Further studies in aesthetic field theory VI: The lorentz group

1975 ◽  
Vol 12 (3) ◽  
pp. 157-160 ◽  
Author(s):  
M. Muraskin ◽  
Beatrice Ring
Keyword(s):  
Field Theory ◽  
Lorentz Group ◽  
Aesthetic Field

A gauge theory of the Weyl group

1974 ◽  
Vol 340 (1622) ◽  
pp. 249-262 ◽  
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conservation Laws ◽  
Weyl Group ◽  
Lorentz Group ◽  
Space Time ◽  
Gauge Fields ◽  
Field Equations ◽  
Covariant Derivatives ◽  
The World

The construction of field theory which exhibits invariance under the Weyl group with parameters dependent on space–time is discussed. The method is that used by Utiyama for the Lorentz group and by Kibble for the Poincaré group. The need to construct world-covariant derivatives necessitates the introduction of three sets of gauge fields which provide a local affine connexion and a vierbein system. The geometrical implications are explored; the world geometry has an affine connexion which is not symmetric but is semi-metric. A possible choice of Lagrangian for the gauge fields is presented, and the resulting field equations and conservation laws discussed.

Particle behavior in aesthetic field theory

1974 ◽  
Vol 4 (3) ◽  
pp. 395-405 ◽  
Author(s):  
Murray Muraskin ◽  
Beatrice Ring
Keyword(s):  
Field Theory ◽  
Particle Behavior ◽  
Aesthetic Field

ON CHIRAL SYMMETRY BREAKING WITH MASSLESS FERMIONS

1994 ◽  
Vol 09 (35) ◽  
pp. 3285-3291
Author(s):  
RAINER DICK
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Lorentz Group ◽  
Chiral Symmetry Breaking ◽  
General Structure ◽  
Transformation Behavior ◽  
Conformal Field ◽  
Massless Fermions

It is shown that Weyl spinors in Minkowski space are isomorphic to primary fields of half-integer conformal weights. This yields representations of fermionic two-point functions in terms of correlators of primary fields with a factorized transformation behavior under the Lorentz group. As an application we determine the general structure of the corresponding Lorentz covariant correlators by methods similar to that employed in conformal field theory to determine two- and three-point functions of primary fields. In particular, the chiral symmetry breaking terms resemble fermionic two-point functions of 2-D CFT up to a function of the product of momenta.

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