Quantum Field Theory and Gravity in Causal Sets.

Causal set is a model of space time that allows to reconcile discreteness and manifest relativistic covariance. This is done by viewing space time as finite, partially ordered set. The elements of the set are viewed as points of space time, or events; the partial ordering between them is viewed as causal relations. It has been shown that, in discrete scenario, the information about causal relations between events can, indeed, approximate the metric. The goal of this thesis is to introduce matter fields and their Lagrangians into causal set context. This is a two step process. The first step is to re-define gauge fields, gravity, and distances in such a way that no reference to Lorentz index is made. This is done by defining gauge fields as two-point real valued functions, and gravitational field as causal structure itself. Once the above is done, Lagrangians have to be defined in a way that they don't refer to Lorentzian indices either. This is done by introducing a notion of type 1 and type 2 Lagrangian generators, coupled with respective machinery that "translates" each generator into corresponding Lagrangian. The fields that are subject to these generators are, respectively, defined as type 1 and type 2. The main difference between two kinds of fields is the prediction of different behavior in different dimensions of type 2 fields. However, despite our inability to travel to different dimensions, gravity was shown to be type 2 based on the erroneous predictions of its 4-dimensional behavior if it was viewed as type 1. However, no erroneous predictions are made if non-gravitational fields are viewed as either type 1 or type 2, thus the nature of the latter is still an open question. Finally, an attempt was made to provide interpretation of quantum mechanics that would allow to limit fluctuations of causal structure to allow some topological background. However, due to its controversial nature, it is placed in the Appendix.Ph.D.PhysicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/62387/1/sverdlov_1.pd