We explicitly derive collective field theory description for the system of fermions in the harmonic potential. This field theory appears to be a coupled system of free scalar and (modified) Liouville field. This theory should be considered as an exact bosonization of the system of non-relativistic fermions in the harmonic potential. Being surprisingly similar to the world-sheet formulation of c...

Two-component spinors are the basic ingredients for describing fermions in quantum field theory in 3 + 1 spacetime dimensions. We develop and review the techniques of the twocomponent spinor formalism and provide a complete set of Feynman rules for fermions using two-component spinor notation. These rules are suitable for practical calculations of crosssections, decay rates, and radiative corre...

We study renormalizable extensions of the standard model that contain vector-like fermions in a (single) complex representation of the standard model gauge group. There are 11 models where the vector-like fermions Yukawa couple to the standard model fermions via the Higgs field. These models do not introduce additional finetunings. They can lead to, and are constrained by, a number of different...

The ensemble projector Monte Carlo method is a lattice Monte Carlo method for studying gauge theories with and without Fermions in the Hamiltonian formulat ion. We study the compact U(1) lattice gauge theory with fermions in d = 2 + 1 dimensions. There are matrix elements with positive and negative signs in lattice gauge theories with fermions. As in the case of the Schwinger model, we find the...

We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action − ∑ P [β cos(ΘP ) + γ cos(2ΘP )], both for dynamical fermions and in the quenched approximation. (ΘP denotes the plaquette angle.) In simulations with dynamical fermions at various γ ≤ −0.2 on 64 lattices we find the energy gap at the phase transition of a size comparable to the pure gauge theory for...

We investigate a proposal for the construction of models with chiral fermions on the lattice using staggered fermions. In this approach the gauge invariance is broken by the coupling of the staggered fermions to the gauge fields. Motivated by previous results in the non-gauge invariant massive Yang-Mills theory and certain gauge-fermion models we aim at a dynamical restoration of the gauge inva...

We discuss non-Abelian bosonization of two and three dimensional fermions using a path-integral framework in which the bosonic action follows from the evaluation of the fermion determinant for the Dirac operator in the presence of a vector field. This naturally leads to the Wess-Zumino-Witten action for massless two-dimensional fermions and to a Chern-Simons action for very massive three dimens...

A new theory makes testable predictions: (1) Higgs fields have an unconventional equation of motion. (2) Fermions have a second-order coupling to gauge fields. (3) Fermion propagators are modified at high energy. (4) There are new scalar bosons which are supersymmetric partners of spin 1/2 fermions. (5) Since W-bosons gravitate differently from fermions and massless gauge bosons, there is a ver...

In this paper we study the properties of a gas of fermions coupling to a U~1! gauge field at wave vectors q,L!kF at dimensions larger than 1, where L!kF is a high-momentum cutoff and kF is the Fermi wave vector. In particular, we shall consider the e2→` limit, where charge and current fluctuations at wave vectors q,L are forbidden. By generalizing a method reported in a previous paper @Phys. Re...

A model is constructed for a chiral abelian gauge-interaction of fermions and a potential of three higgses, so that the potential possesses a discrete symmetry of the vacuum state, which provides the introduction of three generations for the fermions. For the model including charged currents, a matrix of the flavor mixing is described, and a phase giving the violation of CP-invariance is determ...