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Regularization of the vacuum energy in the chiral-soliton model as an energy-eigenvalue sum.

In the chiral-soliton model with a finite ultraviolet cutoff, which describes the low-energy, large-{ital N}{sub {ital c}} limit of the strong interactions, we investigate the fermion vacuum energy, expressed as a sum over the eigenvalues of the relevant single-particle Dirac Hamiltonian, in order to clarify recent claims that it depends strongly on the regularization scheme, and can even exhibit vacuum instability. On the basis of a simple physically motivated criterion, we are able to determine which regulating functions can be considered as well behaved. Aided by a mapping of the problem onto an equivalent one in the proper-time formalism, we show that for these well-behaved regulators the vacuum energy does not depend significantly on the regularization scheme and there is no vacuum instability, in line with original expectations.