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Path Integral Confined Dirac Fermions in a Constant Magnetic Field
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We consider Dirac fermion confined in harmonic potential and submitted to a constant magnetic field. The corresponding solutions of the energy spectrum are obtained by using the path integral techniques. For this, we begin by establishing a symmetric global projection, which provides a symmetric form for the Green function. Based on this, we show that it is possible to end up with the propagator of the harmonic oscillator for one charged particle. After some transformations, we derive the normalized wave functions and the eigenvalues in terms of different physical parameters and quantum numbers. By interchanging quantum numbers, we show that our solutions possed interesting properties. The density of current and the non-relativistic limit are analyzed where different conclusions are obtained.
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Confining kinks. $\zeta$-regularized one-loop kink mass shifts in exotic field theories
New soliton models ('confining kinks') have purely discrete perturbation spectra; their one-loop mass shifts, computed via zeta-function regularization, are finite and negative without vacuum subtractions.
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