A proposal for simulating chiral fermions (original) (raw)

A method for putting chiral fermions on the lattice

Nuclear Physics B - Proceedings Supplements, 1993

We describe a method to put chiral gauge theories on the lattice. Our method makes heavy use of the effective action for chiral fermions in the continuum, which is in general complex. As an example we discuss the chiral Schwinger model.

BFFT FORMALISM APPLIED TO THE MINIMAL CHIRAL SCHWINGER MODEL

Modern Physics Letters A, 2004

We consider the minimal chiral Schwinger model, by embedding the gauge noninvariant formulation into a gauge theory following the Batalin-Fradkin-Fradkina-Tyutin point of view. Within the BFFT procedure, the second class constraints are converted into strongly involutive first-class ones, leading to an extended gauge invariant formulation. We also show that, like the standard chiral model, in the minimal chiral model the Wess-Zumino action can be obtained by performing a q-number gauge transformation into the effective gauge noninvariant action. *

A streamlined method for chiral fermions on the lattice

Nuclear Physics B - Proceedings Supplements, 1993

We discuss the use of renormalization counterterms to restore the chiral gauge symmetry in a lattice theory of Wilson fermions. We show that a large class of counterterms can be implemented automatically by making a simple modification to the fermion determinant.

The Physics of the Chiral Fermions

We review the aspects of chiral gauge theories related to the violation of the decoupling property. The case of the top quark is worked out in detail. The mechanism of anomaly cancellation in the low-energy effective theory is illustrated in a simple model.

Chiral Schwinger model in terms of chiral bosonization

Physical Review Letters, 1990

The chiral Schwinger model is reexamined by Using chiral bosonization. The Lagrangian is obtained as a gauged Floreanini-Jacki~Lagrangian. %'e get a bosonic solution which contains one massive free boson and one (free) self-dual field.

Lattice chiral schwinger model in the continuum formulation

Nuclear Physics B - Proceedings Supplements, 1998

We pursue further an approach to lattice chiral fermions in which the fermions are treated in the continuum. To render the effective action gauge invariant, counterterms have to be introduced. We determine the counterterms for smooth gauge fields, both analytically and numerically. The final result is that the imaginary part of the effective action can be computed analytically from the lattice gauge field, while the real part is given by one half of the action of the corresponding vector model.

Consistent and covariant commutator anomalies in the chiral Schwinger model

1997

We derive all covariant and consistent divergence and commutator anomalies of chiral QED 2 within the framework of canonical quantization of the fermions. Further, we compute the time evolution of all occurring operators and find that all commutators evolve canonically. We comment on the relation of our results to the finding of a nontrivial U (1)-curvature in gauge-field space.

Consistent gauge-invariant chiral theories in two dimensions

We employ a gauge-invariant point-splitting procedure to solve cliiral gauge theories in two dimensions. We present an explicit solution of the chiral Schwinger model. The resulting theory is gauge-invariant and unitary containing a massless physical state. The method is generalizable to higher dimensions.

Worldline Approach to Chiral Fermions

We propose to apply "worldline numerics" to a numerical calculation of quark determinants. The Gross-Neveu model with a U(1) chiral symmetry is considered as a first test. The worldline approach allows for an analytic renormalisation, and only finite parts of the determinant require a numerical calculation. It is shown that the discretisation of the worldlines, which is central to the numerical treatment, preserves chiral symmetry exactly. Numerical results for a kink configuration as a scalar background field are shown and compared with analytical results. The case of finite fermion chemical potential is also briefly discussed.