Institute for Particle, Nuclear and Astronomical Sciences (IPNAS)

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Browsing Institute for Particle, Nuclear and Astronomical Sciences (IPNAS) by Author "Chang, Lay Nam"

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    Classical Implications of the Minimal Length Uncertainty Relation
    Benczik, S. Z.; Chang, Lay Nam; Minic, Djordje; Okamura, Naotoshi; Rayyan, S.; Takeuchi, Tatsu (2002-09-12)
    We study the phenomenological implications of the classical limit of the "stringy" commutation relations [x_i,p_j]=i hbar[(1+beta p^2) delta_{ij} + beta' p_i p_j]. In particular, we investigate the "deformation" of Kepler's third law and apply our result to the rotation curves of gas and stars in spiral galaxies.
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    Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem
    Chang, Lay Nam; Minic, Djordje; Okamura, Naotoshi; Takeuchi, Tatsu (American Physical Society, 2002-06-15)
    We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation [(x) over cap (i),(p) over cap (j)]=i (h) over bar[(1+beta(p) over cap (2))delta(ij)+beta(')(p) over cap (i)(p) over cap (j)]. We point out that this relation, which is an example of a UV/IR relation, implies the finiteness of the cosmological constant. While our result does not solve the cosmological constant problem, it does shed new light on the relation between this outstanding problem and UV/IR correspondence. We also point out that the blackbody radiation spectrum will be modified at higher frequencies, but the effect is too small to be observed in the cosmic microwave background spectrum.
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    Exact solution of the harmonic oscillator in arbitrary dimensions with minimal length uncertainty relations
    Chang, Lay Nam; Minic, Djordje; Okamura, Naotoshi; Takeuchi, Tatsu (American Physical Society, 2002-06-15)
    We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations [(x) over cap (i),(p) over cap (j)]=i (h) over bar[(1+beta(p) over cap (2))delta(ij)+beta(')(p) over cap (i)(p) over cap (j)]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relations which appear in perturbative string theory. Our solutions illustrate how certain features of string theory may manifest themselves in simple quantum mechanical systems through the modification of the canonical commutation relations. We discuss whether such effects are observable in precision measurements on electrons trapped in strong magnetic fields.
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    Hydrogen-atom spectrum under a minimal-length hypothesis
    Benczik, S. Z.; Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu (American Physical Society, 2005-07-01)
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    Hydrogen-atom spectrum under a minimal-length hypothesis
    Benczik, S. Z.; Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu (American Physical Society, 2005-07)
    The energy spectrum of the Coulomb potential with minimal length commutation relations [X-i, P-j] = ih{delta ij(1 + beta P-2) + beta PiPj} is determined both numerically and perturbatively for arbitrary values of beta'/beta and angular momenta l. The constraint on the minimal length scale from precision hydrogen spectroscopy data is of the order of a few GeV-1, weaker than previously claimed.
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    Quantum Gravity, Dynamical Energy-Momentum Space and Vacuum Energy
    Chang, Lay Nam; Minic, Djordje; Takeuchi, Tatsu (World Scientific, 2010-11-01)
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    Short distance versus long distance physics: The classical limit of the minimal length uncertainty relation
    Benczik, S. Z.; Chang, Lay Nam; Minic, Djordje; Okamura, Naotoshi; Rayyan, S.; Takeuchi, Tatsu (American Physical Society, 2002-07-15)
    We continue our investigation of the phenomenological implications of the "deformed" commutation relations [(x) over cap (i),(p) over cap (j)]=i (h) over bar[(1+beta(p) over cap (2))delta(ij)+beta'(p) over cap (i)(p) over cap (j)]. These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relation which appears in perturbative string theory. In this paper, we consider the effects of the deformation on the classical orbits of particles in a central force potential. Comparison with observation places severe constraints on the value of the minimum length.