When a topological order is realized in a certain class of superconductors, it supports Majorana fermions on the edge or in the vortex core. Vortices with Majorana fermion modes are neither fermions nor bosons but non-Abelian anyons, obeying the non-Abelian statistics for which the exchange operations of particles are not commutative. Because of this remarkable feature, Majorana fermions plays ...

We address the locality problem arising in simulations, which take the square root of the staggered fermion determinant as a Boltzmann weight to reduce the number of dynamical quark tastes from four to two. We study analytically and numerically the square root of the staggered fermion operator as a candidate to define a two taste theory from first principles. Although it has the correct weight,...

We demonstrate that the quantum-mechanical description of composite physical systems of an arbitrary number of similar fermions in all their admissible states, mixed or pure, for all finite-dimensional Hilbert-spaces, is not in conflict with Leibniz’s Principle of the Identity of Indiscernibles (PII). We discern the fermions by means of physically meaningful, permutation-invariant categorical r...

The existences of light and fermions are two big mysteries in nature. The mysteries are so deep that the questions like, “What are light and fermions?”, “Where do light and fermions come from?”, “Why do light and fermions exist?”, are regarded by many people as philosophical or even religious questions. To appreciate the physical significance those questions let us ask three simpler questions: ...

Decorrelation of the topological charge in Hybrid Monte Carlo (HMC) simulations of QCD with dynamical fermions is a long standing problem. For staggered fermions an insufficient tunneling rate of the topological charge Qt has been observed [1,2]. For Wilson fermions the tunneling rate is adequate in many cases [3,4]. However on large lattices and for large values of κ near the chiral limit the ...

The subject of topological materials has attracted immense attention in condensed-matter physics because they host new quantum states of matter containing Dirac, Majorana, or Weyl fermions. Although Majorana fermions can only exist on the surface of topological superconductors, Dirac and Weyl fermions can be realized in both 2D and 3D materials. The latter are semimetals with Dirac/Weyl cones e...

We present new techniques for finding anomaly-free sets of fermions. Although the anomaly cancellation conditions typically include cubic equations with integer variables that cannot be solved in general, we prove by construction that any chiral set of fermions can be embedded in a larger set of fermions which is chiral and anomaly-free. Applying these techniques to extensions of the Standard M...

We present preliminary results of light hadron spectroscopy using valence, tadpole-improved, Clover fermions on an ensemble of gauge configurations generated with 2 flavors of staggered fermions at β = 5.6. We compare the slope and intercept of the curve MV vs. M 2 P S for Clover and Wilson fermions. We show that a higher order chiral perturbation theory ansatz works very well for chiral extrap...

We discuss the Schrödinger functional in lattice QCD with staggered fermions including its order O(a) boundary counterterms. We relate it, in the classical continuum limit, to the Schrödinger functional as obtained in the same limit with Wilson fermions. We compute the strong coupling constant defined via the Schrödinger functional with staggered fermions at one loop and show that it agrees wit...

We propose a method to control the number of species of lattice fermions, which yields new classes of minimally doubled lattice fermions with one exact chiral symmetry and exact locality. We classify all the known minimally doubled fermions into two types based on the locations of the propagator poles in the Brillouin zone. We also study higher-dimensional extension of them and show it tends to...