Search results for "Canon"

Coordinate-free quantization of first-class constrained systems

1996

The coordinate-free formulation of canonical quantization, achieved by a flat-space Brownian motion regularization of phase-space path integrals, is extended to a special class of closed first-class constrained systems that is broad enough to include Yang-Mills type theories with an arbitrary compact gauge group. Central to this extension are the use of coherent state path integrals and of Lagrange multiplier integrations that engender projection operators onto the subspace of gauge invariant states.

Electronic Processes in Solid State: Dirac Framework

2019

The present paper proposes canonical Dirac framework adapted for application to the electronic processes in solid state. The concern is a spatially periodic structure of atoms distinguished by birth and annihilation of particle states excited due to interaction with the electromagnetic field. This implies replacing the conventional energy-momentum relation specific of the canonical Dirac framework and permissible for particle physics by a case specific relation available for the solid state. The advancement is a unified and consistent mathematical framework incorporating the Hilbert space, the quantum field, and the special relativity. Essential details of the birth and annihilation of the …

All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order

2019

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions. Our results provide the complete set of two-loop Feynman integrals for any massless 2→3 scattering process, thereby opening up a ne…

Determination of the origin and magnitude of logarithmic finite-size effects on interfacial tension: Role of interfacial fluctuations and domain brea…

2014

The ensemble-switch method for computing wall excess free energies of condensed matter is extended to estimate the interface free energies between coexisting phases very accurately. By this method, system geometries with linear dimensions $L$ parallel and $L_z$ perpendicular to the interface with various boundary conditions in the canonical or grandcanonical ensemble can be studied. Using two- and three-dimensional Ising models, the nature of the occurring logarithmic finite size corrections is studied. It is found crucial to include interfacial fluctuations due to "domain breathing".

2016

The wealth of sensory data coming from different modalities has opened numerous opportunities for data analysis. The data are of increasing volume, complexity and dimensionality, thus calling for new methodological innovations towards multimodal data processing. However, multimodal architectures must rely on models able to adapt to changes in the data distribution. Differences in the density functions can be due to changes in acquisition conditions (pose, illumination), sensors characteristics (number of channels, resolution) or different views (e.g. street level vs. aerial views of a same building). We call these different acquisition modes domains, and refer to the adaptation problem as d…

Suspensions of rod-like colloids and a depleting agent under confinement

2008

We present a computer simulation study of suspensions of rod-like colloids and a depletant in confinement to a slit-pore. Mixtures of hard spherocylinders and ideal spheres were studied by means of Monte Carlo simulations in the grand canonical ensemble. By use of finite size scaling analysis we determined the critical behaviour. In order to overcome large barriers in the free energy we applied the successive umbrella sampling method (Virnau and Muller 2004 J. Chem. Phys. 120 10925). We find that, under confinement, the critical point of gas–liquid demixing shifts to higher concentrations of rods and smaller concentrations of spheres due to the formation of an orientationally ordered surfac…

A Quantum Mechanical Model of the Reissner-Nordstrom Black Hole

1997

We consider a Hamiltonian quantum theory of spherically symmetric, asymptotically flat electrovacuum spacetimes. The physical phase space of such spacetimes is spanned by the mass and the charge parameters $M$ and $Q$ of the Reissner-Nordstr\"{o}m black hole, together with the corresponding canonical momenta. In this four-dimensional phase space, we perform a canonical transformation such that the resulting configuration variables describe the dynamical properties of Reissner-Nordstr\"{o}m black holes in a natural manner. The classical Hamiltonian written in terms of these variables and their conjugate momenta is replaced by the corresponding self-adjoint Hamiltonian operator, and an eigenv…

Covariant phase-space quantization of the induced 2D gravity

1993

Abstract We study in a parallel way the induced 2D gravity and the Jackiw-Teitelboimmodel on the cylinder from the viewpoint of the covariant description of canonical formalism. We compute explicity thhe symplectic structure of both theories showing that their (reduced) phase spaces are finite-dimensional cotangent bundles. For the Jackiw-Teitelboim model the base space (configuration space) is the space of conjugacy classes of the PSL(2, R ) group. For the induced 2D gravity, and Λ > 0, the (reduced) phase space consist of two (identical) connected components each one isomorphic to the contangent bundle of the space of hyperbolic conjugacy classes of the PSL (2, R ) group, whereas for Λ R …

The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics

2020

We know that in Hamiltonian systems a dynamic function f(q, p) develops in time according to

Fundamental Principles of Quantum Mechanics

2001

There are two alternative methods of quantizing a system: a) quantization via the Feynman Path Integral (equivalent to Schwinger’s Action Principle); b) canonical quantization.