Geometry and quantization

Abstract

Gravity is treated geometrically in terms of nonlinear realizations ofGL(4, ℝ) with particular reference to almost complex structures. This approach is used to carry out a Bargmann-Segal type quantization of space-time via the vector and spinor structures of the tangent space that formulates the theory of measurement as a quantum theory quantized in terms of a basic unit of length that appears in a new uncertainty relation. The theory is also used to discuss the gauge conditions for quantum gravity and the Kostant theory of quantization applied using a line bundle with structure groupGL(2, ℂ)/SL(2, ℂ).