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Spin Foams and Canonical Quantization [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2012 This review is devoted to the analysis of the mutual consistency of the spin foam and canonical loop quantizations in three and four spacetime dimensions.
Sergei Alexandrov +2 more
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Canonical quantization on the half-line and in an interval based upon an alternative concept for the momentum in a space with boundaries [PDF]
Physical Review Research, 2021 For a particle moving on a half-line or in an interval the operator p[over ̂]=−i∂_{x} is not self-adjoint and thus does not qualify as the physical momentum. Consequently canonical quantization based on p[over ̂] fails.
M. H. Al-Hashimi, U.-J. Wiese
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Canonical quantization of lattice Chern-Simons theory [PDF]
Journal of High Energy PhysicsWe discuss the canonical quantization of U(1) k Chern-Simons theory on a spatial lattice. In addition to the usual local Gauss law constraints, the physical Hilbert space is defined by 1-form gauge constraints implementing the compactness of the U(1 ...
Theodore Jacobson, Tin Sulejmanpasic
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Canonical Quantization of the Scalar Field: The Measure Theoretic Perspective [PDF]
Advances in Mathematical Physics, 2015 This review is devoted to measure theoretical methods in the canonical quantization of scalar field theories. We present in some detail the canonical quantization of the free scalar field. We study the measures associated with the free fields and present
José Velhinho
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Revisiting Canonical Quantization [PDF]
Modern Physics Letters A, 2012 Conventional canonical quantization procedures directly link various c-number and q-number quantities. Here, we advocate a different association of classical and quantum quantities that renders classical theory a natural subset of quantum theory with ...
J. Klauder
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Canonical quantization and topological theories [PDF]
Nuclear Physics B - Proceedings Supplements, 2000 The canonical quantization of the topological particle is described; it is shown that BRST quantization of the model gives the supersymmetric quantum mechanical model considered by Witten when investigating Morse theory, and the rigorous path integral method appropriate for this model is discussed.
Alice Rogers
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Impenetrable barriers and canonical quantization [PDF]
American Journal of Physics, 2004 We address an apparent conflict between the traditional canonical quantization framework of quantum theory and spatially restricted quantum dynamics when the translation invariance of an otherwise free quantum system is broken by boundary conditions. By considering the example of a particle in an infinite well, we analyze spectral problems for related ...
Piotr Garbaczewski, W. Karwowski
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Canonical quantization of electromagnetism in spatially dispersive media [PDF]
New Journal of Physics, 2014 We find the action that describes the electromagnetic field in a spatially dispersive, homogeneous medium. This theory is quantized and the Hamiltonian is diagonalized in terms of a continuum of normal modes. It is found that the introduction of nonlocal
S A R Horsley, T G Philbin
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Canonical quantization of macroscopic electromagnetism [PDF]
New Journal of Physics, 2010 Application of the standard canonical quantization rules of quantum field theory to macroscopic electromagnetism has encountered obstacles due to material dispersion and absorption.
T. Philbin
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New vertices and canonical quantization [PDF]
Physical Review D, 2010 We present two results on the recently proposed new spin foam models. First, we show how a (slightly modified) restriction on representations in the Engle-Pereira-Rovelli-Livine model leads to the appearance of the Ashtekar-Barbero connection, thus ...
S. Alexandrov
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