In a magazine article [1] on problems and progress in quantum field theory, Wood writes of Feynman path integrals, “No known mathematical procedure can meaningfully average an infinite number of objects covering an infinite expanse of space in general. The path integral is more of a physics philosophy than an exact mathematical recipe.”

This article [2] provides a method for averaging an arbitrary collection of objects; however, the average can be any number in the extension of the range of these objects. (Note, an arbitrary collection of these objects is a function.)

Question: Suppose anything meaningful has applications in quantum field theory. Is there a way to meaningfully choose a unique, finite average of a function whose graph matches the description in Wood's quote?

For more info, see this post [3].

[1]: https://www.quantamagazine.org/mathematicians-prove-2d-version-of-quantum-gravity-really-works-20210617/

[2]: https://arxiv.org/pdf/2004.09103

[3]: https://math.stackexchange.com/q/5052005/125918

#PathIntegral #quantum #FeynmanPathIntegral #mean #average #expectedvalue #quantumfieldtheory

#ICYMI "It’s like black magic...Mathematicians are not comfortable working with things where it’s not clear what’s going on" https://www.quantamagazine.org/how-our-reality-may-be-a-sum-of-all-possible-realities-20230206/ via @QuantaMagazine re: #pathintegral et al.

How about some (theoretical) reality?

#Dirac, #Feynman and what to put in the #PathIntegral.

Very interesting and not too hard to follow.

https://www.quantamagazine.org/how-our-reality-may-be-a-sum-of-all-possible-realities-20230206/

#Physics #QuantumPhysics #TheoreticalPhysics #QuantaMagazine

#Introduction

I’m a #Physicist working in a #Chemistry department, mostly #CompChem. I try and understand functional materials (particularly #semiconductor s) with #QuantumMechanics and #StatisticalMechanics, with a sprinkling of #MachineLearning. I particularly like #PathIntegral approaches. All my work is orientated towards #RenewableEnergy materials.

My favourite programming languages are #C and #JuliaLang. #Unix #CommandLine #HackThePlanet

#AcademicParent to a ~2 and ~4 year old.

And nobody has yet tagged even a single #pathIntegral as far as I can see 😱