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268
Potential approximations to δ′: an inverse Klauder phenomenon with normresolvent convergence
 COMMUN. MATH. PHYS
, 2001
"... We show that there is a family Schrödinger operators with scaled potentials which approximates the δ′interaction Hamiltonian in the normresolvent sense. This approximation, based on a formal scheme proposed by Cheon and Shigehara, has nontrivial convergence properties which are in several respects ..."
Grounding in communication
 In
, 1991
"... We give a general analysis of a class of pairs of positive selfadjoint operators A and B for which A + XB has a limit (in strong resolvent sense) as h10 which is an operator A, # A! Recently, Klauder [4] has discussed the following example: Let A be the operator(d2/A2) + x2 on L2(R, dx) and let ..."
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Cited by 1082 (19 self)
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forms and strong resolvent convergence; see e.g. [3], [5]. Once one decides to analyze Klauder’s phenomenon in the language of quadratic forms, the phenomenon is quite easy to understand and control. In fact, the theory is implicit in Kato’s book [3, VIII.31.
On conformal field theories
 in fourdimensions,” Nucl. Phys. B533
, 1998
"... We review the generalization of field theory to spacetime with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last ..."
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Cited by 366 (1 self)
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We review the generalization of field theory to spacetime with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known to emerge from limits of M theory and string theory, and to describe quantum Hall states. In the last few years they have been studied intensively, and many qualitatively new phenomena have been discovered, both on the classical and quantum level. Submitted to Reviews of Modern Physics.
An example of double confluent Heun equation: Schrödinger equation with supersingular plus Coulomb potential
, 2009
"... A recently proposed algorithm to obtain global solutions of the double confluent Heun equation is applied to solve the quantum mechanical problem of finding the energies and wave functions of a particle bound in a potential sum of a repulsive supersingular term, A r −4, plus an attractive Coulombian ..."
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being the adequate definition of the S matrix. On the other hand, concerned with bound states, a considerable interest on repulsive singular potentials added to an attractive regular one was arisen by the seminal paper of Klauder [7], where the today known as “Klauder phenomenon” was reported. As shown
COHERENT STATES ASSOCIATED TO THE WAVEFUNCTIONS AND THE SPECTRUM OF THE ISOTONIC OSCILLATOR
, 2004
"... Abstract. Classes of coherent states are presented by replacing the labeling parameter z of KlauderPerelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic oscillator Hamiltonian are presented and these states ..."
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Abstract. Classes of coherent states are presented by replacing the labeling parameter z of KlauderPerelomov type coherent states by confluent hypergeometric functions with specific parameters. Temporally stable coherent states for the isotonic oscillator Hamiltonian are presented and these states
Quantum chromodynamics and other field theories on the light cone
, 1997
"... In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground s ..."
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Cited by 65 (14 self)
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In recent years lightcone quantization of quantum field theory has emerged as a promising method for solving problems in the strong coupling regime. The approach has a number of unique features that make it particularly appealing, most notably, the ground state of the free theory is also a ground state of the full theory. We discuss the lightcone quantization of gauge theories from two perspectives: as a calculational tool for representing hadrons as QCD boundstates of relativistic quarks and gluons, and also as a novel method for simulating quantum field theory on a computer. The lightcone Fock state expansion of wavefunctions provides a precise definition of the parton model and a general calculus for hadronic matrix elements. We present several new applications of lightcone Fock methods, including calculations of exclusive weak decays of heavy hadrons, and intrinsic heavyquark contributions to structure functions. A general nonperturbative method for numerically solving quantum field theories, “discretized lightcone quantization”, is outlined and applied to several gauge theories. This method is invariant under the
Between classical and quantum
, 2008
"... The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, inclu ..."
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Cited by 37 (5 self)
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The relationship between classical and quantum theory is of central importance to the philosophy of physics, and any interpretation of quantum mechanics has to clarify it. Our discussion of this relationship is partly historical and conceptual, but mostly technical and mathematically rigorous, including over 500 references. For example, we sketch how certain intuitive ideas of the founders of quantum theory have fared in the light of current mathematical knowledge. One such idea that has certainly stood the test of time is Heisenberg’s ‘quantumtheoretical Umdeutung (reinterpretation) of classical observables’, which lies at the basis of quantization theory. Similarly, Bohr’s correspondence principle (in somewhat revised form) and Schrödinger’s wave packets (or coherent states) continue to be of great importance in understanding classical behaviour from quantum mechanics. On the other hand, no consensus has been reached on the Copenhagen Interpretation, but in view of the parodies of it one typically finds in the literature we describe it in detail. On the assumption that quantum mechanics is universal and complete, we discuss three ways in which classical physics has so far been believed to emerge from quantum physics, namely
Open Access JMP Conventional and Enhanced Canonical Quantizations, Application to Some Simple Manifolds
, 2013
"... Copyright © 2013 Gabriel Y. H. Avossevou et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. It is well known that the representat ..."
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is studied in the framework of the conventional quantization scheme as well as that of the enhanced quantization recently introduced by J. R. Klauder [arXiv:quantph/1204.2870]. The quantum action functional restricted to the phase space coherent states is obtained from the enhanced quantization procedure
1 hepth/0205027
, 2002
"... This is my contribution to the proceedings of Stephen Hawking’s 60th birthday celebration. If the ideas of TeV scale gravity are correct, then black holes should be produced at accelerators that probe the TeV scale, and their decays should evidence one of Stephen’s greatest discoveries, the phenomen ..."
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