The Dirac-Kähler equation and fermions on the lattice

Becher, P.; Joos, H.

doi:10.1007/bf01614426

Cited by 221 publications

(253 citation statements)

References 14 publications

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“…The last case gives a more rigorous restriction of the group: The left-handed part 1−γ 5 2 c as well as the right-handed part 1+γ 5 2 c would have to be preserved separately. Thus, to compute the maximal possible gauge group, we can ignore the last case.…”

Section: Correction Terms For Lattice Deformations While the Considementioning

confidence: 99%

“…For this group, the charge of the translational direction c should be 0. Without restriction of generality, this charge can be taken as I R = 1+γ 5 2 (I 3 − 1 2 ), so that we obtain U (2) L × U (1) R as the maximal possible gauge group. Similarly, for left-handed c, we obtain the equivalent maximal gauge group…”

Section: Correction Terms For Lattice Deformations While the Considementioning

confidence: 99%

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A Condensed Matter Interpretation of SM Fermions and Gauge Fields

Schmelzer¹

2008

Found Phys

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Abstract. We present the bundle (Aff(3) ⊗ C ⊗ Λ)(R 3 ), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (C ⊗ Λ)(R 3 ) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3) ⊗ C)(Z 3 ). This space allows a simple physical interpretation as a phase space of a lattice of cells in R 3 .We find the SMto be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations.The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z 2 -degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z 2 -valued (spin) field theory.A metric theory of gravity compatible with this model is presented too.

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Section: Correction Terms For Lattice Deformations While the Considementioning

confidence: 99%

Section: Correction Terms For Lattice Deformations While the Considementioning

confidence: 99%

A Condensed Matter Interpretation of SM Fermions and Gauge Fields

Schmelzer¹

2008

Found Phys

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“…Next we consider how the relation (2.21) has an effect on the transformation law of component fields. We define the Dirac-Kähler field as follows [42][43][44][45][46][47][48][49],…”

Section: N = 4 Twisted Susy In Four Dimensionsmentioning

confidence: 99%

N=4 twisted superspace from Dirac–Kähler twist and off-shell SUSY invariant actions in four dimensions

2005

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We propose N = 4 twisted superspace formalism in four dimensions by introducing Dirac-Kähler twist. In addition to the BRST charge as a scalar counter part of twisted supercharge we find vector and tensor twisted supercharges. By introducing twisted chiral superfield we explicitly construct off-shell twisted N = 4 SUSY invariant action. We can propose variety of supergauge invariant actions by introducing twisted vector superfield. We may, however, need to find further constraints to identify twisted N = 4 super Yang-Mills action. We propose a superconnection formalism of twisted superspace where constraints play a crucial role. It turns out that N = 4 superalgebra of Dirac-Kähler twist can be decomposed into N = 2 sectors. We can then construct twisted N = 2 super Yang-Mills actions by the superconnection formalism of twisted superspace in two and four dimensions.

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“…This has been done in ref. [7]. The essential difference to the continuum analysis is a weak nonlocality of the Gra£mann and Clifford product.…”

Section: Glossary Of the Dirac-kahler Formalismmentioning

confidence: 99%

“…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.…”

Section: Introductionmentioning

confidence: 99%