Convex valuations invariant under the Lorentz group

TL;DR

This paper classifies translation-invariant and Lorentz-invariant valuations on convex sets, providing a comprehensive understanding of their structure and extending to generalized valuations that are even under Lorentz transformations.

Contribution

It offers an explicit classification of Lorentz-invariant valuations, including continuous and even generalized valuations, advancing the mathematical understanding of valuations under Lorentz symmetry.

Findings

Complete classification of Lorentz-invariant continuous valuations

Classification of Lorentz-invariant even generalized valuations

Extension of valuation theory to Lorentz symmetry context

Abstract

We give an explicit classification of translation-invariant, Lorentz-invariant continuous valuations on convex sets. We also classify the Lorentz-invariant even generalized valuations.