Physics as Math

 


Using mathematics to solve quantum problems may have just gotten a little easier easier. A team led by RIKEN researchers have published a new study in the journal of High Energy Physics.

Quantum field theory is an example of converting math to physics. It’s an attempt to combine three theories, classical field physics, Einstein’s special relativity and quantum mechanics into one math problem.

The main issue is that a lot of computer power is used, however, there has been some successful conversions in both particle physics and condensed matter physics.

Treating space and time as a gridwork of separate points is one way to simplify the mathematics. 

Advanced theory called lattice field theory is tricky, but also feasible. It applies complex algorithms that work within it’s spherical interpretation.

Lingxiao Wang works with the RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS). Working with others in the UK and Germany, they have been studying a new approach called stochastic quantization. 

The basis for the new technique is used in deep learning and is called generative diffusion.

“ We’ve shown that models based on generative diffusion provide a powerful network for exploring quantum field theories on a lattice,” reports Wang.

Generative diffusion models learn in a unique way. It changes the data associated with text or an image, and then fixes it. 

The model learns how to fix the corrupted data and then it can apply the opposite process to random data. This random data is referred to as noisy input.

 The application of the opposite process can create a new realistic image or a sensible text. Wang’s team discovered that the stochastic quantization method works similarly to quantum field theory. 

“stochastic quantization involves introducing quantum noise into the field system, which allows for a probabilistic interpretation of quantum fields. This approach is used in lattice field theory as it provides an alternative way to simulate quantum field theories on a computer,” reports Wang. 

Another view is that generative diffusion creates realistic data from random noise by reverse engineering that noise. Stochastic quantization gives the appearance of a real world quantum model, with measurable quantum mottle (noise). 

Wang tested the theory by applying it to a specific type of lattice field theory simulation. He found that the solutions came much faster than was possible in previous attempts.

Up Next, the team wants to study more intricate systems. “The next step is to explore a quantum field system that has more dimensions, which is closer to our physical world,” summarized Wang.

The conversion from physics to mathematics continues. 


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