Related papers: Entropy and the Link Action in the Causal Set Path…

By adapting Feynman's sum over paths method to a quantum mechanical system whose phase space is a torus, a new proof of the Landsberg-Schaar identity for quadratic Gauss sums is given. In contrast to existing non-elementary proofs, which…

An important question that discrete approaches to quantum gravity must address is how continuum features of spacetime can be recovered from the discrete substructure. Here, we examine this question within the causal set approach to quantum…

For a relativistic particle moving in the presence of mean scalar and vector fields, the energy at second order in the scalar field is shown to contain two contributions in general. One is a momentum-dependent repulsive interaction…

We study solutions to systems of stream inclusions of the form 'f in T(f)', where the nondeterministic transformer 'T' on omega-infinite streams is assumed to be causal in the sense that elements in output streams are determined by a finite…

A general principle called "conservation of the ellipsoid of concentration" is introduced and a generalized entropic form of order 'alpha' is optimized under this principle. It is shown that this can produce a density which can act as a…

We study the problem of identifying the causal relationship between two discrete random variables from observational data. We recently proposed a novel framework called entropic causality that works in a very general functional model but…

Unlike the relativity theory it seeks to replace, causal set theory has been interpreted to leave space for a substantive, though perhaps 'localized', form of 'becoming'. The possibility of fundamental becoming is nourished by the fact that…

In theories of communication, it is usually presumed that the involved parties perform actions in a fixed causal order. However, practical and fundamental reasons can induce uncertainties in the causal order. Here we show that a maximal…

A path integral approach has been generalized for the non-relativistic electron charge transfer processes. The charge transfer - the capture of an electron by an ion passing another atom or more generally the problem of rearrangement…

The combination of functional limit theorems with the pathwise analysis of deterministic and stochastic differential equations has proven to be a powerful approach to the analysis of fast-slow systems. In a multivariate setting, this…

We consider quantization of the Baierlein-Sharp-Wheeler form of the gravitational action, in which the lapse function is determined from the Hamiltonian constraint. This action has a square root form, analogous to the actions of the…

This monograph introduces the basic concepts of the theory of causal fermion systems, a recent approach to the description of fundamental physics. The theory yields quantum mechanics, general relativity and quantum field theory as limiting…

This work is devoted to the analysis of a Gibbs partition model, also known as a composition scheme. We consider a natural new condition on the component weights. It leads to a new behavior for the total number of components. We discover a…

In higher derivative theories, gravity can travel slower or faster than light. With this feature in mind, we revisit the construction of the causal and entanglement wedges in this type of theories, and argue that they must be constructed…

Artificial intelligence models and methods commonly lack causal interpretability. Despite the advancements in interpretable machine learning (IML) methods, they frequently assign importance to features which lack causal influence on the…

The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived…

Cosmological correlators from inflation are often generated at tree level and hence loop contributions are bounded to be small corrections by perturbativity. Here we discuss a scenario where this is not the case. Recently, it has been shown…

The Causal Set Theory (CST) approach to quantum gravity is motivated by the observation that, associated with any causal spacetime (M,g) is a poset (M,<), with the order relation < corresponding to the spacetime causal relation. Spacetime…

Structural causal models are the basic modelling unit in Pearl's causal theory; in principle they allow us to solve counterfactuals, which are at the top rung of the ladder of causation. But they often contain latent variables that limit…

Entropy of measure preserving or continuous actions of amenable discrete groups allows for various equivalent approaches. Among them are the ones given by the techniques developed by Ollagnier and Pinchon on the one hand and the…