Functional Integration for the Fermionic Field

J. E. Hirsch

A new functional-integral formulation of the Hubbard model is introduced that interpolates smoothly between the world-line formulation, which involves a direct-space--imaginary-time representation of the fermion fields, and a determinantal formulation, where auxiliary boson fields are introduced and the fermions are integrated out. Various features of the new formulation, particularly in connection with numerical simulations, are discussed.

Joel Feldman, Horst Knörrer, Eugene Trubowitz B

Wolfgang Weller, Frank Stefani, M. Souleiman

Following a proposal by Aronov and Ioselevich, we express the Green functions (GF) of a noninteracting disordered Fermi system as a functional integral on a real time/frequency lattice. The normalizing denominator of this functional integral is equal to unity, because of identities satisfied by the GF. The GF can then be simply averaged with respect to the random disorder potential. We describe the fermionic fields not belonging to the external frequency by means of a bosonic auxiliary field g. The Hubbard-Stratonovich field Q is introduced only with respect to the fermionic fields for the external frequency.

David Borthwick

The construction of Euclidean Majorana fermions on a two-dimensional cylindrical space–time is discussed, based on a given real-time theory. After a review of the basics of defining Euclidean fermions in the free theory, a functional integral formulation for the Euclidean theory is introduced. This functional integral connects the expectation values of the Euclidean fields with the theory of relative Pfaffians. A proof, which draws on these ideas, is given for the Feynman–Kac formula of a general interacting theory.

Luca Salasnich