Mathematics reveals the possibility of particles long thought impossible

Since the early days of quantum mechanics, scientists have believed that all particles can be classified into one of two groups based on their behavior: boons or fermions.

But new research by Rice University physicist Kayden Hazard and former Rice graduate student Zhiyuan Wang suggests particles that are neither boons nor fermions. Their research, published in the journal Nature, provides mathematical proof for the existence of paraparticles, long thought to be impossible.

“We determined that a new type of particle is possible that we didn’t know about before,” said Hazard, an associate professor of physics and astronomy.

Quantum mechanics has long held that all observable particles are either fermions or bosons. These two types of particles are distinguished by how they behave when near other particles in specific quantum states. Although an unlimited number of bosons can come together, only one fermion can exist in a particular state. This behavior of fermions is called the Pauli exclusion principle, which states that no more than two electrons, each with opposite spin, can occupy the same orbital in an atom.

“This behavior involves the entire structure of the periodic table,” Hazzard says. “That’s why you don’t just pass the chair when you sit down.”

In the 1930s and 1940s, researchers began trying to understand whether other types of particles might exist. A specific quantum theory of such particles, known as paraparticles, was formulated in 1953 and extensively studied by the high-energy physics community. But by the 1970s, mathematical studies seemed to show that so-called paraparticles were actually just bosons or fermions in disguise. The only exception is the existence of anyons, an exotic type of particle that exists only in two dimensions.

However, mathematical theories since the 1970s have been based on assumptions that do not necessarily hold true in physical systems. Hazzard and Wang used the solution of the Yang-Baxter equation, an equation that helps describe the exchange of particles, along with group theory and other mathematical tools to prove that paraparticles theoretically exist and with known constraints. We have started work to demonstrate that it is fully compatible. of physics.

The researchers focused on excitations (which can be thought of as particles) in condensed matter systems, such as magnets, to provide a concrete example of how paraparticles arise in nature.

“Particles are not just fundamental,” Hazzard says. “They are also important in explaining the material.”

“This is an interdisciplinary study involving several areas of theoretical physics and mathematics,” said Wang, who is currently a postdoctoral fellow at the Max Planck Institute for Quantum Optics in Germany.

Hazard and Wang used advanced mathematics such as Lie algebra, Hopf algebra, representation theory, and pictorial techniques based on what are known as tensor network diagrams to better handle equations to perform abstract algebraic calculations. I was able to run and develop a condensed matter model. A system in which paraparticles appear.

They showed that, unlike fermions and bosons, paraparticles behave in strange ways when they exchange positions with the particle’s internal state, which changes in the process.

These models are groundbreaking in their own right, but they are the first step toward a deeper understanding of the many new physical phenomena that can occur in quasiparticle systems. Further development of this theory could lead to experiments that can detect paraparticles in condensed matter excitations.

“More realistic theoretical proposals are needed to realize paraparticles in experiments,” Wang said.

The discovery of new elementary particles and properties of matter could be used for quantum information and calculations, such as manipulating the internal states of particles to secretly transmit information.

Consideration of potential applications is at an early stage and is still largely speculative. This work is an early step in the study of quasi-statistics in condensed matter, but it is unclear where these discoveries will lead. Further exploration of the new type of theory discovered and the observation of paraparticles in condensed matter and other materials will be the subject of future research.

“I don’t know where it’s going to go, but I know it’s going to be exciting to find out,” Hazard said.