paralleltransport said:
Hi Jedi, thanks. I already have worked through about 2/3 of the standard QFT book (Peskin & Schroeder), which covers a typical 2 semester QFT course. This means I am familiar with all the QFT prerequisites, and some condensed matter (second quantization, perturbation theory, path integrals, etc...). I'm asking for resources beyond this bridge the gap between peskin and current research papers at the interface between CMT and QFT.
For example, peskin & schroeder only covers OPE pretty late, little on CFT like virasoro algebra, fusion algebra or TQFT, the relation between topology and instantons & confinement (non-perturbative effects). It just seems very out-dated.
Here are some things I see that I don't know:
- "higgsing" a theory
- intuition for local vs. non-local order parameters (obstruction for them).
- relation between chern class and application to gauge theories.
- higher form symmetries.
- confinement due to instantons and monopoles in gauge theory, how topological effects (non-zero chern number) can protect you from that.
- "integrate out fermions" to get chern simons term.
- quasi-particle fusion algebra in TQFT.
- various dualities between XY model, Z2 gauge theory, their phase transitions etc... EM dualities, maxwell theory in other dimensions than 4.
- c-theorem, central charges, relation to entanglement entropy.
A different strategy than finding a book on these subjects is to find an article that is squarely discussing one of these subjects, to identify the most pertinent references (especially from the introduction and key parts of the analysis), and then to look at those articles and do the same thing, recursively working your way back in the chain of citations until you go back far enough that they reach a point where you can engage with it.
In almost all of these areas, the literature will go back no further than about 50 years, and in many cases significantly less. Also, the literature on anyone of these subfields isn't all that voluminous if you really focus in on it.
A related strategy is to focus especially on terminology that you can't precisely define in your head when you are reading it, and likewise make sure that you have a firm grasp of all of the notation that is being used.
I find that a lot of the fog can clear when you know exactly what the notation means and you have a precise definition of the relevant terms in your head, or at least, a working glossary of what these terms mean in a document that you develop as a study tool and revise from time to time as you learn more and discover that one or more of your previous definitions wasn't quite right (or that the same term or phrase was used in multiple senses with subtly different meanings). It is always tempting in the moment to continue reading when you have only an approximate idea of what something means informed by context, rather than breaking up the process of reading a paper to go confirm what something you thought you knew the meaning of sort of means more exactly, but it is usually worth it if you have the kind of learning objectives that you've expressed.
Also, some sources explaining the meaning of a term will reference either the original paper where the term was introduced (especially in the case of concepts that are named after someone), or at least an early paper utilizing the term that allows you to skip a lot of steps when backtracking the chains of citations in the literature. You can also sometimes find citations to these seminal papers in online biographies of the people these concepts are named after.
If you are interested in the work of Dr. Chern and Dr. Simons, for example, go read their original papers that gave rise to the terminology and then trace its development forward, learning about the development of those ideas the way that the people actively doing research in that subfield at the time did. Also, as you do so, keep a particular eye out for review articles that come up for air to see the forest, so that you don't get too lost in the trees.
One reason to do this, rather than relying exclusively or predominantly on book length texts, is that new research inevitably and almost by definition, is at the cutting edge. Also a paraphrase or summary in a book length treatment can often lose key qualifications or specifications found in early articles that are more important to understanding that the person who wrote them (who almost always understands the topic extremely deeply, to the point of not really remembering where the bumps in the road to acquiring that knowledge are anymore) overlooks or omits as "obvious".
It takes more time for book length treatments to catch up to current research than it does for published articles and preprints to do so. This is the same basic reason that you can find a wealth of good books on music history and music genres up through about mid-20th century jazz, but really need to turn to a more real time resource, like Wikipedia, to find good treatments of more recent musical genres.
Book length treatments also tend to include overemphasis on one or more subjects or perspectives that have subsequently born out to be dead ends and aren't the subject of active research anymore. But it tends to be very hard to find book length treatments the discuss dead ends and explain why they died. Extending the music history analogy, you might very well find book length treatments that go on and on about how tone poems that use every note in the scale, or extreme dissonance, or disco are the future of music despite the fact that they subsequently fizzled, without ever anticipating the global musical influence that rap would end up having.
Further, try not to fall into the trap of thinking about the things you don't know to understand current research as a collective body of knowledge. There are lots of individual things that you don't know, some of which are related to each other, but most of which are more or less independent of each other for someone with your level of baseline knowledge. If you conceive of it as lots of little independent research projects, rather than one big one, and focus on the ones that come up in the papers that interest you the most first, it doesn't become such an insurmountable challenge.
Each week or two you learn one or two more terms, and one or two more concepts. Some weeks will be boom weeks when you learn several. Other times, the process of recursively tracing back through references and trying to find definitions that don't contain terms you don't understand will be frustrating and it may take several weeks to break through that one. If you get really stumped on something, come here, or to Physics.SE and ask, but it is best to gain confidence by trying to figure things out yourself for a while first.
