- lengthened the Outline effectively into an Introduction, to better show the organization & content
- incorporated all the minor corrections
- added new subsections IC6 (cosets), IIIB6 (superparticle), XC7 (10D IIB supergravity on AdS
_{5}×S^{5}), XIA8 (AdS/CFT), XIA9 (superstring), and XIB8 (vertex operators) - changed the definition of Dirac γ-matrices to be more conventional
*will extend some subsections by including new notes on*RNS string & string lightcone Lorentz algebra- finally used a spell checker

- p.140, IA6.7: "number" → "operator". The basic idea is that γ should not be treated as a matrix when considering transposes in this problem. (This is not to say that it's a symmetric matrix.)
- p.186: Too many G's in the expression "GDGg".
- p.192: "each column in g
^{–1}a representation" - p.194, additions to exercise IC6.9:

see IC1.2- What is the symmetry of the surviving coset matrices?
- Do the same for SO → Sp.

- p.207, new exercise IIA4.3:

In subsection IIB6 we'll learn about "twistors" as square roots of 4D position. Now we do 3D:- Show the vector of the previous problem can be written in terms of

X^{αβ}= ζ^{(α}ζ̅^{β)}, ζ^{α}= (x+iy, r+z)/√(r+z) - Compare exercise IIA3.1.
- Relate to g of SU(2)/U(1) discussed in subsection IC6.

- Show the vector of the previous problem can be written in terms of
- p.212, bottom, wrt spinors, esp.: CPT = π rotation (@ least after Wick rotation)
- p.214-6,231,234,659-661,829,1047: γ
_{–1}as used here differs by a factor of "i" from what would be the γ for an extra spatial dimension. - p.238, new exercise IIB6.2 (re# following exercises):

Show we can choose

p^{α}= (p^{+},p^{t})/√p^{+} - p.240, bottom: (See exercise IIA4.3 for 3D position twistors.)
- p.255: Another way to understand P, and its relation to S, is in terms of the commutation relations when the S and P generators are left in: Since str[ , } = 0, S can only appear on the left-hand side of the relations, in 1 of the G's. On the other hand, since [I, ] = 0, P can appear only on the right-hand side of a nontrivial commutator.
- p.258: Using Abelian factors in H to define G
_{0}and G_{–}, for the nonchiral cases one also uses a U(1) of the R-symmetry, analogous to the dilatations of conformal. - p.258: Missing factors of 2 for θ and θ̅ counting.
- p.259: The covariant derivatives for supersymmetry (like those for translations) never have "spin" pieces. So if any of them are in the coset gauge group, they vanish identically, not up to a matrix representation. This implies that twisted chiral superspaces have no (Lorentz) spin, and chiral superspaces lack antichiral spin (dotted spinor indices), and the reverse for antichiral superspaces, since they are in the same G
_{0}subgroups. Similar remarks apply to parts of R-symmetry. These results also follow from the fact these subgroups also contain some S-supersymmetry. - p.259: In cases with super(iso)spin, they also contribute to the field equations, as in the bosonic case (see subsection IIB1).
- p.260: The SO(6) = SU(4) vector & spinor should be discussed as representations of SO(4)⊗SO(2) = SU(2)⊗SU(2)⊗U(1): 6 = (1,1,1)⊕(2,2,0)⊕(1,1,–1), 4 = (2,1,½)⊕(1,2,–½).
- p.261: According to scale weight and Lorentz representations, the superconformal generators can be divided up as
Depending on which 2 diagonal squares are chosen for GG _{A}^{B}β b̲ β̇ α (2) J+Δ S K a̲ (N) Q R S̅ α̇ (2) P Q̅ J̅–Δ _{0}, we get supertwistor, (anti)chiral superspace, or twisted projective superspace. - p.264: For twice-odd N, the scalars are pseudoreal representations of SU(N) (the ε tensor is antisymmetric in its pair of N/2 indices), so CPT self-conjugacy isn't possible.
- p.266: Ref.7 should loc.cit. ref.2.
- p.295:
- δq = ζ
- x
^{–}+ … → x^{–}+ p^{–}τ (temporarily)

- p.375,590: remove √2 from γ
_{–1} - p.390: Drop redundant "tr" for S
_{sYM,1}. - p.438: Another way to understand Wick rotation is by dimensional reduction from a space with 1 extra spatial dimension. (This is also useful for introducing mass: See subsection IIB4.) Then reduction of that spatial dimension gives the original theory, while reduction of the time dimension instead gives that theory in Euclidean space. For Dirac spinors (see subsection IIA6), the latter makes it clear why the γ
_{0}drops out of ψ̅, as it now plays the role of γ_{–1}in Weyl projection, since x^{0}has been reduced instead of x^{–1}. - p.584, bottom: Another example is the graviton vertex (kk). The resulting tadpole gives the cosmological constant term. This integral is sometimes called the "zero-point energy", and is often misattributed to graphs without external lines.
- p.623: fig. @ bottom → next p.
- p.703, top: effects of masses
- inside: exp(-Tm²/2) IR regulator; same near s=0
- outside: pole shift, s → s – m²N/4

- p.764, IXC2.3: Use the metric (ds²).
- p.843: The vector (4,1) is really a (2,2,1) of SL(2,C)⊗SU(4), & the spinor (4,4) is really (2,1,4)⊕(1,2,4̅).
- p.843: CP symmetry of 4D N=4 super Yang-Mills also can be derived by dimensional reduction: In D=10, where there's neither P nor CP, it's a continuous SO(9,1) symmetry, changing the sign of 6 spatial directions via rotations through π. On reduction, choose 3 to be in SO(6) (C) & 3 in SO(3,1) (P).
This is the same way C arises in the SO(10) GUT on breaking to the Pati-Salam SU(4)SU(2)
^{2}model. (See subsection IVB4.) - p.846: Bosons always form representations of G (coset for scalars, singlet for metric), but fermions represent only H. This is analogous to representations of coordinate/Lorentz as GL(D)/SO(D–1,1) (coset for metric, singlet for scalars).
- p.852: g
_{mn}~ Φ^{–2}~ ℛ^{2}, R ~ Φ^{2}~ ℛ^{–2}⇒ ℛ → 0 is lim R → ∞. - p.853, bottom: A̲ → 𝒜
- p.857, ref.7, Strathdee: v.1 → 2
- p.877, XIA3.1: g
_{±}→ g_{∓}(notation change) - p.887, bottom: τ ↔ σ
- p.904: (D
_{+})^{2j+1} - p.905: Replace {S,Q} & its discussion: Before the P and S conditions on the symmetry group, there were 4 Abelian generators that could appear in the coset gauge group. After applying P and S, the 2 remaining are
½G But the part of the gauge group G_{α}^{α}= –½G_{α̇}^{α̇}= Δ, ½G_{a}^{a}= –½G_{a'}^{a'}= R_{0}can contain only SU(1,1|2) groups, not PS, since P was already gauge. The S of the gauge group kills Δ–R in G₀, leaving Δ+R (the P part) there. - p.920: The covariant form of the integral is ∫dσ
^{m}ε_{mn}P^{+n}, since P is a density. - p.925: N → 𝒩
- p.940, bottom: GSO is identification of states under vector → –vector. This means φⁱ → φⁱ + π. This takes one Weyl spinor into itself, the other into minus itself.
- p.955, XIB8.1: Instead of the propagator, look @ the kinetic operator c₀H₀.
- p.959: The ghost factors can also be treated by 0th-quantized BRST for Sp(2)
Q = (c₁+c₀z+c₋₁z²)∂/∂z + pure-ghost terms by applying the usual insertions (e.g., from integrating out antighosts and Nakanishi-Lautrup fields)δ(f)δ([Q,f}) for gauge-fixing functionsf = z₁–z̊₁, z where all N vertices are integrated, and these 3 z's are the 3 integration variables, while the 3 z̊'s are the values to which they're fixed. Gauge fixing then gives_{N–1}–z̊_{N–1}, z_{N}–z̊_{N}δ(z₁–z̊₁)δ(z reproducing the previous result after integrating over the 3 0th-quantized ghosts and the 3 extra z's._{N–1}–z̊_{N–1})δ(z_{N}–z̊_{N})c₁c₀c₋₁(z̊₁–z̊_{N–1})(z̊_{N–1}–z̊_{N})(z̊_{N}–z̊₁) - p.962: The coupling normalization can also be explained by noting the Yang-Mills vertex really wants to be A•P.
- p.970: Bosonization was discussed in subsection VIIB5.
- p.971, XIC2.1a: bosonized
*oscillators*; put H & J here. - p.978, end of subsection: missing a comma — ν’,τ’.
- p.994, new ref. 3: J.J. Atick and E. Witten, Nucl. Phys. B310 (1988) 291: disappearance of states in parton phase of string.
- p.1055, CFT: Fix signs on T & L to be consistent with subsections XIB4-5.
- p.1056: Bosonization …,C2
- p.1059: Lightcone gauge…IXB3…

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- It's free.
- It's fast. You can download it from arXiv.org or its mirrors, just like preprints, without a trip to the library or bookstore or waiting for an order from the publisher.
- It's electronic. You can print it, but the PDF version has many advantages, like:
- Download it at work, home, etc. (or carry it on a USB flash drive), rather than carrying a book or printing multiple copies.
- Get updates just as quickly, rather than printing yet again.
- It has the usual Web links, so you can get the referenced papers just as easily.
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- Save trees (and ink).
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- No wear or tear.
- No paper cuts.
- It can't be eaten.

- It covers many recent topics at an introductory yet nontrivial level, such as:
- supersymmetry
- general relativity
- supergravity
- strings

- It introduces many topics not appearing in other textbooks, including:
- 1/N expansion (color ordering) in QCD, including relation to random worldsheets
- spacecone (spinor helicity), including explicit calculations of 4- and 5-point S-matrices in Yang-Mills
- many useful gauges, such as Gervais-Neveu, Nielsen-Kallosh, unitary lightcone, and even string gauges in gravity
- finite N=1 supersymmetric theories

- It is
**NOT**:- a history book.
- All the other recent, comprehensive field theory texts take the "traditional" approach of covering topics in chronological (rather than logical) order, in storybook fashion. (This is strongly reminiscent of introductory classical mechanics courses that still teach Newton's laws before energy-momentum conservation.)
- This book takes advantage of hindsight, using what we now know to be the most efficient and general approaches. (For example, these other texts still quantize QED canonically, even though they know that method is inadequate for QCD. Some even claim path integrals are less rigorous, even though constructive quantum field theory has shown the opposite to be true.)
- Whenever I have questioned anyone who prefers the traditional approach, after eliminating all the spurious clichés, it all boils down to nostalgia. (I have even heard the excuse that it is useful to learn the less useful approaches simply because they ultimately failed --- certainly an excellent reason to relegate these topics to true history courses, for those who have the time and interest.) This really means that most professors simply teach things the way they learned them, and (ironically) will not bother to learn a new way, or even to check if it has any advantages. (Unfortunately, similar remarks often apply to research.)

- a cookbook. Some books race to Feynman diagrams as quickly as possible, because they either consider them the only useful part of field theory, or they think such an approach is an introductory one. One consequence is that the Higgs effect must take a back seat, and thus weak interactions are underemphasized or explained more phenomenologically.
- a concept book. All the recent texts that use a modern approach, although giving the appearance of being comprehensive except for conciseness, are curiously deficient in explicit S-matrix calculations, especially for QCD. This book both includes modern concepts and calculates with them, since the dualistic approach of concept book plus calculation book has always proved deficient for lack of two good books that work well together.
- a survey. With few exceptions, theories are described in this book at a level that allows explicit calculations.
- an art book. It covers topics that have proven useful, not those that have appealed to certain tastes.

- a history book.

- It's too broad.
- It's really big. You might never finish it. You will be exposed to too many interesting topics that you know you'll never learn.
- It's not about just LHC physics. If you read this book you'll actually learn quantum field theory, which is about more than just 1 lab.
- It takes too much time to get to Feynman diagrams. That means you might have to read the chapters out of order (as suggested in the Preface), which is too much trouble.
- It has string theory in the last couple chapters. Why would you want to learn anything that might also be applicable to string theory, & suffer guilt by association?

- It's too narrow.
- You can actually read it without reading another QFT book 1st. So if you already read another book 1st, you might have to unlearn stuff you thought you actually understood, but is really just baggage. In fact, if you learn canonical quantization of QFT you'll already have to unlearn that to understand Yang-Mills in any textbook, so better to not get as far as the Standard Model, or to read a book on just QED.
- There is too much math. Multiplying 2×2 matrices & doing Gaussian integrals, & having to look @ lots of indices. Why can't everything be explained with just words?
- There are too many words. Why can't there be more calculations? There are explicit calculations of only 4-gluon & 5-gluon amplitudes, why not 6 & 7?

- It isn't available printed on dead trees.
- How valuable can it be if I don't have to break my back lugging it around?
- Printed books are more sensually appealing: I love the way paper looks. I love the sound the pages make when I turn them. I love the feel of paper. I love the smell of paper. I love the taste of paper.

- It's too different & unconventional.
- Science is decided by tradition: It doesn't use the same explanations all the other textbooks use.
- Science is decided by authority: All the leaders in the field (or so I'm told) use other books, so they must be the best.
- Science is decided by democratic majority: Nobody else uses it to teach a course, therefore something must be wrong with it.
- Science is decided by capitalism: It's free. You get what you pay for.

- You won't get it. It might confuse you. That means you might have to think about new things. That can be hard. Maybe something awful will happen if you try it.

- information on my course based on this book:
**PHY 610-611** **overview of the course**- parts of the book used to teach my section of the string course:
**PHY 622-623**(which varies from year to year) -
**APS News article** - an interesting article on
**open source books**