What knowledge is needed to understand modern QFT research?

[paralleltransport]

TL;DR Summary

I'd like to know what subject is part of general knowledge for theorist

Hi all,

I'm interested in the interplay between condensed matter and high energy theory. I'm a bit more than half-way through peskin and schroeder (done with part II, RG and critical phenomena).

What I find out is that I'm still sorely lacking in ability to read any of the current research in the following subjects:

1) Condensed matter: in particular, a lot of the modern papers uses CFT, TQFT knowledge, and intuition about topological phases and entanglement/phase transition I just don't know.

2) HEP research related to QFT: here, it relies both heavily intuition from CFT knowledge, TQFT, representation/group theory, duality of field theories (strong vs. weak coupling etc...) none of which is mentioned in peskin & schroeder, and gauge theory formulated in differential form notation.

It seems to make progress I'd like some idea of what I can study further, aka supplement a "standard" text like Peskin & Schroeder to enrich my understanding.

What resource do you recommend to supplement a standard text like Peskin and Schroeder to understand modern HEP research?
In particular am I ready to read supplement knowledge or should I just keep trying to finish a standard QFT book and come back then.

 

[jedishrfu]

This might be a good question for your college prof or course advisor.

 

[paralleltransport]

Thanks but I'm no longer in school. Just learning physics for fun. I was hoping there was people out there who went through the process and had tips on progressing.

 

[jedishrfu]

Okay so I would start with an online course for QFT or Condensed Matter and recursively work through the prerequisites making list of courses to see what was needed to take the selected course. Repeat with each prereq to see what they need…

Mathwise I’d look into the Garrity book “All the Mathematics You Missed but Need for Grad School”. It likely covers ninety percent of what you’ll need If you can master it.

 

[paralleltransport]

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.

 

[PAllen]

Okay so I would start with an online course for QFT or Condensed Matter and recursively work through the prerequisites making list of courses to see what was needed to take the selected course. Repeat with each prereq to see what they need…

Mathwise I’d look into the Garrity book “All the Mathematics You Missed but Need for Grad School”. It likely covers ninety percent of what you’ll need If you can master it.

Beware there are a few embarrassing errors in this book. I got it as a refresher, and I like it for that, but, if I remember correctly, there are some bad errors in areas related to point set topology.

Also, I’ll put in a plug for @Orodruin ’s book on mathematics for physicists.

 

[paralleltransport]

I took a look at the book. It covers topics I've already learned either through a course or self study. Just to be clear, I had enough math and physics to read peskin & schroeder. But there's a lot of QFT intuition I am missing when I read modern research at the interface between QFT and CMT.

 

[jedishrfu]

Beware there are a few embarrassing errors in this book. I got it as a refresher, and I like it for that, but, if I remember correctly, there are some bad errors in areas related to point set topology.

Sadly every technical book I’ve ever read had small hidden errors. In Arfken, in the first few pages of chapter 1 there was a 3D chart of a vector and it’s direction angles.

The chart implied that one of the angles came from the projection of the vector onto the XY plane. Earlier editions of the book had it right but later editions had this new chart that was misleading and wrong.

The Garitty book has published a new edition recently according to Amazon. The old one was circa 2002.

There is likely an errata sheet somewhere that identifies the known errors in the book.

 

[MathematicalPhysicist]

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 list of a few books on my reading list.
You might find something good in this list:
1. https://www.amazon.com/dp/038794785X/?tag=pfamazon01-20

2. https://www.amazon.com/dp/B00DBO3B9E/?tag=pfamazon01-20

3. Ed Manoukian's two QFT books.

4. Marino's TQFT and 4 manifolds.

5. Sonnenschein's and Frishman's red book on QCD.
6. there are several books on QFT in CMT.
And the list goes on forever...

 

[MathematicalPhysicist]

Also shifman's books, Introduction to confinement by Greenslite.

 

[ohwilleke]

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.

 

[PeroK]

Summary:: I'd like to know what subject is part of general knowledge for theorist

Hi all,

I'm interested in the interplay between condensed matter and high energy theory. I'm a bit more than half-way through peskin and schroeder (done with part II, RG and critical phenomena).

What I find out is that I'm still sorely lacking in ability to read any of the current research in the following subjects:

1) Condensed matter: in particular, a lot of the modern papers uses CFT, TQFT knowledge, and intuition about topological phases and entanglement/phase transition I just don't know.

2) HEP research related to QFT: here, it relies both heavily intuition from CFT knowledge, TQFT, representation/group theory, duality of field theories (strong vs. weak coupling etc...) none of which is mentioned in peskin & schroeder, and gauge theory formulated in differential form notation.

It seems to make progress I'd like some idea of what I can study further, aka supplement a "standard" text like Peskin & Schroeder to enrich my understanding.

What resource do you recommend to supplement a standard text like Peskin and Schroeder to understand modern HEP research?
In particular am I ready to read supplement knowledge or should I just keep trying to finish a standard QFT book and come back then.

I'm sceptical that you can get up to this level without going all-in and making physics a career. One problem is having no supervisor or colleagues to guide, help and support you. Many papers today are a team effort, often involving collaboration between theory groups around the world. You need to be plugged into that network.

Published textbooks must be at least a decade behind current research. Peskin and Schroeder will only take you so far.

 

[ohwilleke]

Thanks but I'm no longer in school. Just learning physics for fun. I was hoping there was people out there who went through the process and had tips on progressing.

Don't be afraid to pose the kind of questions you have posed here in a somewhat more focused email to a corresponding author of a relevant hot off the presses paper.

Most of the authors have spent a significant part of their career as college level physics educators, spend free time going to conferences to talk about this stuff, and have only a few graduate students or nearly graduating undergraduates, and few peers at their own institution that they can really talk to about something that is their core passion and the trademark of their identity as a research physicist. They usually can't talk meaningfully about this passion to their spouses, children, parents or siblings, or to fellow members of in person social or religious groups that they are a part of. These are the discussions they want to have in life, but aren't getting due to the nature of how society is set up.

An email asking informed questions about modern research at the interface between QFT and CMT, instead of undergraduate level intro to physics questions or how to keep one's indexes straight when doing tensor mathematics, and also not pitching some crackpot theory or asking for an explanation of the latest incorrectly explained idea that the New York Times is talking about this week, is usually going to be received quite receptively (especially if your question is "a quick question" that isn't going to require multiple pages of exposition to explain).

Not every corresponding author of a paper will be receptive, but you'd be surprised at how many are to that kind of question.

If you find even one or two unofficial mentors in professional physics who are willing to correspond with you about questions of this nature, both sides of the conversation will find it very rewarding.

 

[paralleltransport]

I'm sceptical that you can get up to this level without going all-in and making physics a career. One problem is having no supervisor or colleagues to guide, help and support you. Many papers today are a team effort, often involving collaboration between theory groups around the world. You need to be plugged into that network.

Published textbooks must be at least a decade behind current research. Peskin and Schroeder will only take you so far.

Hi PeroK,

Thank you. I was trying to gauge how far away from the boundary of current knowledge I was. If that's true then it seems I'm quite close and this is the point where I can strengthen my fundamentals are start doing research (pick a topic of interest and dive deep like ohwilleke discussed). When I was doing research in undergrad, it was definitely easier because you would attend the same seminars and there would always be grad students buzzing & brainstorming those topics day in and day out.

I was asking because I thought the body of knowledge I said was missing from pesking and schroeder all fall under the standard QFT lore a grad student should know. Maybe they are part of multiple stashes as mentioned, in which case it's OK I don't know all of it.

I do find the textbook literature of even 1970-80's physics very piecemeal. Things like exact RG (polchinski '83), gauge theory phases (shenker & fradkin '79) are not discussed in peskin, or delegated very late.

I think someone needs to write a more modern QFT textbook that starts discussing non-perturbative things (TQFT, instanton correction, ERG) before diving deep into QED perturbative calculation. The order things are presented in textbook makes no logical sense to me. From a self-learner perspective, it was very confusing :)

 

[George Jones]

I think someone needs to write a more modern QFT textbook that starts discussing non-perturbative things (TQFT, instanton correction, ERG) before diving deep into QED perturbative calculation. The order things are presented in textbook makes no logical sense to me. From a self-learner perspective, it was very confusing :)

Caveat emptor: I am not well-versed in quantum field theory.

I think that the the standard order results because many physicists consider this to be the "nuts and bolts" of many qft calculations, and because of inertia. These two things have non-zero intersection.

The text "Quantum Field Theory: From Basics to Modern Topics" by Francois Gelis, starting in Chapter 10, covers many topics that are not in Peskin and Schroeder. You can look at the Table of Contents on Amazon. I do not know how useful this is. I think that some of the material in Chapter 14 (or related material) is used to compare theory and experiment at the LHC.

PS My visit to amzon.com seconds ago has revealed that Gelis more recently has published a companion problem book.

 

[paralleltransport]

Caveat emptor: I am not well-versed in quantum field theory.

I think that the the standard order results because many physicists consider this to be the "nuts and bolts" of many qft calculations, and because of inertia. These two things have non-zero intersection.

The text "Quantum Field Theory: From Basics to Modern Topics" by Francois Gelis, starting in Chapter 10, covers many topics that are not in Peskin and Schroeder. You can look at the Table of Contents on Amazon. I do not know how useful this is. I think that some of the material in Chapter 14 (or related material) is used to compare theory and experiment at the LHC.

PS My visit to amzon.com seconds ago has revealed that Gelis more recently has published a companion problem book.

I will check it out, it does have some of the things I was looking for. The ordering of topics is highly traditional, feynman diagrams & perturbation theory first, and RG last.

My (biased) perspective on QFT is that it is more than about collider physics. The unifying principle is that QFT is the study of collective degrees of freedom (whether they be statistical or quantum in fact) and their interaction. Side benefit is one of its incarnation (the standard model) is a good model for our universe's vacuum. Things like effective field theory, RG and universality/scaling should be put first. When I was in school, my physics PI used to say like you alluded the only reason feynman diagram first instead of RG first is because of historical reasons.

... :). One day once I understand this better I'll probably write a set of notes and post it.

 

[gleem]

My experience in QFT is extremely limited ( 1 semester of Bjorken and Drell 1966). Anyway, we do not know your academic background nor do we know your interpretation of understanding or intent of using the understanding of this newly acquired knowledge. With the view of @PeroK, how realistic is a goal to understand current knowledge in a very dynamic research subject based on a book that is 25 years old? Certainly, the subject has fanned out into a myriad of approaches that Peshkin and Schroeder had not foreseen. as has been noted. It may be a good start but if one wanted to make some early progress shouldn't narrowing down the goal be of primary concern and maybe consider a less dated reference. Having done this and mastered this area you can, if desired, move on to a different aspect of the subject but better prepared.

BTW have you searched this forum for the best introduction to QFT? It seems to me that it has come up a number of times.

 

[paralleltransport]

My experience in QFT is extremely limited ( 1 semester of Bjorken and Drell 1966). Anyway, we do not know your academic background nor do we know your interpretation of understanding or intent of using the understanding of this newly acquired knowledge. With the view of @PeroK, how realistic is a goal to understand current knowledge in a very dynamic research subject based on a book that is 25 years old? Certainly, the subject has fanned out into a myriad of approaches that Peshkin and Schroeder had not foreseen. as has been noted. It may be a good start but if one wanted to make some early progress shouldn't narrowing down the goal be of primary concern and maybe consider a less dated reference. Having done this and mastered this area you can, if desired, move on to a different aspect of the subject but better prepared.

BTW have you searched this forum for the best introduction to QFT? It seems to me that it has come up a number of times.

Hi,

Yes I'm quite familiar with the introduction to QFT books (schwartz, srednicki, peskin, weinberg, zee...). I'm looking for more advanced things that would bridge from that to our current (post 1980's) understanding of QFT. Most of the advice I've seen is for people who are still trying to learn the basics.

My background: I had BS in physics, with grad level quantum/statmech/E&M/solid-state a long time ago. I self studied Peskin & schroeder up to ch. 16 (quantization of non-abelian gauge), attempting some of the problems (not all).

My goal: Be able to read the current QFT/CMT literature. Mainly for fun, I'm not a professional physicist (not in school).

 

[Haelfix]

I recommend reading one of the modern revisions of A Zee QFT in a nutshell. Not to learn, but to skim the relevant material (eg renormalization group). You can read the chapter in like an hour, understand the cartoon of what's going on, and then dive into the more technical material elsewhere.

For instance if you want to learn conformal field theory, at some point you will have to read conformal field theory by Di Francesco. For TQFTs, many of the early papers are actually really good (see eg Wittens papers).

Its hard to be more specific b/c you have picked extremely broad subject matters.

 

[jedishrfu]

I’ve heard Zee can be extremely hard to read at least his GR text is that way.

 

[vanhees71]

I will check it out, it does have some of the things I was looking for. The ordering of topics is highly traditional, feynman diagrams & perturbation theory first, and RG last.

This makes a lot of sense. You simply have to learn the first things first. The important thing with QFT is that you have to do some calculations for yourself to understand it. I think a good strategy is to focus on QED first. Start with understanding gauge theory on the classical level, i.e., formulate classical electrodynamics in terms of the action principle, derive the observables via Noether's theorem and then quantize it (most easily by using the path-integral formalism), deriving the Feynman rules, calculate some tree-level observable S-matrix elements, then turn to radiative corrections by calculating the 1PI divergent one-loop diagrams (most conveniently in dim. reg.) and understand what renormalization is about. Then you have a very good hands-on understanding what the RG is good for.

I don't see, what should be wrong with this traditional order of presentation. It's hard to imagine, how to really understand it in different order.

 

[vanhees71]

I’ve heard Zee can be extremely hard to read at least his GR text is that way.

Zee's QFT in a nutshell is fun to read if you already know the material, but it's too superficial to really learn the material such that you can really do calculations yourself.

 

[paralleltransport]

I don't see, what should be wrong with this traditional order of presentation. It's hard to imagine, how to really understand it in different order.

imo, the natural starting point of QFT is a finite euclidean lattice with periodic boundary condition of +/-1 spin degrees of freedom. There's no infinities, no gauge redundancy, no spinors, no lorentz invariance to worry about. All the math is well defined and can be chunked on a computer. In fact someone mentioned di-francesco's book. I'd say the first 4 chapters of that book is the natural starting point of QFT. The closest I think to that approach in intro qft books is kardar and srednicki, except srednicki uses a weird signature so a bit annoying sometimes for the signs.

From there one introduce the regularized path integral as a way to compute partition function and correlations. Taking the UV or IR infinite limit one clearly sees why one has to be careful.

Throwing perturbative QED as a starting point doesn't make sense to me since it has a bunch of complications (gauge invariance, spinors, the fact it is not UV complete due to landau pole etc...) which makes it quite hard.

 

[vanhees71]

Ok, then you have to look for textbooks about lattice QCD, but also there you need to understand the foundations of the subject first too, which includes for sure gauge invariance and spinors. There's no royal road in QFT.

 

[paralleltransport]

Ok, then you have to look for textbooks about lattice QCD, but also there you need to understand the foundations of the subject first too, which includes for sure gauge invariance and spinors. There's no royal road in QFT.

Ah i see. That means the last few chapters of the modern books it seems. I do know gauge invariance and spinors having had to suffer through most of peskin ;).

 

[vanhees71]

It's usually in the very beginning of the books. Everything starts with a more or less through treatment of the representation theory of the Poincare group, leading to the various types of fields (massive and massless representations as the ones admitting a Poincare-invariant time-ordering operator and then local, microcausal field theories). For massless fields of spin $s \geq 1$ you necessarily have gauge invariance. That Abelian gauge invariance then is generalized to non-Abelian gauge groups. This is the minimum prerequisite to be able to formulate the standard model of particle physics. This you need, no matter, which further topic/application you are interested in.