Solutions to gauge field equations in eight dimensions. conformal invariance and the last Hopf map

1989 ◽  
Vol 220 (3) ◽  
pp. 431-434 ◽  
Author(s):  
Bernard Grossman ◽  
Thomas W. Kephart ◽  
James D. Stasheff
Keyword(s):  
Gauge Field ◽  
Conformal Invariance ◽  
Field Equations ◽  
Hopf Map

Strength of the Poincaré gauge field equations in first order formalism

1989 ◽  
Vol 139 (1-2) ◽  
pp. 21-26 ◽  
Author(s):  
Michael Sué ◽  
Eckehard W. Mielke
Keyword(s):  
Gauge Field ◽  
Field Equations ◽  
First Order

scholarly journals NEW GEOMETRIC FORMALISM FOR GRAVITY EQUATION IN EMPTY SPACE

2005 ◽  
Vol 14 (06) ◽  
pp. 1009-1022 ◽  
Author(s):  
XIN-BING HUANG
Keyword(s):  
Differential Equations ◽  
Gauge Field ◽  
Empty Space ◽  
Space Time ◽  
Gravity Theory ◽  
Spin Connection ◽  
Square Root ◽  
Field Equations ◽  
Complex Spin ◽  
Set Up

In this paper, a complex daor field which can be regarded as the square root of space–time metric is proposed to represent gravity. The locally complexified geometry is set up, and the complex spin connection constructs a bridge between gravity and SU(1, 3) gauge field. Daor field equations in empty space are acquired, which are one-order differential equations and do not conflict with Einstein's gravity theory.

GENERALIZED GRAVITY IN CLIFFORD SPACES, VACUUM ENERGY AND GRAND UNIFICATION

2011 ◽  
Vol 08 (06) ◽  
pp. 1239-1258 ◽  
Author(s):  
CARLOS CASTRO
Keyword(s):  
Cosmological Constant ◽  
Gauge Field ◽  
Constant Term ◽  
Gauge Field Theories ◽  
Field Equations ◽  
Spectral Action ◽  
Action Model ◽  
The One ◽  
Curvature And Torsion ◽  
Vacuum Solutions

Polyvector-valued gauge field theories in Clifford spaces are used to construct a novel Cl (3, 2) gauge theory of gravity that furnishes modified curvature and torsion tensors leading to important modifications of the standard gravitational action with a cosmological constant. Vacuum solutions exist which allow a cancelation of the contributions of a very large cosmological constant term and the extra terms present in the modified field equations. Generalized gravitational actions in Clifford-spaces are provided and some of their physical implications are discussed. It is shown how the 16 fermions and their masses in each family can be accommodated within a Cl (4) gauge field theory. In particular, the Higgs fields admit a natural Clifford-space interpretation that differs from the one in the Chamseddine–Connes spectral action model of non-commutative geometry. We finalize with a discussion on the relationship with the Pati–Salam color-flavor model group SU (4)C × SU (4)F and its symmetry breaking patterns. An Appendix is included with useful Clifford algebraic relations.

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