A Lorentz Gauge Theory of Gravity

Abstract

Gauge theories have proven to be very successful in describing the fundamental interactions in physics. There are two different disciplines where the gauge theories work extremely well in terms of explaining the observations. On the one hand, the standard model (SM) is a gauge theory of the group SU(3) × SU(2)  × U(1), which describes three of the physics interactions in terms of the geometry of internal spaces over space-time. On the other hand, general relativity is a gauge theory of the Poincare group. Although they are both gauge theories, there is a glaring difference in their dynamical variables. In the former, the connections known as the vector bosons are the dynamical variables, while in the latter it is the metric and not the connections that is dynamical. Consequently, the standard model Lagrangian is only a fourth order polynomial, while that of general relativity is not even a polynomial. One, however, can always expand the metric around a classical background which results in a polynomial of infinite orders and the theory becomes more and more divergent as one goes to higher orders in the perturbative expansion.

This chapter published as: Ahmad Borzou, “A Lorentz Gauge Theory of Gravity,” Class. Quan. Grav., 33 (2016) 025008.