A chiral invariant decoupling of replica lattice fermions

A chiral invariant lattice fermion action which solves the species-doubling problem of Dirac fermions on a lattice for (even) dimensions of space-time less than eight is presented. The decoupling of replica fermions requires to give up rotational and gauge symmetry in the regularization procedure. The corresponding lattice Schwinger model reproduces all the results of the continuum theory.     

Comments on chiral fermions in stochastic quantization

The subject of this Letter is twofold. First, a recently claimed failure of stochastic quantization scheme (SQS) to describe standard chiral anomalies at finite stochastic time is shown to result from an elementary mathematical error. The consistent approach of treating chiral fermions in SQS is briefly sketched and full agreement with previous investigations is established. Second, a serious new limitation on SQS is found, namely, its incapability to reproduce global chiral- and odd-dimensional parity-violating anomalies.     

Correspondence principle and quantum gauge theories with chiral fermions

The correspondence principle is used to extend nonabelian gauge theories with chiral fermions up to anomaly-free theories by introducing unitary scalar fields. Resulting theories can be treated as a low-energy approximation to left-right theories. This approach fixes the Weinberg angle of the electroweak theory at _w=30°.     

The effective action for chiral fermions

We present an exact formula for the imaginary part of the effective action for chiral fermions in complex representations of the gauge group G, in the presence of an arbitrary external gauge field configuration. This result provides a unified treatment of both local and global anomalies and a precise characterization of some of the special properties of chiral fermions.     

On the chiral limit in lattice gauge theories with Wilson fermions

The chiral limit κ ? κ _c (β) in lattice gauge theories with Wilson fermions and problems related to near-to-zero (’exceptional’) eigenvalues of the fermionic matrix are studied. For this purpose we employ compact lattice QED in the confinement phase. A new estimator $\tilde m_\pi$ for the calculation of the pseudoscalar mass m _π is proposed which does not suffer from ’divergent’ contributions at κ ? κ _c (β)We conclude that the main contribution to the pion mass comes from larger modes, and ’exceptional’ eigenvalues play no physical role. The behaviour of the subtracted chiral condensate $\left\langle {\bar \psi \psi } \right\rangle _{subt}$ near κ _c (β) is determined. We observe a comparatively large value of $\left\langle {\bar \psi \psi } \right\rangle _{subt} \cdot Z_P^{ - 1}$ , which could be interpreted as a possible effect of the quenched approximation.     

Weak localization in disordered spin-1 chiral fermions

We theoretically investigate the quantum interference theory of magnetotransport of the three-component or spin-1 chiral fermions, which possess two linear Dirac bands and a flat band. For isotropic scalar impurities, the correction of conductivity from the coherent backscatter and non-coherent backscatter contributions cancel out in the intravalley scattering, leading to a weak localization correction to the Drude conductivity from the intervalley scattering. For the anisotropic impurities, the above cancelation is removed, we find the approximative quantum interference conductivity in the weak anisotropy case. The contributions from the chiral anomaly and classical Lorentz force are also discussed. Our work reveals some intriguing and detectable transport signatures of the novel spin-1 chiral fermions.     

Broken chiral symmetries and light composite fermions

We elaborate on a mechanism for obtaining naturally light composite fermions in a strongly interacting gauge theory. A simple toy model is used to illustrate the basic ideas.     

2D quantum spin models and Jordan-Wigner fermions

We apply the 2D Jordan-Wigner fermionization to examine the ground state and thermodynamic properties of the square-lattice s=1/2 anisotropic XY model. We compare our findings with the results of different analytical and numerical approaches.     

A 2D Luttinger Model

A detailed derivation of a two dimensional (2D) low energy effective model for spinless fermions on a square lattice with local interactions is given. This derivation utilizes a particular continuum limit that is justified by physical arguments. It is shown that the effective model thus obtained can be treated by exact bosonization methods. It is also discussed how this effective model can be used to obtain physical information about the corresponding lattice fermion system.     

Converting heat to electricity by a graphene stripe with heavy chiral fermions

A conversion of thermal energy into electricity is considered in the electricallypolarized graphene stripes with zigzag edges where the heavy chiral fermion (HCF) statesare formed. The stripes are characterized by a high electric conductance G _e and by a significantSeebeck coefficient S. The electric current in the stripes is induced due toa non-equilibrium thermal injection of “hot” electrons. This thermoelectric generationprocess might be utilized for building of thermoelectric generators with an exceptionallyhigh figure of merit ZδT ?1 and with an appreciable electric power densities ~1 MW/cm².     

Topology of chiral superfluid: Skyrmions,Weyl fermions,and chiral anomaly

The influence of electric stochastic fields on the relativistic charged particles is investigated in the gauge invariant path integral formalism. Using the cumulant expansion one finds the exponential relaxation of the charge Green’s function both for spinless and Dirac charges.