Bengtsson picks up on Krasnov's non-metric gravity

[marcus]

For anyone not familiar with Bengtsson here are 34 papers in gr-qc, hep-th, and quant-ph going back to 1992
http://arxiv.org/find/grp_physics/1/au:+Bengtsson_I/0/1/0/all/0/1

He picked up fast on Krasnov's idea for (renormalizable) non-metric gravity.
http://arxiv.org/abs/gr-qc/0703114
Note on non-metric gravity
Ingemar Bengtsson
9 pages

"We discuss a class of alternative gravity theories that are specific to four dimensions, do not introduce new degrees of freedom, and come with a physical motivation. In particular we sketch their Hamiltonian formulation, and their relation to some earlier constructions."

This refers to two recent papers by Kirill Krasnov
http://arxiv.org/abs/hep-th/0611182
Renormalizable Non-Metric Quantum Gravity?
http://arxiv.org/abs/gr-qc/0703002
Non-Metric Gravity I: Field Equations

It's a new idea. Krasnov gave a seminar talk at Perimeter about it recently, available video in PIRSA, with Smolin asking him questions.

Here is Bengtsson's opening paragraph:
A class of alternative gravity theories were recently introduced, under the name of “non-metric gravity” [1]. There are reasons to take this class seriously, in particular arguments were advanced why this class—which is defined by one free function of two variables—should be closed under renormalization [2]. Indeed the construction is interesting already on the classical level, since it does not introduce any new degrees of freedom, as compared to GR (which is a member of the class); moreover the construction is intrinsically four dimensional (arguably a good thing), and is based on a clean split between conformal structure and conformal factor of the metric. In fact the split is so clean that the latter is largely lost track of, which brings us to some weak points of these models. The first of those is that the models describe complex spacetimes, and it is not clear how to recover the Lorentzian sector. The second is that they appear to be quite difficult to couple to matter (but this may turn out to be a strong point in the end).

The purpose of this note is to clarify the relation between non-metric gravity and an earlier class of models with similar properties [3, 4]. The starting point is Plebánski’s action for vacuum general relativity...

 

[marcus]

Bengtsson seems to be very likeable, from his homepage
http://www.physto.se/~ingemar/

His Erdos number is 3 and his Einstein number is 4.
I think he was born around 1960 and he was at Chalmers, CERN, and London Imperial before going back to Sweden in 1993 to be a lecturer, and then professor, in physics at Stockholm.

He has engagingly frank opinions which he expresses peacefully.

He has written a book, together with another physicist, that was published by Cambridge University Press in March 2004. The first edition sold out and a second (more expensive) edition was published in June 2006. It is called
The Geometry of Quantum States
https://www.amazon.com/dp/0521814510/?tag=pfamazon01-20

 

[Entropia]

I find Bengtsson's response to Krasnov's non-metric gravity theory to be intriguing and worth further exploration. The fact that this theory is specific to four dimensions and does not introduce new degrees of freedom is a promising aspect, and the idea that it may be closed under renormalization is also interesting.

However, there are also some potential weaknesses in this theory, such as the difficulty in coupling it to matter and the fact that it describes complex spacetimes. These are important considerations that will need to be addressed in future research.

It is also worth noting that Bengtsson's work on this theory dates back to 1992, which shows that this is not a new idea and has been studied for many years. This further emphasizes the importance of continued research and exploration in this field.

Overall, I believe that Bengtsson's response provides valuable insights into Krasnov's non-metric gravity theory and highlights both its strengths and weaknesses. I look forward to seeing further developments in this area of research.