We discuss the improvement of flavour non-singlet point and one-link lattice quark operators, which describe the quark currents and the first moment of the DIS structure functions respectively. Suitable bases of improved operators are given, and the corresponding renormalisation factors and improvement coefficients are calculated in one-loop lattice perturbation theory, using the Sheikholeslami...

Dirac-like electrons in solid state have been of great interest since they exhibit many peculiar physical behaviors analogous to relativistic mechanics. Among them, carriers in graphene and surface states of topological insulators are known to behave as massless Dirac fermions with a conical band structure in the two-dimensional momentum space, whereas electrons in semimetal bismuth (Bi) are ex...

Lattice fermions obeying the Ginsparg-Wilson relation do correctly represent the physical properties related to chirality. This can be achieved by local fermions, which involve an infinite number of couplings, however. For practical purposes, it is useful to first construct approximate Ginsparg-Wilson fermions within a short range. We report on a successful construction in QCD at β = 6. The goo...

The gravitational force is assumed to be mediated by spin 2 gravitons which are composed of four spin 1/2 (sub-) fermions. The dynamics is governed by a nonlinear spinorfield equation with nonperturbative Pauli-Villars regularization and canonical quantization. On the quantum level the fermion dynamics is expressed by a functional equation for algebraic state functionals, and the "graviton" (fu...

We delineate, as an analog of two-flavor dense quark matter, the phase structure of a many-body mixture of atomic bosons and fermions in two internal states with a tunable boson-fermion attraction. The bosons b correspond to diquarks, and the fermions f to unpaired quarks. For weak b-f attraction, the system is a mixture of a Bose-Einstein condensate and degenerate fermions, while for strong at...

We present in this paper empirical formulas for the number of angular momentum I states for three and four identical fermions or bosons. In the cases with large I we prove that the number of states with the same M and n but different J is identical if I ≥ (n − 2)J − 1 2 (n − 1)(n − 2) for fermions and I ≥ (n − 2)J for bosons, and that the number of states is also identical for the same M but di...

Taking into account the transverse gauge field fluctuations, which interact with composite fermions, we examine the finite temperature compressibility of the fermions as a function of an effective magnetic field ∆B = B − 2nehc/e (ne is the density of electrons) near the half-filled state. It is shown that, after including the lowest order gauge field correction, the compressibility goes as ∂n ∂...

We generalize the Jackiw-Rebbi-Hasenfratz-’t Hooft construction of fermions from bosons to demonstrate the fermionic nature of certain bound states involving SU(N) instantons in even spatial dimensions and SO(N) instantons in 8k + 1 spatial dimensions. We use this result to identify several fermionic excitations in various perturbatively bosonic string theories. In some examples we are able to ...

In this work, we find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counterpropagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin p...