I am following peskin QFT book. I don't find the material convincing. Makes QFT seem like a fairytale from a mathematical standpoint.  Are there more convincing texts, or is the mathematics poorly understood?
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I'm a student of mathematics with not much background in physics. I'm interested in learning Quantum field theory from a mathematical point of view.  Are there any good books or other reference material which can help in learning about quantum field theory? What areas of mathematics should I be familiar with before reading about Quantum field theory?
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Hello Physics StackExchange!  I will put the TL;DR in the beginning: I need a self contained, relatively hand-holding sequence of textbooks that covers up from the end of Griffith's Intro to QM to relativistic QM/particle physics to QFT.    This will be my first post. I'm a medical physics grad student who majored in biomedical engineering for my undergrad, with serious regrets about not doing math/physics double major in hindsight. Oh well. I've made it my goal to eventually understand QFT.  My background in relevant subjects is Calc 1 to 3 and Diff EQ, 2 part freshman physics, an E&amp;M course that used Griffiths Electrodynamics, a summer of self studying Griffith's QM (got most of the way through). I will also be officially taking a class in QM using Griffith's textbook this next spring. I am aware of the Lagrangian and Hamiltonian approaches to mechanics as well. In addition I have familiarity with special and basic general relativity using tensors and all this. What would be the best way for me to get from where I am now to a strong understanding of QFT autodidactically? I have no aversion to studying pure maths where I need to.  EDIT: My question is much different than simply asking for a handholding explanation of QFT. Generally these textbooks assume a certain amount of physics/math background, and I was asking for a sequence of textbooks leading up to QFT from the end of a specific textbook, Griffith's QM. Did you even read my question? Did you read the thing you linked me to?
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I am looking for an introductory textbook on QFT in curved space-time via the path integral method. I want to understand the following:   How to build a generic perturbative QFT in curved space-time Are there some specific difficulties with normalization How to derive observables / particle states in curved space-time The Unruh effect The Hawking radiation   I would appreciate if the author would use path integrals instead of the canonical formalism when possible. The reason for this is purely aesthetic.
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I'm just tasting a bit of QFT and want to get started. I got stuck right at the start: what is a quantum field, and how should I look at it?  This question can be a follow up of the  question.  For me a field can be seen as a function. So saying "vector field" is the shorthand of saying a "function that maps from whatever domain to vectors of some dimensions".   What's the type of the value this function maps to when speaking of quantum fields?  In this . They says it's operator valued. As far as I can remember operators can be seen as "ket-bras" so the matrix product of an infinitely long column and row vector. So an infinitely large matrix. Or in other words a function that takes 2 parameters and gives back a scalar. Is that right?  So if I'm right a quantum field is a "scalar field field". So a function that maps space-time coordinates to functions that maps 2 scalars to a scalar.   In this yet . It's said it's a scalar valued in path integral formalism. I'm yet to understand that formalism so far. But for now I don't see how a scalar and a function valued field be equivalent...  On the other hand just out of curiosity, how many fields do we need to deal with in QFT? In classical electromagnetics we had two vector fields the electric and magnetic and the Maxwell equations that describes the time evolution. After some googling I can see there are boson fields, fermion fields, higgs field, whatever field... Are all of these quantum fields (so operator valued)? Do we have the field equations that describe all the relationship between these fields (just like the Maxwell-equations do in EM)?
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I am totally a beginner in QFT, here's the problem that I got: for the real scalar fields, are there any elementary particles descriped by them. If so, how to understand the negative probability problem?
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Are there nowadays any actual devices or experimental applications which are based on the quantum field theory and if so, how are they related to QFT?  I could not find any similar question besides  one.
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I'd like some suggestions for good reading materials on the Keldysh formalism in the condensed matter physics community. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but lately, I've been seeing Keldysh more and more in papers. My understanding is that it is superior to the imaginary time formalism at least in that one can evaluate non-equilibrium expectations.
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What would be your recommendation for the text which could be useful for someone starting with lattice theory? Suggestion for both books and online materials/lecture notes are welcome.    This was asked as a part of  and I did not like that it was combination of two different questions. (One of them on geometric modular lattices and the other one about text recommendation.)  I don't expect the user to post a follow-up question, since he was not seen at MSE for some time. I think that this could be a useful for some users here, so I've decided to post it myself.
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{{Under Construction}}      Short question: What published works and what research groups are investigating the possibility of non-existence of gravity at quantum level?  Long question: I am no physicist, but of what I read and understand of the subject, no-one has been able to fit the graviton into the standard model, it seems that the equations won't re-normalize, thus it would be useless for predictions. Gravity also is undetectable at the quantum level, it seems because the force is too small. Also, about every book about the subject traces a strong distinction between "quantum level" and "classical level", almost if they were different worlds that obey different laws of nature, and how they relate to each other is an open question. Finally, at least two sources I have seen state that Einstein's General Relativity is the most well verified theory of all physics, because of something related to pulsars.  Thus there are two distinct "worlds": in one gravity is pretty much settled, while in the other, it is neither detectable nor mathematically explainable in the most successful model. From that, the most logical and simple explanation I can have is that simply there is no such thing as quantum gravity, and that it is a purely classical phenomenon that arises from whatever may be the relation between both "worlds".  I like to imagine that space coordinates of both worlds are not quite the same, although very similar locally, thus, if classical world emerges from a projection of the quantum world, like a shadow, gravity is bumps in the surface where that shadow is projected (holographic principle comes in my mind now).  It doesn't seems to be the mainstream view of the problem, with millions of dollars spent in trying to find the mythical graviton (that is what a physicist of INPE, Brazilian's spacial research institute, told me yesterday). Thus, I want to know, what are the works, and what people shares with me this view of the problem?
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I'm interested in learning about the basics of group theory. My background is in statistics so I have barely any knowledge about group theory. I've had some work with proofs and I have also taken classes at university such as multivariable calculus, linear algebra, and differential equations. Any beginner resource would be helpful but nothing too technical.
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Could someone please provide an explanation for the origin of ? (Ideally someone who I have been speaking with on the h-bar)  Any advanced maths beyond basic calculus will most probably leave me at a loss, though I do not mind a challenge! Please assume little prior knowledge, as over the past few days I have discovered that much of my understanding surrounding the process as virtual particle pairs is completely wrong.
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I am curious about which areas of mathematics one should be comfortable with before learning QFT.  I am familiar with the "learn-it-as-you-go" approach often advocated in physics, but would like to know how to avoid that in learning QFT.  Naming of specific textbooks is appreciated.  (For the sake of this discussion, "learning QFT" can be taken to mean "learning at the level of/from Peskin and Schroeder's text.")  In particular, I would like to know what, in addition to the material in Rudin's Real and Complex Analysis, one should know.  Would this be sufficient?  How about Folland's Real Analysis?
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While it is quite common to use piecewise constant functions to describe reality, e.g. the optical properties of a layered system, or the  at (the impossible to reach exactly) $T=0$, I wonder if in a fundamental theory such as QFT some statement on the analyticity of the fields can be made/assumed/proven/refuted?  Take for example the Klein-Gordon equation. Even if you start with the non-analytical Delta distribution, after infinitesimal time the field will smooth out to an analytical function. (Yeah I know, that is one of the problems of relativistic quantum mechanics and why QFT is "truer", but intuitively I don't assume path integrals to behave otherwise but smoothing, too).
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I'm wondering about current efforts to provide mathematical foundations and more solid definition for quantum field theories. I am aware of such efforts in the context of the simpler topological or conformal field theories, and of older approaches such as algebraic QFT, and the classic works of Wightman, Streater, etc. etc . I am more interested in more current approaches, in particular such approaches that incorporate the modern understanding of the subject, based on the renormalization group. I know such approaches exists and have had occasions to hear interesting things about them, I'd be interested in a brief overview of what's out there, and perhaps some references.  Edit: Thanks for all the references and the answers, lots of food for thought! As followup: it seems to me that much of that is concerned with formalizing perturbative QFT, which inherits its structure from the free theory, and looking at various interesting patterns and structures which appear in perturbation theory. All of which is interesting, but in addition I am wondering about attempts to define QFT non-perturbatively, by formalizing the way physicists think about QFT (in which the RNG is the basic object, rather than a technical tool). I appreciate this is a vague question, thanks everyone for the help.
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I have a background in QFT, GR and differential geometry at the level of a master student in theoretical physics. I would like to touch the area of CFT. I know the textbook of Philippe Di Francesco. It may be too big for the beginner like me. Are there some good introductory lectures or textbooks adapted to the needs of beginners?
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There exists this famous  which basically states that the interaction picture in QFT cannot exist. Yet, everyone uses it to calculate almost everything in QFT and it works beautifully.    Why? More specifically to particle physics: In which limit does the LSZ formula work? Can someone give me an example of a QFT calculation (of something measurable in current experiments, something really practical!) in which the interaction picture fails miserably due to Haag's theorem?
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What I am interested to see are specific examples/reasons why gravity should be quantized. Something more than "well, everything else is, so why not gravity too". For example, isn't it possible that a quantum field theory on curved space-time would be the way treat QFT and gravity in questions where the effects of neither can be ignored?