An introduction to symmetric inflated probabilities

Abstract

Traditionally, probability is treated as a function that takes values in the interval [0, 1]. All conventional interpretations of probability support this assumption, while all popular formal descriptions, e.g., axioms for probability, such as Kolmogorov’s axioms, canonize this premise. However, researchers found that negative, as well as larger than 1 probabilities could be a useful tool in physics. Some even assert that probabilities that can be negative, larger than 1 or less than −1 are necessary for physics. Here we develop an axiomatic system for such probabilities, which are called symmetric inflated probabilities and reflect interaction of particles and antiparticles, and study their properties.