A Is It Known For Sure Infinites In QFT Are Caused Using a Continuum?

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The discussion centers on the relationship between infinities in Quantum Field Theory (QFT) and the use of continuous models. It highlights that the idealization of physical space as R3 leads to both ultraviolet (UV) and infrared (IR) infinities, with UV infinities arising from the continuum assumption. The conversation also touches on effective field theory (EFT) and the use of cutoffs to yield finite results, suggesting a potential connection to lattice models. Additionally, there is mention of the Nielson-Ninomiya theorem, which may limit the possibility of a fundamental lattice structure in spacetime. Overall, the consensus is that the infinities in QFT are indeed linked to the continuum model, though the discussion remains open to differing interpretations.
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I am reading WHAT IS A QUANTUM FIELD THEORY?" A First Introduction for Mathematicians.

The author states (2.4 Finite versus Continuous Models) that the use of continuity causes the infinities in QFT:

'Mathematicians are trained to think of physical space as R3. But our continuous model of
physical space as R3 is of course an idealization, both at the scale of the very large and
at the scale of the very small. This idealization has proved to be very powerful, but in the
case of Quantum Field Theory, it creates multiple problems, and in particular the infamous
infinities (in the form of diverging integrals).'

I think that, based on what I have read, it is a likely cause, but has it been proven?

It is not an issue in EFT because a cutoff is used to get finite answers. Could a cutoff be looked at as approximating a lattice model?

Thanks
Bill
 
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There are two kinds on infinities in QFT, UV infinities and IR infinities. UV infinities are due to using a continuum (in both space and time), while IR infinities are due to using infinite extension (in both space and time). And yes, it is known for sure that this is the case.
 
I've always been under the impression that the Nielson-Ninomiya theorem precludes the possibility of spacetime having a fundamental lattice-type structure, and that the infinities that appear in QFT a result of using the unphysical bare coupling constants🤔
 

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