Continuous‐Representation Theory. V. Construction of a Class of Scalar Boson Field Continuous Representations

1965 ◽  
Vol 6 (1) ◽  
pp. 68-87 ◽  
Author(s):  
John R. Klauder ◽  
James McKenna
Keyword(s):  
Representation Theory ◽  
Continuous Representation ◽  
Boson Field ◽  
Scalar Boson ◽  
Continuous Representations

Continuous Representation Theory Using the Affine Group

1969 ◽  
Vol 10 (12) ◽  
pp. 2267-2275 ◽  
Author(s):  
Erik W. Aslaksen ◽  
John R. Klauder
Keyword(s):  
Representation Theory ◽  
Affine Group ◽  
Continuous Representation

scholarly journals Strongly Continuous Representations in the Hilbert Space: A Far-Reaching Concept

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 285
Author(s):  
Julio Marny Hoff da Silva ◽  
Gabriel Marcondes Caires da Rocha
Keyword(s):  
Hilbert Space ◽  
Representation Theory ◽  
Quantum Physics ◽  
Fundamental Notion ◽  
Significant Aspect ◽  
Projective Representations ◽  
Continuous Representations

We revisit the fundamental notion of continuity in representation theory, with special attention to the study of quantum physics. After studying the main theorem in the context of representation theory, we draw attention to the significant aspect of continuity in the analytic foundations of Wigner’s work. We conclude the paper by reviewing the connection between continuity, the possibility of defining certain local groups, and their relation to projective representations.

Preference orders and continuous representations

2011 ◽  
Vol 61 (1) ◽  
Author(s):  
Alessandro Caterino ◽  
Rita Ceppitelli ◽  
Ghanshyam Mehta
Keyword(s):  
Representation Theorem ◽  
Topological Spaces ◽  
Continuous Representation ◽  
Representation Theorems ◽  
Preference Orders ◽  
Separable Spaces ◽  
Path Connected ◽  
Continuous Representations ◽  
Connected Spaces

AbstractIn this paper we prove some general theorems on the existence of continuous order-preserving functions on topological spaces with a continuous preorder. We use the concepts of network and netweight to prove new continuous representation theorems and we establish our main results for topological spaces that are countable unions of subspaces. Some results in the literature on path-connected, locally connected and separably connected spaces are shown to be consequences of the general theorems proved in the paper. Finally, we prove a continuous representation theorem for hereditarily separable spaces.

Comparison of Monte Carlo Surface Exchange With Radiative Continuum Results in Large Particle Dispersions

2000 ◽  
Vol 122 (3) ◽  
pp. 503-508 ◽  
Author(s):  
E. Nisipeanu ◽  
P. D. Jones
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Radiation Intensity ◽  
Large Particle ◽  
Continuous Representation ◽  
Surface Exchange ◽  
Discontinuous Surface ◽  
Radiative Fluxes ◽  
Low Volume ◽  
Continuous Representations

A Monte Carlo technique follows radiation intensity rays through a dispersion of particles. Rays reflect from and are absorbed by the surfaces of the particles that they encounter. Transmitted radiative fluxes are compared with Monte Carlo simulations of a radiative continuum, using properties from both independent and correlated scattering theories. Whereas both discontinuous (surface) and continuous representations of the medium yield similar results for high porosities (low volume fractions), the continuous representation yields transmission overpredictions for porosities less than 0.9, using independent scattering properties, and for porosities less than 0.7, using correlated scattering properties. The overprediction is less severe for less reflective particle surfaces. [S0022-1481(00)01603-0]

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