Fermionic Field Theory and Gauge Interactions on Random Lattices

Fermionic Field Theory and Gauge Interactions on Random Lattices

Random-lattice fermions have been shown to be free of the doubling problem if there are no interactions or interactions of a non-gauge nature. However, gauge interactions impose stringent constraints as expressed by the Ward-Takahashi identities which could revive the free-field suppressed doubler modes in loop diagrams. After introducing a formulation for fermions on a new kind of random latti...

Fermionic un - particles , gauge interactions and the β function

The dynamics of fermionic unparticles is developed from first principles. It is shown that any unparticle, whether fermionic or bosonic, can be recast in terms of a canonically quantized field, but with non-local interaction terms. We further develop a possible gauge theory for fermionic unparticles. Computing the consequent contribution of un-fermions to the β function of the theory, it is sho...

Fermionic field theory for trees and forests.

We prove a generalization of Kirchhoff's matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a q-->0 limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that thi...

On a Gauge Theory of Elementary Interactions

One of the problems engaging current interest in field theory is the problem of determining which fields are (~ elementary ,> in some fundamenta l sense, and which are not. An equally, if not more, import~nt, problem is tha t of finding ,~ guiding principe for writina" fundamenta l interactions of fields. The only such principle which exists at the present time seems to be the gauge-principle. ...

Gauge Field Theory Models