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I have often heard about how when the quantum equations dealing with the other forces are applied to gravity they produce infinities. Can anyone point me to these equations? What exactly are they?
f-h said:you will see that unlike the infinities in the Standard Model, the infinities in the resulting perturbative QFT can not be removed perturbatively
marcus said:I suspect you are a QG grad student somewhere with a good background in QFT and probably string as well, and I am wanting very much to see more posts from you----at whatever mathematics level. It's all good. thanks.
f-h said:And another point I want to emphasize here: Nonrenormalizability means we can not define the theory perturbatively, it does not mean that it can not be defined and it does not mean it doesn't have a well defined perturbative expansion once defined nonperturbatively.
An example would be 2+1 gravity.
selfAdjoint said:Yes this is a very important point. Perturbation and renormalization are strategies for getting approximate answers, not deep ontological criteria. What may be true in the end is not clear from the current state of QFT.
One of the brags of string physics is that it doesn't require renormalization, but it still is heavily, heavily dependent on the perturbative strategy.
f-h said:Careful, this is a widely held assumption, that is known to fail for some models. Quoting from Ashtekar:
http://www.gravity.psu.edu/people/Ashtekar/articles/final.pdf
"There exist quantum Field theories (such as the Gross-Neveu model in three dimensions) in which the standard perturbation expansion is not renormalizable although the theory is exactly soluble!"
A small remark, as far as I know gravitation is not *perturbatively* renormalizable, meaning that you have to add an infinite number of counterterms in the action to make the formal power series well defined (the resulting series won't converge even then I guess - but nobody really knows that). A theory which is exactly soluble always has a formal power series expansion, the solution is just of C infinity class in the coupling constant and not analytic. So, the Gross-Neveu model would still be perturbatively renormalizable around a value of the coupling constant in which the exact solution is of C infinity class, while gravity isn't unless you can rigorously show that perturbation theory is formally well defined around a nontrivial background (but I do not believe it to be the case).f-h said:Careful, this is a widely held assumption, that is known to fail for some models. Quoting from Ashtekar:
http://www.gravity.psu.edu/people/Ashtekar/articles/final.pdf
"There exist quantum Field theories (such as the Gross-Neveu model in three dimensions) in which the standard perturbation expansion is not renormalizable although the theory is exactly soluble!"
The purpose of exploring quantum equations and gravity is to gain a deeper understanding of the fundamental forces and laws that govern our universe. By studying these concepts, scientists hope to uncover new insights and potentially develop new technologies.
Quantum mechanics is a theory that explains the behavior of matter and energy at a microscopic level. Gravity, on the other hand, is a force that governs the movement of massive objects in space. While they may seem unrelated, scientists are currently working on theories that aim to unify these two concepts and provide a more complete understanding of the universe.
One current theory is string theory, which proposes that the fundamental building blocks of the universe are not particles, but tiny strings that vibrate at different frequencies. Another theory is loop quantum gravity, which suggests that space and time are made up of tiny, indivisible units. Both of these theories attempt to reconcile quantum mechanics and gravity.
Scientists use a variety of methods to study quantum equations and gravity, including mathematical models, computer simulations, and experiments. They also rely on data from observations made by telescopes and other scientific instruments to test and refine their theories.
Understanding quantum equations and gravity could lead to significant advancements in fields such as quantum computing, space travel, and even medicine. It could also provide a deeper understanding of the origins and evolution of the universe.