## 3 Citations

Causal evolution of probability measures and continuity equation

- Mathematics
- 2021

We study the notion of a causal time-evolution of a conserved nonlocal physical quantity in a globally hyperbolic spacetime M. The role of the ‘global time’ is played by a chosen Cauchy temporal…

Comment on "Born's rule for arbitrary Cauchy surfaces"

- Physics
- 2020

A recent article has treated the question of how to generalize the Born rule from non-relativistic quantum theory to curved spacetimes (Lienert and Tumulka, Lett. Math. Phys. 110, 753 (2019)). The…

On the Differentiation Lemma and the Reynolds Transport Theorem for Manifolds with Corners

- Mathematics
- 2019

We state and prove generalizations of the Differentiation Lemma and the Reynolds Transport Theorem in the general setting of smooth manifolds with corners (e.g. manifolds with or `without' boundary,…

## References

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The optimal mass transport problem for relativistic costs

- Mathematics
- 2013

In this paper, we study the optimal mass transportation problem in $${\mathbb{R}^{d}}$$ for a class of cost functions that we call relativistic cost functions. Consider as a typical example, the cost…

Optimal transport by omni-potential flow and cosmological reconstruction

- Mathematics
- 2012

One of the simplest models used in studying the dynamics of large-scale structure in cosmology, known as the Zeldovich approximation, is equivalent to the three-dimensional inviscid Burgers equation…

Operational causality in spacetime

- PhysicsPhysical Review A
- 2020

The no-signalling principle preventing superluminal communication is a limiting paradigm for physical theories. Within the information-theoretic framework it is commonly understood in terms of…

ASPECTS OF NONCOMMUTATIVE LORENTZIAN GEOMETRY FOR GLOBALLY HYPERBOLIC SPACETIMES

- Mathematics
- 2003

Connes' functional formula of the Riemannian distance is generalized to the Lorentzian case using the so-called Lorentzian distance, the d'Alembert operator and the causal functions of a…

Time Functions as Utilities

- Philosophy, Mathematics
- 2010

Every time function on spacetime gives a (continuous) total preordering of the spacetime events which respects the notion of causal precedence. The problem of the existence of a (semi-)time function…

A causal order for spacetimes with Lorentzian metrics: proof of compactness of the space of causal curves

- Mathematics
- 1996

We recast the tools of `global causal analysis' in accord with an approach to the subject animated by two distinctive features: a thoroughgoing reliance on order-theoretic concepts, and a utilization…

On the Wave Function of the Photon

- Physics
- 1994

It is believed that certain matrix elements of the electromagnetic field operators in quantum electrodynamics, in close analogy with nonrelativistic quantum theory of massive particles, may be…

Displacement convexity of Boltzmann’s entropy characterizes the strong energy condition from general relativity

- Mathematics
- 2018

On a Riemannian manifold, lower Ricci curvature bounds are known to be characterized by geodesic convexity properties of various entropies with respect to the Kantorovich-Rubinstein-Wasserstein…

Recent developments in bimetric theory

- Physics
- 2015

This review is dedicated to recent progress in the field of classical, interacting, massive spin-2 theories, with a focus on ghost-free bimetric theory. We will outline its history and its…

Time functions and $K$-causality between measures

- Mathematics
- 2018

Employing the notion of a coupling between measures, drawn from the optimal transport theory, we study the extension of the Sorkin-Woolgar causal relation $K^+$ onto the space…