Covariant Harmonic Oscillators and the Quark Model

Kim, Y. S.; Noz, Marilyn E.

doi:10.1007/978-94-009-3051-3_19

Cited by 9 publications

(19 citation statements)

References 21 publications

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“…What is new in this paper? In our first paper on this subject [44], we started with a Lorentz-covariant Gaussian form proposed by Yukawa's in his 1953 paper [8], and its applications to high-energy physics [45,46,47,48,49]. We were particularly interested in how the Gaussian form becomes deformed under Lorentz boosts.…”

Section: Discussionmentioning

confidence: 99%

Entropy and Temperature from Entangled Space and Time

Kim

Noz²

2014

PSIJ

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Two coupled oscillators provide a mathematical instrument for solving many problems in modern physics, including squeezed states of light and Lorentz transformations of quantum bound states. The concept of entanglement can also be studied within this mathematical framework. For the system of two entangled photons, it is of interest to study what happens to the remaining photon if the other photon is not observed. It is pointed out that this problem is an issue of Feynman's rest of the universe. For quantum bound-state problems, it is pointed out the longitudinal and time-like coordinates become entangled when the system becomes boosted. Since time-like oscillations are not observed, the problem is exactly like the two-photon system where one of the photons is not observed. While the hadron is a quantum bound state of quarks, it appears quite differently when it moves rapidly than when it moves slowly. For slow hadrons, Gell-Mann's quark model is applicable, while Feynman's parton model is applicable to hadrons with their speeds close to that of light. While observing the temperature dependence of the speed, it is possible to explain the quark-to-parton transition as a phase transition.to be published in the Physical Science International Journal.

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Section: Discussionmentioning

confidence: 99%

Entropy and Temperature from Entangled Space and Time

Kim

Noz²

2014

PSIJ

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“…The series of the form of Eq. (1) was developed earlier for studying harmonic oscillators in moving frames [24,20,25,26,27,28]. Here z and t are the space-like and time-like separations between the two constituent particles bound together by a harmonic oscillator potential.…”

Section: Space-time Entanglementmentioning

confidence: 99%

“…where the x and y variables are replaced by z and t respectively. If Lorentz-boosted, this Gaussian function becomes squeezed to [24,20,25]…”

Section: Space-time Entanglementmentioning

confidence: 99%

“…In Sec. 8, we note that most of the mathematical formulas in this paper have been used earlier for understanding relativistic extended particles in the Lorentz-covariant harmonic oscillator formalism [24,20,25,26,27,28]. These formulas allow us to transport the concept of entanglement from the current problem of physics to quantum bound states in the Lorentz-covariant world.…”

Section: Introductionmentioning

confidence: 95%

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Entangled Harmonic Oscillators and Space-Time Entanglement

2016

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Abstract:The mathematical basis for the Gaussian entanglement is discussed in detail, as well as its implications in the internal space-time structure of relativistic extended particles. It is shown that the Gaussian entanglement shares the same set of mathematical formulas with the harmonic oscillator in the Lorentz-covariant world. It is thus possible to transfer the concept of entanglement to the Lorentz-covariant picture of the bound state, which requires both space and time separations between two constituent particles. These space and time variables become entangled as the bound state moves with a relativistic speed. It is shown also that our inability to measure the time-separation variable leads to an entanglement entropy together with a rise in the temperature of the bound state. As was noted by Paul A. M. Dirac in 1963, the system of two oscillators contains the symmetries of the O(3, 2) de Sitter group containing two O(3, 1) Lorentz groups as its subgroups. Dirac noted also that the system contains the symmetry of the Sp(4) group, which serves as the basic language for two-mode squeezed states. Since the Sp(4) symmetry contains both rotations and squeezes, one interesting case is the combination of rotation and squeeze, resulting in a shear. While the current literature is mostly on the entanglement based on squeeze along the normal coordinates, the shear transformation is an interesting future possibility. The mathematical issues on this problem are clarified.

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“…The relativistic harmonic oscillator appeared in the first works of Born on reciprocity [2,3] and in the context of the study of relativistic bound states [4,5] (see [6,7] for recent analysis and more references). In our context is that the coordinate x subject to the harmonic oscillator potential is not a relative position between two constituents, but the actual coordinate of the particle.…”

Section: Introductionmentioning

confidence: 99%

A cosmology of a trans-Planckian theory and dark energy

Bolognesi

2014

Int. J. Mod. Phys. D

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We investigate a model based on a generalized version of the Fourier transform for curved spacetime manifolds. This model is possible if the metric has an asymptotic flat region which allows a duality to be implement between coordinates and momenta, hence, the model's name, trans-Planckian. The theory and the action are based on the postulate of the absolute egalitarian relation between coordinates x and momenta p. We show how to implement this construction in a cosmological setting, on a Friedman-Robertson-Walker (FRW) metric background, where the asymptotic time infinity plays the role of the required asymptotic flat region. We discuss the effect of gravity, and, in particular, of the Hubble expansion of the universe scale factor on the Fourier map. The dual-inflationary stage is responsible for making the dual-sector of the action inaccessible at ordinary low energies. We propose a scenario in which an effective positive cosmological constant is caused by how the dual-sector of the theory affects the equation of state for matter particles. © 2014 World Scientific Publishing Company

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Covariant Harmonic Oscillators and the Quark Model

Cited by 9 publications

References 21 publications

Entropy and Temperature from Entangled Space and Time

Entropy and Temperature from Entangled Space and Time

Entangled Harmonic Oscillators and Space-Time Entanglement

A cosmology of a trans-Planckian theory and dark energy

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