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Manuscript Title: Self-consistent solution to a complex fermion determinant with space dependent fields.
Authors: U. Zuckert, R. Alkofer, H. Weigel
Program title: vecscal
Catalogue identifier: ACVB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 82(1994)42
Programming language: Fortran.
Computer: DEC-5000.
Operating system: UNIX.
RAM: 2392K words
Peripherals: disc.
Keywords: Particle physics, Elementary, Empirical model, Nambu-jona-lasinio model, Chiral soliton, Hedgehog ansatz, Complex functional, Determinant, Static energy functional.
Classification: 11.6.

Nature of problem:
Quark fields are integrated out from a generalized Nambu-Jona-Lasinio model yielding a complex functional determinant which involves composite meson fields. This determinant is evaluated for static but space- dependent meson field configurations. The configuration which minimizes the corresponding energy functional is constructed.

Solution method:
A basis for the quark spinors suited for spherically symmetric configurations is provided. The one-particle Dirac Hamiltonian involving space-dependent meson fields is diagonalized using this basis. Special to this case is the non-hermiticity of the Hamiltonian. The fermion determinant is calculated by summing over the resulting complex eigenvalues. The corresponding eigenfunctions serve to set up the equations of motion for the meson fields. The solution to these equations is obtained by iteration.

Unusual features:
Access to the IMSL library is needed [1].

Running time:
The running time strongly depends on the size of the momentum space basis as well as the number of lattice points. Typical parameters yield for a single iteration 92 min (DEC), 19.5 min (HP) cpu-time.

[1] IMSL, Inc. (1989), IMSL MATH/LIBRARY User's Manual, version 1.1, IMSL, Houston.