SPEEDING UP PATH INTEGRALS

By lowering the resolution of a snapshot we loose many of its details – until recently, the same was true of path integrals. We’ve now learned to relate path integrals of different coarseness, decreasing information loss a hundred million fold. The result is a substantial computational speed up. Feynman’s path integrals are compact and rich tools for dealing with quantum theories. Using them we’ve learned about symmetries, phase transitions, connections between different models. They have allowed us to quantize complicated systems and have brought about a rich cross fertilization of ideas between different areas of physics, chemistry, materials science, modern finance. The bad news is that we still don’t know enough about these intriguing objects and can solve only a small fraction of them. Path integrals have helped us derive new approximation techniques, however, a predominance of interesting models can only be treated numerically. Numerical integration of path integrals has been notoriously demanding of computing time, often serving to benchmark the fastest supercomputers. The newly uncovered speed up is a result of novel analytical input and will be of direct practical use. Its ultimate benefit, however, may be in giving us a better intuitive grasp of quantum processes.