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Currents and charges for mixed fields

Blasone, M, Jizba, P, Vitiello, G

Published Jan 1, 2001• 46 citations
OpenAlex

Abstract

We present an analysis of currents and charges for a system of two mixed fields, both for spinless bosons and for Dirac fermions. This allows us to obtain in a straightforward way the exact field theoretical oscillation formulas exhibiting corrections with respect to the usual ones derived in quantum mechanics.

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Tunneling between a point contact and a one-dimensional wire is usually described with the help of a tunneling Hamiltonian that contains a $\ensuremath{\delta}$ function in position space. Whereas the leading-order contribution to the tunneling current is independent of the way this $\ensuremath{\delta}$ function is regularized, higher-order corrections with respect to the tunneling amplitude are known to depend on the regularization. Instead of regularizing the $\ensuremath{\delta}$ function in the tunneling Hamiltonian, one may also obtain a finite tunneling current by invoking the ultraviolet cutoffs in a field-theoretic description of the electrons in the one-dimensional conductor, a procedure that is often used in the literature. For the latter case, we show that standard ultraviolet cutoffs lead to different results for the tunneling current in fermionic and bosonized formulations of the theory, when going beyond leading order in the tunneling amplitude. We show how to recover the standard fermionic result using the formalism of functional bosonization and revisit the tunneling current to leading order in the interacting case.