6,646 research outputs found

    Gauge invariant hydrogen atom Hamiltonian

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    For quantum mechanics of a charged particle in a classical external electromagnetic field, there is an apparent puzzle that the matrix element of the canonical momentum and Hamiltonian operators is gauge dependent. A resolution to this puzzle is recently provided by us in [2]. Based on the separation of the electromagnetic potential into pure gauge and gauge invariant parts, we have proposed a new set of momentum and Hamiltonian operators which satisfy both the requirement of gauge invariance and the relevant commutation relations. In this paper we report a check for the case of the hydrogen atom problem: Starting from the Hamiltonian of the coupled electron, proton and electromagnetic field, under the infinite proton mass approximation, we derive the gauge invariant hydrogen atom Hamiltonian and verify explicitly that this Hamiltonian is different from the Dirac Hamiltonian, which is the time translation generator of the system. The gauge invariant Hamiltonian is the energy operator, whose eigenvalue is the energy of the hydrogen atom. It is generally time-dependent. In this case, one can solve the energy eigenvalue equation at any specific instant of time. It is shown that the energy eigenvalues are gauge independent, and by suitably choosing the phase factor of the time-dependent eigenfunction, one can ensure that the time-dependent eigenfunction satisfies the Dirac equation.Comment: 7 pages, revtex4, some further discussion on Dirac Hamiltonian and the gauge invariant Hamiltonian is added, one reference removed; new address of some of the authors added, final version to appear in Phys. Rev.

    Some Problems Concerning Interchange of Order of Integration in Functional Integral Formalism of U(1) Gauge Field Theories

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    We show that in the functional integral formalism of U(1) gauge field theory some formal manipulation such as interchange of order of integration can yield erroneous results. The example studied is analysed by Fubini theorem.Comment: 3 pages, revte

    Black Hole Hyperaccretion Inflow-outflow Model. I. Long And Ultra-long Gamma-ray Bursts

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    Long-duration gamma-ray bursts (LGRBs) and ultra-LGRBs (ULGRBs) originate from collapsars, in the center of which a newborn rotating stellar-mass black hole (BH) surrounded by a massive accretion disk may form. In the scenario of the BH hyperaccretion inflow-outflow model and Blandford-Znajek (BZ) mechanism to trigger gamma-ray bursts (GRBs), the real accretion rate to power a BZ jet is far lower than the mass supply rate from the progenitor star. The characteristics of the progenitor stars can be constrained by GRB luminosity observations, and the results exceed usual expectations. LGRBs lasting from several seconds to tens of seconds in the rest frame may originate from solar-metallicity (Z ∼ 1 Z⊙, where Z and Z⊙ are the metallicities of progenitor stars and the Sun), massive (M ≳ 34 M⊙, where M and M⊙ are the masses of progenitor stars and the Sun) stars or some zerometallicity (Z ∼ 0) stars. A fraction of low-metallicity (Z ≲ 10-2Z⊙) stars, including Population III stars, can produce ULGRBs such as GRB 111209A. The fraction of LGRBs lasting less than tens of seconds in the rest frame is more than 40%, which cannot conform to the fraction of the demanded type of progenitor star. It possibly implies that the activity timescale of the central engine may be much longer than the observed timescale of prompt emission phase, as indicated by X-ray late-time activities. Alternatively, LGRBs and ULGRBs may be powered by a millisecond magnetar central engine. © 2017. The American Astronomical Society. All rights reserved
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