论文信息 - Gravity as a Gauge Theory in the Spacetime Algebra

Gravity as a Gauge Theory in the Spacetime Algebra

We outline a theory of gravitational interactions utilising the spacetime algebra - the geometric algebra of spacetime. The theory arises by demanding invariance under active Poincare transformations. Making this symmetry local results in a first-order theory with 40 degrees of freedom. The matter-free field equations are presented, and are solved for radially-symmetric static fields. We discuss the behaviour of point particles under the fields described by these solutions, and compare and contrast the results with those of general relativity.

[1] Chris Doran,et al. Imaginary numbers are not real—The geometric algebra of spacetime , 1993 .

[2] David Hestenes,et al. Proper particle mechanics , 1974 .

[3] George F. R. Ellis,et al. The Large Scale Structure of Space-Time , 2023 .

[4] D. Hestenes. The design of linear algebra and geometry , 1991 .

[5] T. Kibble. Lorentz Invariance and the Gravitational Field , 1961 .

[6] Daniel Kleppner. The Gem of General Relativity , 1993 .

[7] Ryoyu Utiyama,et al. Invariant theoretical interpretation of interaction , 1956 .

[8] S. Gull,et al. Electron paths, tunnelling, and diffraction in the spacetime algebra , 1993 .

[9] Daniel Kleppner. Thoughts on Being Bad , 1993 .

[10] Chris Doran,et al. States and operators in the spacetime algebra , 1993 .

[11] D. Hestenes,et al. Clifford Algebra to Geometric Calculus , 1984 .

[12] Chris Doran,et al. A multivector derivative approach to Lagrangian field theory , 1993 .

[13] David Hestenes,et al. Space-time algebra , 1966 .