Bibliografias temáticas: "Rule commutation"

1

Evans, D. Gwion, John E. Gough, and Matthew R. James. "Non-abelian Weyl commutation relations and the series product of quantum stochastic evolutions." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 370, no. 1979 (2012): 5437–51. http://dx.doi.org/10.1098/rsta.2011.0525.

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We show that the series product, which serves as an algebraic rule for connecting state-based input–output systems, is intimately related to the Heisenberg group and the canonical commutation relations. The series product for quantum stochastic models then corresponds to a non-abelian generalization of the Weyl commutation relation. We show that the series product gives the general rule for combining the generators of quantum stochastic evolutions using a Lie–Trotter product formula.

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2

Bulathsinghala, D. L., and K. A. I. L. Wijewardena Gamalath. "Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields." International Letters of Chemistry, Physics and Astronomy 48 (March 2015): 68–86. http://dx.doi.org/10.18052/www.scipress.com/ilcpa.48.68.

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In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

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3

Bulathsinghala, D. L., and K. A. I. L. Wijewardena Gamalath. "Implementation of a Quantized Line Element in Klein-Gordon and Dirac Fields." International Letters of Chemistry, Physics and Astronomy 48 (March 25, 2015): 68–86. http://dx.doi.org/10.56431/p-36k0sm.

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In this paper an ansatz that the anti-commutation rules hold only as integrated average over time intervals and not at every instant giving rise to a time-discrete form of Klein-Gordon equation is examined. This coarse-grained validation of the anti-commutation rules enables us to show that the relativistic energy-momentum relation holds only over discrete time intervals, fitting well with the time-energy uncertainty relation. When this time-discrete scheme is applied to four vector notations in relativity, the line-element can be quantized and thereby how the physical attributes associated with time, space and matter can be quantized is sketched. This potentially enables us to discuss the Zeno’s arrow paradox within the classical limit. As the solutions of the Dirac equation can be used to construct solutions to the Klein-Gordon equation, this temporal quantization rule is applied to the Dirac equation and the solutions associated with the Dirac equation under such conditions are interpreted. Finally, the general relativistic effects are introduced to a line-element associated with a particle in relativistic motion and a time quantized line-element associated with gravity is obtained.

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4

Narendran, Paliath, and Friedrich Otto. "Preperfectness is undecidable for thue systems containing only length-reducing rules and a single commutation rule." Information Processing Letters 29, no. 3 (1988): 125–30. http://dx.doi.org/10.1016/0020-0190(88)90049-x.

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5

Chin, Hee-Kwon. "The Study of the Commutation Principles (of General rule) in T’ang Code." Journal of Social Thoughts and Culture 21, no. 4 (2018): 143–71. http://dx.doi.org/10.17207/jstc.2018.12.21.4.5.

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6

Savasta, Salvatore, Omar Di Stefano, and Franco Nori. "Thomas–Reiche–Kuhn (TRK) sum rule for interacting photons." Nanophotonics 10, no. 1 (2020): 465–76. http://dx.doi.org/10.1515/nanoph-2020-0433.

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AbstractThe Thomas–Reiche–Kuhn (TRK) sum rule is a fundamental consequence of the position–momentum commutation relation for an atomic electron, and it provides an important constraint on the transition matrix elements for an atom. Here, we propose a TRK sum rule for electromagnetic fields which is valid even in the presence of very strong light–matter interactions and/or optical nonlinearities. While the standard TRK sum rule involves dipole matrix moments calculated between atomic energy levels (in the absence of interaction with the field), the sum rule here proposed involves expectation values of field operators calculated between general eigenstates of the interacting light–matter system. This sum rule provides constraints and guidance for the analysis of strongly interacting light–matter systems and can be used to test the validity of approximate effective Hamiltonians often used in quantum optics.

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7

Skála, Lubomír, and Vojtěch Kapsa. "Quantum Mechanics Needs No Interpretation." Collection of Czechoslovak Chemical Communications 70, no. 5 (2005): 621–37. http://dx.doi.org/10.1135/cccc20050621.

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Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule, probability density current, commutation and uncertainty relations, momentum operator, rules for including scalar and vector potentials and antiparticles can be derived from the definition of the mean values of powers of space coordinates and time. Equations of motion of quantum mechanics, the Klein-Gordon equation, Schrödinger equation and Dirac equation are obtained from the requirement of the relativistic invariance of the theory. The limit case of localized probability densities leads to the Hamilton-Jacobi equation of classical mechanics. Many-particle systems are also discussed.

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8

Chin, Hee-Kwon. "The Study of the Commutation Principles (of General rule) in T��ang Code." Journal of Social Thoughts and Culture 21, no. 04 (2018): 143–71. http://dx.doi.org/10.17207/jstc.2018.12.21.4.143.

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9

SOW, C. L., and T. T. TRUONG. "QUANTUM GROUP APPROACH TO A SOLUBLE VERTEX MODEL WITH GENERALIZED ICE RULE." International Journal of Modern Physics A 11, no. 10 (1996): 1747–61. http://dx.doi.org/10.1142/s0217751x96000936.

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Using the representation of the quantum group SL q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

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10

Derzhko, O. V., and A. Ph. Moina. "Bose commutation rule approximation in the theory of spin systems and elementary excitation spectrum." physica status solidi (b) 196, no. 1 (1996): 237–41. http://dx.doi.org/10.1002/pssb.2221960123.

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