The motivation to open this discussion is due to this question: can Mach’s principle explain away dark matter?

In 1918, Einstein wrote: “... in a consistent relativity theory there cannot be inertia relative to “space” but only inertia of masses relative to each other”. Later in life, he retracted his support of Mach's principle because he had linked it to general relativity and general relativity was criticised because of that link.

From the quote, we should understand that masses determines the inertial reference. In a galaxy, as the stars are rotating, the inertial reference is rotating with the stars. As the inertial reference is rotating, individual stars have no relative speed (relative to the inertial reference), so no centrifugal force, no reason for the stars to escape the galaxy, no need for dark matter. ]]>

created a minimum at *Penrose-Hawking singularity theorem*

quick note for *5-dimensional Chern-Simons theory*, for the moment just to record some references

started *M-theory on G2-manifolds*

As a welcome means of procrastinating work on *spectral sequence*, I created *G2-MSSM* and touched or created stubs for a bunch of related entries, such as adding references to *G2-manifold*, creating *model (in particle physics)*, disambiguating at *model* etc. pp.

In my master thesis I have stumbled upon some issue which makes me go crazy. I want to state the problem but I should discuss it so that it would not mislead me.

There is a model at hand, a field theory which interacts with gravity non minimally via metric in the lagrangian. This field theory is nontrivial topologically and prequantizes. Nonetheless, it has a prequantization when we fix the metric but it seems that it has no canonical prequantization as a field theory on the bundle of fields + metrics (satisfying certain conditions). Moreover, there is an obstruction to prequantization of such a field theory, since if we compute metric energy-momentum tensor locally it shall not glue properly to a global one.

Initially I intended to find out how gravity interacts with nontrivial topologically field theories so as to conclude inconsistencies with gravity even at the level of prequantization.

It seems that given a prequantum field theory which has interaction with gravity (via energy-momentum tensor) we must deform it (canonically some way, so that it could be functorial, may be additive…) so as to extend the prequantization to the bundle of fields + metrics.

Why this idea? I guess the answer is that we already do this with even locally-defined field theories. An obstruction to a proper nonminimal interaction (via Energy-Momentum tensor) of a field theory with gravity is that the Energy-Momentum tensor must be divergence-free. When we deform a given field theory we usually fall to such field configurations that satisfy divergence-freeness or even fall on-shell of the theory.

So we had:

obstruction to nonminimal interaction - divergence-freeness of EMT (analytical condition). We deform a bundle of a theory but not lagrangians. This deformation is “canonical”.

Now we have in addition:

obstruction to nonminimal interaction - EMT should be a globally defined tensor on a manifold (topological condition). We deform a field theory but I guess here we change the Lagrangians so that they could prequantize on a bundle of fields + metrics.

What do you think I could do in this case? ]]>

created *worldline formalism* to go with this Physics.SE answer

I gave *Seiberg-Witten theory* an Idea-paragraph, added the orinal reference and cross-linked with *N=2 D=4 super Yang-Mills theory* and with *electric-magnetic duality*.

added briefly the definition to *Einstein-Yang-Mills theory*

stub for *dark matter*

I have started adding references to *string field theory* , in particular those by Jim Stasheff et al. on the role of L-infinity algebra and A-infinity algebra. Maybe I find time later to add more details.

stub for *quantum computation*

Am working on the entry *higher Cartan geometry*. Started writing a *Motivation* section.

This is just the first go, need to quit now, will polish tomorrow.

]]>added a brief historical comment to *Higgs field* and added the historical references

I am beginning to give the entry *FQFT* a comprehensive *Exposition and Introduction* section.

So far I have filled some genuine content into the first subsection *Quantum mechanics in Schrödinger picture*.

But I have to quit now. This isn’t even proof-read yet. So don’t look at it unless you feel more in editing-mood than in pure-reading-mood.

]]>added a few more references with brief comments to *QFT with defects*

(this entry is still just a stub)

]]>Started an entry in “category:motivation” on *fiber bundles in physics*.

(prompted by this Physics.SE question)

]]>recorded some recent surveys of the status of MOND at *MOND*

stub for *confinement*, but nothing much there yet. Just wanted to record the last references there somewhere.

am in the process of adding some notes on how the D=5 super Yang-Mills theory on the worldvolume of the D4-brane is the double dimensional reduction of the 6d (2,0)-superconformal QFT in the M5-brane.

started a stubby *double dimensional reduction* in this context and added some first further pointers and references to *M5-brane*, to *D=5 super Yang-Mills theory* and maybe elsewhere.

But this still needs more details to be satisfactory, clearly.

]]>started something stubby at *Liouville theory*, for the moment just so as to record some references and provide for a minimum of cross-links (e.g. with Chern-Simons gravity).

(also created a stub for quantum Teichmüller theory in the course of this, but nothing there yet except a pointer to reviews)

]]>I have touched the Idea-section at *first-order formulation of gravity*, trying to improve a little.

added a bunch of pointers to the literature (with brief comments) at *string scattering amplitude*.

Also added a corresponding paragraph at *effective field theory*.

(this is still in reaction to that MO discussion, specifically to the question here)

]]>added to *S-matrix* a useful historical comment by Ron Maimon (see there for citation)