Related papers: Path Sums for Propagators in Causal Sets
We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be…
In quantum field theory the path integral is usually formulated in the wave picture, i.e., as a sum over field evolutions. This path integral is difficult to define rigorously because of analytic problems whose resolution may ultimately…
The causal set approach to quantum gravity models spacetime as a discrete structure - a causal set. Recent research has led to causal set models for the retarded propagator for the Klein-Gordon equation and the d'Alembertian operator. These…
Graph or network representations are an important foundation for data mining and machine learning tasks in relational data. Many tools of network analysis, like centrality measures, information ranking, or cluster detection rest on the…
The machine learning community has recently devoted much attention to the problem of inferring causal relationships from statistical data. Most of this work has focused on uncovering connections among scalar random variables. We generalize…
The essence of the path integral method in quantum physics can be expressed in terms of two relations between unitary propagators, describing perturbations of the underlying system. They inherit the causal structure of the theory and its…
We use purely combinatorial arguments to give a formula to compute all graded Betti numbers of path ideals of line graphs and cycles. As a consequence we can give new and short proofs for the known formulas of regularity and projective…
Causal inference is a crucial goal of science, enabling researchers to arrive at meaningful conclusions regarding the predictions of hypothetical interventions using observational data. Path models, Structural Equation Models (SEMs), and,…
Path-integral expressions for one-particle propagators in scalar and fermionic field theories are derived, for arbitrary mass. This establishes a direct connection between field theory and specific classical point-particle models. The role…
An ordinary unambiguous integral representation for the finite propagator of a quantum system is found by starting of a privileged skeletonization of the functional action in phase space, provided by the complete solution of the…
We introduce a new class of higgs type complex-valued scalar fields $U$ with Feynman propagator $\sim 1/p^4$ and consider the matching to the traditional fields with propagator $\sim 1/p^2$ in the viewpoint of effective potentials at tree…
In causal set theory the gravitational path integral is replaced by a path-sum over a sample space $\Omega_n$ of $n$-element causal sets. The contribution from non-manifold-like orders dominates $\Omega_n$ for large $n$ and therefore must…
We address the calculation of transition probabilities in multiplicative noise stochastic differential equations using a path integral approach. We show the equivalence between the conditional probability and the propagator of a quantum…
We discuss the radial spectrum of light scalar mesons in the framework of spectral sum rules in the large-Nc (planar) limit of QCD. Two methods based on the use of linear radial Regge trajectories are presented. A special emphasis is placed…
Causal discovery can be a powerful tool for investigating causality when a system can be observed but is inaccessible to experiments in practice. Despite this, it is rarely used in any scientific or medical fields. One of the major hurdles…
Recent approaches to the problem of inferring a continuous probability distribution from a finite set of data have used a scalar field theory for the form of the prior probability distribution. This letter presents a more general form for…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
Recent works have suggested that the no-boundary proposal should be defined as a sum over regular, not necessarily compact, metrics. We show that such a prescription can be implemented in the presence of a scalar field. For concreteness, we…
Several extensions of General Relativity and high energy physics include scalar fields as extra degrees of freedom. In the search for predictions in the non-linear regime of cosmological evolution, the community makes use of numerical…
Results of a general study on the dynamics of cosmological scalar fields with arbitrary potentials are presented. Exact and approximate attractor solutions are found, with applications to quintessence, moduli stabilization and inflation.