Paraparticles may upend standard model of physics
The simplest explanation is often the wrong one. Physics has long divided the universe into two kinds of particles: fermions, which make up matter, and bosons, which carry forces. This binary seemed complete, written into the mathematical structure of quantum mechanics. But recent mathematical work by Zhi Li, Shang Yu, and Kaden Hazzard has revealed a potential third category These so-called paraparticles would be neither matter nor force, but something stranger in between. [3] They obey an alternate set of quantum rules first proposed in 1953 by physicist Herbert Green, then largely dismissed for decades. Thanks to new mathematical insights, paraparticles may be more viable than anyone thought. No one has seen one in nature, but if they exist, it would shake our understanding of reality. As Vlatko Vedral at the University of Oxford puts it: “This would be huge. It could mean the standard model is badly wrong.” [3]
The Hidden Compartments of Quantum Reality
The standard model of particle physics is our best current theory of the universe’s fundamental ingredients. It already has gaps: it omits gravity and cannot explain dark matter or dark energy. Paraparticles might offer a new way into those missing parts. To understand why paraparticles once seemed impossible, one must return to the two kinds of particle we know exist. Fermions, such as electrons and quarks, make up matter. Bosons, such as photons and gluons, carry forces. Together, they compose all fundamental particles in the standard model. Matter and messenger — the division between the two is not merely superficial; it seems written into the very mathematical structure of quantum mechanics.
Quantum mechanics treats particles in a strange but strict way. Two electrons are not just very alike. As far as the theory is concerned, they are interchangeable. Swap them in the maths and no experiment should be able to tell that anything has happened. The maths in question is the wave function: a mathematical object that encodes the probabilities of finding them in particular states, defined by properties such as location, energy and spin — a kind of internal angular momentum. Wave functions contain odd-looking components, including negative signs and imaginary numbers. But experiments only ever yield ordinary probabilities. To get these, physicists square the wave function, making some of the mathematical oddness disappear from view.
When two identical particles are swapped, there are two possible outcomes: the wave function can stay as it is or it can flip sign. After squaring, both options give the same positive probabilities. But physically, they describe very different kinds of particles. In one case, identical particles can crowd together. These are bosons, a family that includes photons, which mediate the electromagnetic force, and gluons, which carry the strong nuclear force that binds quarks into protons and neutrons. Because bosons can have the same quantum properties at the same time, they tend to be quite gregarious. Photons, for instance, can pile together in the beam of a laser.
In the other case, identical particles are barred from sharing a quantum state. These are fermions, including electrons, quarks and ghostly particles known as neutrinos. They are mathematically forbidden from overlapping, making electrons antisocial and explaining why they occupy different shells around atomic nuclei. It is also what gives ordinary matter its stubborn solidity: squeeze atoms too tightly and their electrons have nowhere new to go, producing a quantum pressure that resists further compression. For decades, that seemed to exhaust all the possibilities. There was no obvious third option.
Herbert Green found one in 1953. He suggested that the wave function might have more structure inside it than physicists had assumed. When two identical particles were swapped, the wave function need not simply stay the same or flip sign. It could also rearrange hidden internal states that do not show up directly in ordinary measurements. Think of two identical-looking boxes. From the outside, swapping them changes nothing: the same boxes are still there, and any ordinary inspection gives the same result. But what if there are unseen compartments inside? If so, the external sameness is preserved, even though something concealed within has changed. These are often referred to as “hidden states,” and the particles that possessed them were named “paraparticles.”
These hidden states became a source of scepticism around paraparticles. No one knew what they corresponded to physically. They might be nothing more than a mathematical trick. Or they might turn out to be similar to spin — a quantum mechanical property with no straightforward classical equivalent — except hidden from ordinary measurement. As Kaden Hazzard at Rice University in Texas explains: “The physical meaning attached to them is going to be dependent on what they actually are in a real physical system.” [2] Because of this, Green faced an uphill struggle. Francesco Toppan, a theoretical physicist at the Brazilian Center for Research in Physics in Rio de Janeiro, notes: “Already at the beginning, people started asking: ‘If these exist, why don’t we observe them?’ People argued you can’t see them because they are actually equivalent to bosons and fermions.” [1]
The DHR Verdict and Its Exceptions
In 1971, that argument seemed to triumph. Three physicists — Sergio Doplicher, Rudolf Haag and John E. Roberts, known as DHR — showed that, in a three-dimensional world, any theory of paraparticles could be recast as ordinary standard-model physics in disguise. Space itself would force paraparticles to behave as either fermions or bosons. Their verdict soon hardened into textbook wisdom: paraparticles were a fun idea, but not real. Still, some were undeterred. In the 1980s, Nobel laureate Frank Wilczek showed that particles confined to two dimensions — as they can be within thin layers of materials — could indeed obey different rules. He called them “anyons,” and they were a remarkable challenge to the accepted orthodoxy.
“When I first proposed anyons, I thought of it as just kind of a lark and a curiosity,” says Wilczek. “But soon they turned up experimentally.” Not as free-floating fundamental particles, however. Anyons emerge in certain materials and are known as “quasiparticles” — collective disturbances that behave like particles. A phonon is a simpler example. It is essentially a packet of sound, produced by atoms vibrating in a material, rather like a Mexican wave travelling through a packed stadium. No single person is the wave, yet the wave moves as if it were an object in its own right. Anyons are now taken seriously as possible building blocks for fault-tolerant quantum computers. An experiment in 2024 showed how swapping them around allows information to be stored in a form that is more resilient to errors.
But anyons looked like a special loophole to the rule DHR had established: exotic and useful in the laboratory, but nowhere close to a rebuttal of the standard model’s grand binary. In three dimensions, making paraparticles work is quite a bit more difficult. In 2021, Toppan tried to introduce a different type of algebra for describing paraparticles in the laboratory. With this maths, he found that ordinary space no longer forced paraparticles to collapse back into fermions or bosons. The trick was to stop looking at particles one by one. On their own, they could still pass for ordinary particles, but in groups their shared quantum state carried an extra mathematical fingerprint, unique to paraparticles.
The 2026 Breakthrough and Its Limits
In 2026, a new mathematical paper by researchers Zhi Li, Shang Yu, and Kaden Hazzard, published on the arXiv preprint server as reference 2607.11867v1, cracked the code further. They developed a framework that describes how paraparticles could exist in three dimensions without collapsing into fermions or bosons. The key was to treat the hidden states not as extra baggage but as part of a larger mathematical structure called a “braided tensor category.” This allowed the wave function to rearrange itself in ways that are neither symmetric nor antisymmetric, but something else entirely.
The researchers showed that paraparticles could carry a new kind of quantum number, one that does not appear in the standard model. This quantum number would be conserved in interactions, meaning paraparticles could not decay into ordinary particles without violating the rules. This makes them potentially stable, like dark matter candidates. The paper does not claim to have found paraparticles in nature. It only shows that the mathematics allows them. As Hazzard states: “We have shown that there is no mathematical obstruction to paraparticles existing in our three-dimensional world. Whether they actually exist is an experimental question.”
This experiment’s contribution to fundamental research is clear: it removes a theoretical barrier that stood for over 50 years. The DHR theorem, which had seemed to forbid paraparticles, now has an exception. The researchers do not promise applications. They do not claim that paraparticles will solve dark matter or dark energy. They only show that the door is open. The next step, the researchers state, is to look for paraparticles in experiments No one has seen one yet. But the stakes are high. If paraparticles exist, they would force a revision of the standard model. They would add a third category to the binary of matter and force — neither bosons nor fermions, but something stranger in between. And they might hold the key to the missing parts of our universe.