Recent content by ErikZorkin

I recently watched this video by David Tong on computer simulation of quantum fields on lattices, fermionic fields in particular. He said it was impossible to simulate a fermionic field on a lattice so that the action be local, Hermitian and translation-invariant unless extra fermions get...

Found this interesting article which seems quite related to our discussion. It is called "Pilot-Wave Quantum Theory in Discrete Space and Time and the Principle of Least Action"

Perhaps, your theory has some mathematical equivalence to a lattice field theory with on an infinite space-time lattice?

Yes. But it is mostly numerical studies an no convergence can be proven in the general case. Actually, your integral might be something else because the particle quantity is at least countable. I am just wondering how convergence of your apparatus would look like with a finite particles cutoff.

Addendum: just came across this paper. See the example on the first page Also this.

I think (not a specialist though) that this is quite often the case (the path integral cannot be well defined in the first place -- there is a theorem that forbids any complex-valued Lebesgue measure on an infinite-dimensional Hilbert space). Furijawa wrote a book on time discretization approach...

Right. But in the case of the path integral, it doesn't always make that much sense -- the approximations don't converge (or misbehave). I was thinking maybe in your application of Bohmian mechanics to QFT they would behave better.

Thank a lot! I've read this section and briefly browsed through the rest of the book. However, I didn't fully get how it addresses finite-dimensional QFT. I was still able to find this article and some other materials on QM on finite-dimensional Hilbert spaces for position and momentum. Do you...

Yes, it sounds interesting.

Right, this is what I thought of. I think, mathematically, those are the same things and, thus, problematic. So, all in all, it seems you don't need the path integral, but an integral over all particles. Have you, or anyone else, thought about lattice and/or finite-dimensional variants of the...

Exactly. But the integral (28) used the pseudo-measure (30). How come (28) is an ordinary integral as you said in your 1st post?

This is what I meant. It is not even a measure

Glad that I came across an expert! So, (30) is mathematically the same "measure" as the one used in the Feynman integral, I guess. "Measure" in quotes because there is no infinite-dimensional Lebesgue measure. The mathematical problem is thus the same as in the de Broglie theory and Feynman...

I am looking for good references / clarifications on the subject. First of all, my question is concerned only with mathematical formulation of something that sort of plays the role of the Feynman path integral of the "standard" QFT. It is not concerned with the physical or philosophical...

I also heard time travel enabled such things as indefinite energy magnification, hypercomputation and stuff like that. These are hard to call physical