Dirac fermions on the lattice - a local approach without spectrum degeneracy

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

“…4 Thus, to obtain neutrality of the ground state, the trace of the charges has to be zero. Thus, the group 4 In a similar way, a condensed matter approach promises to solve the cosmological constant problem [27]: "The 3 He analogy suggests that a zero value of the cosmological term in the equilibrium vacuum is dictated by the Planckian or trans-Planckian degrees of freedom: ∂Svac/∂gµν = 0 has to be a special group, with determinant 1. This postulate allows to get rid of the field U (1) B .…”

“…It is a staggered discretization, with only one complex component on each lattice node, and eight different types of lattice nodes. Similar to the four-dimensional staggered discretization of Λ(R 4 ) on Z 4 (see [2,3,4,5,24,26]), it is a doubler-free discretization of the Dirac equation on (C ⊗ Λ)(R 3 ). In other words, we obtain a lattice evolution equation on a three-dimensional lattice C(Z 3 ), which gives, in the continuous limit, two Dirac fermions.…”

On the geometric lattice approximation to a realistic model of QCD

“…have the (2,6) where a is the Laplacean. In this equation, ~ denotes a linear functional defined on the elements of a (cubic) lattice~ points (x) , links (x~, plaquettes (x,;'<'.,/"'.V, cubes {xyc..,~-"/"J),…”

“…However, one would expect that an appropriate treatment of fermions is decisive for the advanced problems. For t~is reason we performed an analysis of the lattice fermion problem [6,7] based on a geometric description of Dirac_particles by differential forms due to E. Kahler {8], For this_ Oirac-Kahler equation there exists a straightforward correspondence between the continuum and the lattice description with no degeneracy problem as a lattice artifact. -2 -In this letter, we give a short glossary of our results and we apply them in a suggestion of an economic formulation of QCD with four quarks with arbitrary bare masses.…”

Note on Dirac–Kähler massless fields

“…The Dirac−Kähler (DK) fields [1], [2] are paid much attention to due to the development of quantum chromodynamics (QCD) on a lattice [3], [4], [5], [6], [7], [8], [9], [10]. Kähler postulated an equation in terms of inhomogeneous differential forms which is equivalent to a set of antisymmetric tensor fields [1], [11], [12].…”