the Cartesian coordinate system has fundamental importance…
We investigate the relationship between symmetries and thermodynamic transformations by analyzing how global energy conservation and coherence resources affect the local dynamics of subsystems. We prove that U(1) conservation fundamentally…
We upper- and lower-bound the optimal precision with which one can estimate an unknown Hamiltonian parameter via measurements of Gibbs thermal states with a known temperature. The bounds depend on the uncertainty in the Hamiltonian term…
The entropy of a de Sitter horizon was derived long ago by Gibbons and Hawking via a gravitational partition function. Since there is no boundary at which to define the temperature or energy of the ensemble, the statistical foundation of…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
A powerful tool for studying geometrical problems in Hilbert space is developed. In particular, we study the quantum pure state tomography problem in finite dimensions from the point of view of dynamical systems and bifurcations theory.…
The paper addresses the quantization of minisuperspace cosmological models, with application to the Taub Model. By desparametrizing the model with an extrinsic time, a formalism is developed in order to define a conserved Schr\"{o}dinger…
We have calculated the quenching parameter, $\hat{q}$ in a model-independent way using the gauge-gravity duality. In earlier calculations, the geometry in the gravity side at finite temperature was usually taken as the pure AdS blackhole…
We propose a method to obtain physical quantities in the theta vacuum from those at fixed topology, which are different by finite size effects. Extending the work by Brower et al., we derive the formula to estimate these finite size…
The use of geometric methods has proved useful in the hamiltonian description of classical constrained systems. In this note we provide the first steps toward the description of the geometry of quantum constrained systems. We make use of…
The long-standing problem of time in canonical quantum gravity is the source of several conceptual and technical issues. Here, recent mathematical results are used to provide a consistent algebraic formulation of dynamical symplectic…
In this second paper on loop quantization of Gowdy model, we introduce the kinematical Hilbert space on which appropriate holonomies and fluxes are well represented. The quantization of the volume operator and the Gauss constraint is…
Starting from the temporal gauge Hamiltonian for classical pure Yang-Mills theory with the gauge group SU(2) a canonical transformation is initiated by parametrising the Gauss law generators with three new canonical variables. The…
Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…
Motivated by the notion that the mathematics of gravity can be reproduced from a statistical requirement of maximal entropy, we study the consequence of introducing an entropic source term in the Einstein-Hilbert action. For a spatially…