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Tunneling between a point contact and a one-dimensional wire is usuallydescribed with the help of a tunneling Hamiltonian that contains a deltafunction in position space. Whereas the leading order contribution to thetunneling current is independent of the way this delta function is regularized,higher-order corrections with respect to the tunneling amplitude are known todepend on the regularization. Instead of regularizing the delta function in thetunneling Hamiltonian, one may also obtain a finite tunneling current byinvoking the ultraviolet cut-offs in a field-theoretic description of theelectrons in the one-dimensional conductor, a procedure that is often used inthe literature. For the latter case, we show that standard ultraviolet cut-offslead to different results for the tunneling current in fermionic and bosonizedformulations of the theory, when going beyond leading order in the tunnelingamplitude. We show how to recover the standard fermionic result using theformalism of functional bosonization and revisit the tunneling current toleading order in the interacting case.

Tunneling into quantum wires: regularization of the tunneling Hamiltonian and consistency between free and bosonized fermions