Quantum mechanics has long classified particles into just two distinct types: fermions and bosons.

Now physicists from Rice University in the US have found a third type might be possible after all, at least mathematically speaking. Known as a paraparticles, their behavior could imply the existence of elementary particles nobody has ever considered.

“We determined that new types of particles we never knew of before are possible,” says Kaden Hazzard, who with co-author Zhiyuan Wang formulated a theory to demonstrate how objects that weren’t fermions or bosons could exist in physical reality without breaking any known laws.

From the early days of quantum mechanics, scientists have thought that all particles can be categorized into one of two groups—bosons or fermions—based on their behavior.

However, new research by Rice University physicist Kaden Hazzard and former Rice graduate student Zhiyuan Wang shows the possibility of particles that are neither bosons nor fermions. Their study, published in Nature, mathematically demonstrates the potential existence of paraparticles that have long been thought impossible.

“We determined that new types of particles we never knew of before are possible,” said Hazzard, associate professor of physics and astronomy.

Beyond fermions and bosons: unveiling new particle behaviors in mechanics.

In the world, particles traditionally fall into two categories: fermions (like electrons) and bosons (like photons), each obeying distinct exchange rules. These “exchange statistics” shape the behaviors of particles, from the structure of atoms to the glow of lasers. In two dimensions, a peculiar third type, called anyons, has been theorized and observed, adding a twist to this framework. But could there be even more possibilities?

This study ventures into uncharted territory by revisiting “parastatistics,” an idea from theory that goes beyond fermions and bosons. Previously dismissed as merely theoretical and equivalent to the known particle types, parastatistics now emerges in a new light. The researchers reveal that particles obeying non-trivial parastatistics can exist in real physical systems and behave in fundamentally different ways. These “paraparticles” follow unique rules of exclusion, resulting in strange and exotic thermodynamic behaviors unlike any seen in fermions or bosons.

To bring this concept to life, the team developed a mathematical framework for paraparticles, showing how they naturally fit within the broader universe. They designed solvable models where paraparticles arise as quasiparticles—tiny, particle-like excitations in materials—observable through their distinct exchange behavior. Remarkably, these models work in both one and two dimensions, demonstrating the tangible potential of paraparticles in real-world systems.

The findings hint at exciting possibilities: a new class of quasiparticles in condensed matter physics and, perhaps more provocatively, the existence of elementary particles governed by entirely novel statistics. This discovery could expand our understanding of the world and open the door to unimagined phenomena in both theory and experiment.