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Entropies associated with spatial subsystems in conventional local quantum field theories are typically divergent when the spatial regions have boundaries. However, in certain linear combinations of the entropies for various subsystems,…

High Energy Physics - Theory · Physics 2025-09-01 Mark Van Raamsdonk

We address numerical challenges in solving hyperbolic free boundary problems described by spherically symmetric conservation laws that arise in the modeling of tumor growth due to immune cell infiltrations. In this work, we normalize the…

Numerical Analysis · Mathematics 2018-09-11 Xianyi Zeng , Mashriq Ahmed Saleh , Jianjun Paul Tian

We apply the notion of polar duality from convex geometry to the study of quantum covariance ellipsoids in symplectic phase space. We consider in particular the case of "quantum blobs" introduced in previous work; quantum blobs are the…

Quantum Physics · Physics 2022-08-24 Maurice de Gosson , Charlyne de Gosson

The purpose of this paper is twofold: On the one hand, after a thorough review of the matter free case, we supplement the derivations in our companion paper on 'loop quantum gravity without the Hamiltonian constraint' with calculational…

General Relativity and Quantum Cosmology · Physics 2013-05-14 Norbert Bodendorfer , Alexander Stottmeister , Andreas Thurn

We describe the programming method for generating the spectrum of bound states for relativistic quantum field theories using the nonperturbative Hamiltonian approach of Discretized Light-Cone Quantization. The method is intended for…

High Energy Physics - Theory · Physics 2007-05-23 Stephan Elser , Hans-Christian Pauli , Alex C. Kalloniatis

The open string on the plane-wave limit of $dS_n\times S^n $ with constant $B_2$ and dilaton background fields is canonically quantized. This entails solving the classical equations of motion for the string, computing the symplectic form,…

High Energy Physics - Theory · Physics 2008-11-26 G. Horcajada , F. Ruiz Ruiz

Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…

Cosmology and Nongalactic Astrophysics · Physics 2021-01-01 Julien Grain , Vincent Vennin

There exists a physically well motivated method for approximating manifolds by certain topological spaces with a finite or a countable set of points. These spaces, which are partially ordered sets (posets) have the power to effectively…

High Energy Physics - Theory · Physics 2009-10-22 A. P. Balachandran , G. Bimonte , E. Ercolessi , P. Teotonio-Sobrinho

We introduce geometric quantization for constant rank presymplectic structures with Riemannian null foliation and compact leaf closure space. We prove a quantization-commutes-with-reduction theorem in this context. Examples related to…

Symplectic Geometry · Mathematics 2022-09-29 Yi Lin , Yiannis Loizides , Reyer Sjamaar , Yanli Song

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…

Quantum Physics · Physics 2024-04-12 Andrew Osborne , Trevyn Larson , Sarah Jones , Ray W. Simmonds , András Gyenis , Andrew Lucas

Classical physics is reformulated as a constrained Hamiltonian system in the history phase space. Dynamics, i.e. the Euler-Lagrange equations, play the role of first-class constraints. This allows us to apply standard methods from the…

High Energy Physics - Theory · Physics 2007-05-23 T. A. Larsson

We advocate an alternative description of canonical gravity in 3+1 dimensions, obtained by using as the basic variable a real variant of the usual Ashtekar connection variables on the spatial three-manifold. With this ansatz, no non-trivial…

General Relativity and Quantum Cosmology · Physics 2007-05-23 R. Loll

In the usual approaches to mechanics (classical or quantum) the primary object of interest is the Hamiltonian, from which one tries to deduce the solutions of the equations of motion (Hamilton or Schr\"odinger). In the present work we…

Mathematical Physics · Physics 2020-03-09 Maurice A. de Gosson

A complete quantization of a homogeneous and isotropic spacetime with closed spatial sections coupled to a massive scalar field is provided, within the framework of Loop Quantum Cosmology. We identify solutions with their initial data on…

General Relativity and Quantum Cosmology · Physics 2012-08-31 Mikel Fernández-Méndez , Guillermo A. Mena Marugán , Javier Olmedo

A (1+1)-dimensional quantum field theory with a degenerate vacuum (in infinite volume) can contain particles, known as kinks, which interpolate between different vacua and have nontrivial restrictions on their multi-particle Hilbert space.…

High Energy Physics - Theory · Physics 2009-10-22 Timothy R. Klassen , Ezer Melzer

The method of geometric quantization is applied to a particle moving on an arbitrary Riemannian manifold $Q$ in an external gauge field, that is a connection on a principal $H$-bundle $N$ over $Q$. The phase space of the particle is a…

High Energy Physics - Theory · Physics 2015-06-26 M. A. Robson

Using non-relativistic effective Lagrangians in the particle-dimer picture, we rederive the expression for the energy shift of a loosely bound three-particle bound state of identical bosons in the unitary limit. The effective field theory…

High Energy Physics - Lattice · Physics 2017-10-25 H. -W. Hammer , J. -Y. Pang , A. Rusetsky

We construct a symplectic realisation of the twisted Poisson structure on the phase space of an electric charge in the background of an arbitrary smooth magnetic monopole density in three dimensions. We use the extended phase space…

High Energy Physics - Theory · Physics 2018-08-15 Vladislav G. Kupriyanov , Richard J. Szabo

The aim of this article is to study the functorial properties of the ``formal geometric quantization'' procedure which is defined for non-compact Hamiltonian manifolds (when the moment map is proper). For this purpose, we introduce a…

Symplectic Geometry · Mathematics 2007-05-23 Paul-Emile Paradan

We present a new method for the quantization of totally constrained systems including general relativity. The method consists in constructing discretized theories that have a well defined and controlled continuum limit. The discrete…

General Relativity and Quantum Cosmology · Physics 2008-11-26 Miguel Campiglia , Cayetano Di Bartolo , Rodolfo Gambini , Jorge Pullin