The Dirac-Kahler Equation and Fermions on the Lattice

Becher, P.; Joos, H.

doi:10.1007/BF01614426

The Dirac-Kahler Equation and Fermions on the Lattice

P. Becher
(
- Wurzburg U.
)
,
H. Joos
(
- DESY
)

May, 1982

69 pages

Published in:

Z.Phys.C 15 (1982) 343

DOI:

10.1007/BF01614426

Report number:

DESY-82-031

View in:

AMS MathSciNet

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Abstract: (Springer)

The geometrical description of spinor fields by E. Kähler is used to formulate a consistent lattice approximation of fermions. The relation to free simple Dirac fields as well as to Susskind's description of lattice fermions is clarified. The first steps towards a quantized interacting theory are given. The correspondence between the calculus of differential forms and concepts of algebraic topology is shown to be a useful method for a completely analogous treatment of the problems in the continuum and on the lattice.

QUANTUM CHROMODYNAMICS
FERMION: FIELD THEORY
SPINOR: FIELD THEORY
FIELD THEORY: SPINOR
APPROXIMATION: LATTICE
Dirac-Kaehler equation
ALGEBRA: CLIFFORD
FIELD EQUATIONS: SYMMETRY
CURRENT: CONSERVATION LAW
QUANTIZATION

References(32)

Figures(0)

Confinement of Quarks

Kenneth G. Wilson
(
- Cornell U., LNS
)

- Phys.Rev.D 10 (1974) 2445-2459,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 45-59. ( Phys. Rev. D10 ( 1974) 2445-2459) and Cornell Univ. Ithaca - CLNS-74-262 (74,REC.MAR.) 47p,
•
DOI:
- 10.1103/PhysRevD.10.2445

Asymptotic Freedom Scales

Michael Creutz
(
- Brookhaven
)

- Phys.Rev.Lett. 45 (1980) 313,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 266-269. ( Phys. Rev. Lett. 45 ( 1980) 313-316) and Brookhaven Nat. Lab. Upton - BNL-27752 (80,REC.JUL.) 11p
•
DOI:
- 10.1103/PhysRevLett.45.313

Plaquette-plaquette Correlations in the SU(2) Lattice Gauge Theory

B. Berg
(
- Hamburg U.
)

- Phys.Lett.B 97 (1980) 401-404
•
DOI:
- 10.1016/0370-2693(80)90628-0

- Nucl.Phys.B 189 469

The Glueball Mass Spectrum in {QCD}: First Results of a Lattice Monte Carlo Calculation

- Phys.Lett.B 110 (1982) 399-405
•
DOI:
- 10.1016/0370-2693(82)91281-3

- Phys.Rev.Lett. 47 1972

Computer Estimates of Meson Masses in SU(2) Lattice Gauge Theory

E. Marinari
(
- Rome U. and
- INFN, Rome
)
,
G. Parisi
(
- Rome U. and
- Frascati
)
,
C. Rebbi
(
- Brookhaven
)

- Phys.Rev.Lett. 47 (1981) 1795,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 623-627. ( Phys. Rev. Lett. 47 (1981) 1795-1799) and Brookhaven Nat. Lab. Upton - BNL-30212 (81,REC.NOV.) 14p
•
DOI:
- 10.1103/PhysRevLett.47.1795

Monte Carlo Evaluation of Hadron Masses in Lattice Gauge Theories with Fermions

Don Weingarten
(
- Indiana U.
)

- Phys.Lett.B 109 (1982) 57,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 631-636. ( Phys. Lett. B109 (1982) 57-62) and Indiana Univ. Bloomington - IUHET-69 (81,REC.OCT.) 17p
•
DOI:
- 10.1016/0370-2693(82)90463-4

Lattice Fermions: Species Doubling, Chiral Invariance, and the Triangle Anomaly

Luuk H. Karsten
(
- Stanford U., ITP
)
,
Jan Smit
(
- Amsterdam U.
)

- Nucl.Phys.B 183 (1981) 103,
- In *Rebbi, C. ( Ed.): Lattice Gauge Theories and Monte Carlo Simulations*, 495-532. ( Nucl. Phys. B183 ( 1981) 103-140) and Stanford Univ. - ITP-677 (80,REC.NOV.) 71p
•
DOI:
- 10.1016/0550-3213(81)90549-6