Quantum fields forever

Academy Professor Antti Kupiainen has received a €2.5 million ERC Advanced Grant.

Antti Kupiainen, whose research deals with quantum fields and probability theory, applies methods from theoretical physics to the mathematical models of stochastic phenomena.

In nature, such complex phenomena can be observed in the patterns of gushing streams or in the tracks of lightning bolts.

The theory of everything explains randomness

Quantum field theory was created in the mid-20th century to describe the interactions between elementary particles. It is currently known as the “theory of everything” in particle physics, and is used to describe electrons, quarks, photons and other fundamental particles.

Quantum field theory has since become a tool used to study a vast variety of complex phenomena, such as phase transitions or turbulence in fluids.

Universal phenomena

These complex natural phenomena have two important things in common.

“They are universal, and they invariant under a change of the scale we observe them. For example, the laws of turbulence are the same for water, air and mercury,” Antti Kupiainen states.

The concept of renormalisation was developed to study these two properties. Renormalisation theory describes mathematically how the system’s behaviour changes as the scale of our observations changes.

“Renormalisation is a central mathematical tool in my ERC project,” he says.

Properties change as the scale changes

Antti Kupiainen applies renormalisation to the study of non-linear partial differential equations.

Such equations can describe various natural phenomena: heat conductivity, the motion of a fluid in a medium, the dynamics of the surfaces bounding two different phases of matter and various growth processes.

Such phenomena share one crucial characteristic: they are stochastic, or random.

Professor Kupiainen explains:

“Natural systems rarely exist in isolation. Instead, their environment has random impacts on them and causes ‘noise’. Meanwhile, the dynamics of nonlinear systems are chaotic, and their regularities typically are statistical."

“No unifying theory has been found for such stochastic equations, so the renormalisation theory from quantum field theory is helpful.”

Quantum field theory describes stochastic surfaces

Antti Kupiainen also uses methods from quantum field theory to study stochastic geometry, which seeks to classify random curves, surfaces and other geometric structures.

“Natural geometric structures, such as clouds, the eddies in a rushing river or lightning bolts are very different from the straight lines, circles and spheres described by classical geometry,” he says.

“Even though individual clouds are all different, they may be statistically identical.”

Statistically speaking, natural structures often display beautiful symmetries, even though individual structures may be completely asymmetrical. Such structures are also often statistically identical at different scales, and their statistical properties universal.

ERC funding for five years

The new ERC grant provides the Academy Professor with sufficient resources to study exactly what he wants.

According to Kupiainen, there is another bonus to the grant:

“As the grant is very competitive, it has a certain charisma or reputation. My experience from my previous ERC Advanced Grant period is that its reputation helped me recruit the best postdoctoral researchers.”

Translation: University of Helsinki Language Services