We consider the general form of "Correlated Worldline" (CWL) theories of quantum gravity. We show that one can have 2 different kinds of CWL theory, in which the generating functional is written as either a sum or a product over multiple copies of the coupled matter and gravitational fields. In both versions, the paths in a functional formulation are correlated via gravity itself, causing a breakdown of the superposition principle; however, the product form survives consistency tests not satisfied by the summed form. To better understand the structure of these two theories, we show how to perform diagrammatic expansions in the gravitational coupling for each version of CWL theory, using particle propagation and scalar fields as examples. We explicitly calculate contributions to 2-point and 4-point functions, again for each version of the theory, up to 2nd-order in the gravitational coupling.

1 aBarvinsky, Andrei, O.1 aCarney, Daniel1 aStamp, Philip, C. E. uhttps://arxiv.org/abs/1806.0804301157nas a2200121 4500008004100000245006200041210006000103520076900163100001900932700002500951700002200976856003700998 2018 eng d00aTabletop experiments for quantum gravity: a user's manual0 aTabletop experiments for quantum gravity a users manual3 aRecent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

1 aCarney, Daniel1 aStamp, Philip, C. E.1 aTaylor, Jacob, M. uhttps://arxiv.org/abs/1807.1149401157nas a2200121 4500008004100000245006200041210006000103520076900163100001900932700002500951700002200976856003700998 2018 eng d00aTabletop experiments for quantum gravity: a user's manual0 aTabletop experiments for quantum gravity a users manual3 aRecent advances in cooling, control, and measurement of mechanical systems in the quantum regime have opened the possibility of the first direct observation of quantum gravity, at scales achievable in experiments. This paper gives a broad overview of this idea, using some matter-wave and optomechanical systems to illustrate the predictions of a variety of models of low-energy quantum gravity. We first review the treatment of perturbatively quantized general relativity as an effective quantum field theory, and consider the particular challenges of observing quantum effects in this framework. We then move on to a variety of alternative models, such as those in which gravity is classical, emergent, or responsible for a breakdown of quantum mechanics.

1 aCarney, Daniel1 aStamp, Philip, C. E.1 aTaylor, Jacob, M. uhttps://arxiv.org/abs/1807.11494