
Corrections to Second Edition, 2^{nd} revision (July 2015) of Student Friendly Quantum Field Theory
Note: 1st edition and 2^{nd} edition (prior versions) users also need to check this 2^{nd} edition, 2nd revision corrections page for additional corrections.

Sorted by Date Posted: This Page 
Sorted by Page Number: Click Here 
Significant Corrections (may impact learning process)


Pg 
Chap 
Date Posted 
Significant Correction 
Reported by (blank = the author) 
384 
15 
Jan 15, 2018 
Paragraph above (1555): After “as” insert “in (1555).” Change the parenthetical remark to a sentence reading as follows:  In order for this to work, we have to change the propagator of the socalled heavy particle a bit. We give it a negative sign and keep the “m” in the numerator without changing it to “Λ”, like we do in the denominator. This makes the whole procedure work mathematically (which is our goal), even though it tarnishes the analogy to a heavy particle propagator a bit.  
Tom Bartholet 
381 
15 
Dec 15, 2017 
Pedagogic improvement: Change last sentence to We will retain only retain the leading log terms (see Sect. 15.1.15, pg. 378), with Λ^{2} >> k^{ }^{2}. As shown in the appendix (see Chap 15 addition to appendix), the first two terms in the integral of (1544) and the two directly below them are of order 1, so relative to Λ^{2 }(and k^{2}, since we are assuming k^{2} >> m^{2} where m^{2}>>1), they can be ignored. Doing this, we get (1545). 
Tom Bartholet 
353 
14 
Dec 7, 2017 
Wholeness Chart 142, second row, last (Chapter) column: After “8”, insert pg. 235 . After that, insert 9, pg. 257  
Tom Bartholet 
363 
14 
Dec 7, 2017 
2^{nd} pargraph on pg beginning with “Moreover..”: Move this entire sentence down below eq (1486) and just above the paragraph beginning “Bottom line”. Also, at the end of the sentence, add in light of (1486).  
Tom Bartholet 
370 
14 
Dec 7, 2017 
Wholeness Chart 144, col (VII), 2^{nd} row: After “A=” insert a minus sign. Wholeness Chart 145, col (VII), 2^{nd} row: A_{nth} should approach negative infinity. 
Tom Bartholet 
370 
14 
Dec 7, 2017 
Wholeness Chart 144, col (X): subscripts “e_{0} Mod“ should have “2^{nd} “ after them. 2 places. Wholeness Chart 145, col (X): subscripts “e_{0} Mod“ should have “nth “ after them. 2 places. 
Tom Bartholet 
371 
14 
Dec 7, 2017 
Wholeness Chart 144, col (X): “(Z_{V}^{2nd})” needs to be squared. 
Tom Bartholet 
462 
17 
Oct 25, 2017 
(1794): Notation under the Sigmas should be r′_{1} = 1, r′_{2} = 1 … r_{1} = 1, r_{2} = 1, respectively. 
John Davidson 
10 
1 
Oct 13, 2017 
Prob 6, 3^{rd} line: before “determine”, insert  assuming p_x is a single term,  
Harm van der Lek 
323 
13 
Oct 13, 2017 
Fig. 131: Under the first diagram, insert ie_{o}^{2} before Pi. Under the 2^{nd} diagram, insert ie_{o}^{2} before Sigma. In the 3^{rd} diagram, insert ie_{o}^{3} before Lambda. Add to text above the figure: Applying Feynman’s rules in Fig. 131, excluding the incoming and outgoing particles, yields the amplitudes under each diagram, where the symbols are defined in (131) to (133). 
Tom Bartholet 
328 
13 
Oct 13, 2017 
7^{th} line down on page: Change “each of these terms must equal zero” to  these terms must sum to zero  
Tom Bartholet 
337a 
13 
Oct 13, 2017 
(1383): both lines need a summation over r symbol inserted (1384): needs same summation over r inserted 
Tom Bartholet 
337a 
13 
Oct 13, 2017 
Paragraph after (1384): the operator atilde_r(k) should have a summation over r symbol in front of it. Same for adaggertilde_r(k). 
Tom Bartholet 
310 
12 
Sept 11, 2017 
Comment (not correction) on (1217) RHS: The superscript (2) might be confusing. Here the notation, along with the subscripts, means we take the 2^{nd} order in e form of the amplitudes but use the modified versions for e, photon propagator, and vertex gamma matrix (as described in under bracket note). 
Tom Bartholet 
310311 
12 
Aug 21, 2017 
(1216): delete the minus sign after the equal sign (2 places). ((1218), 4^{th} line: change minus sign on LHS to plus sign (1221), last line: change minus sign on LHS to plus sign 
Tom Bartholet 
340 
14 
Aug14, 2017 
(141), 1^{st} line: Delete “p’ = “ 
Vasudev Godbole 
298299 
11 
June 13, 2017 
(1142) insert minus sign after 2^{nd} equal sign. (1144). same change (minus sign) after each equal sign. 
Tom Bartholet 
21,31 
2 
May 31, 2017 
I was a bit sloppy in two blocks near the ends of Wholeness Charts 22 and 25. See corrections at Changes to Charts 22 and 25. As I noted in the text, it may be best not to get too deeply into Chart 22, as it is primarily a summary of classical variational mechanics, and the changes made here relate to subtle aspects of that theory, which are not so relevant for QFT. 
Allan Tameshtit 
239 
8 
May 12, 2017 
First line: insert “ e” after equal sign. 
Tom Bartholet 
205 
7 
May 9, 2017 
First paragraph following (782), “C_{3}D_{4}=  D_{3}C_{4}” should be “C_{3}D_{4}=  D_{4}C_{3}” 
Tom Bartholet 
217 
8 
May 9, 2017 
(89), after 2^{nd} equal sign: The S_{fi} should be inside the Sigma and all f except that in the bra should be primed. 
Tom Bartholet 
231 
8 
May 9, 2017 
(874) and (875) both need to insert “i” in front of the expression for S_{F} 
Tom Bartholet 
235 
8 
May 9, 2017 
(889): Insert a delta function with argument zero on the RHS outside the integral. 
Tom Bartholet 
61 
3 
May 8, 2017 
Mid page, after 2^{nd} paragraph after “Caveat”. If normal ordering were only used in QFT to get a Delta E energy level (as that is all that is relevant in classical theory) one might concede some justification for it. However, as one will see in Chap 4 (pg. 112 after “End of Derivation”), it is also commonly invoked to get the correct charge operator for spin 1/2 fields. Otherwise, the vacuum would have an infinite charge. Since we have no theories where that can simply be subtracted, it is hard to justify use of normal ordering for charge derivation, and one’s confidence in it is further eroded. Note that on pg. 112, I present an alternative derivation to the charge operator that does not depend on normal ordering. 

271 
10 
May 8, 2017 
Sect. 10.2.4. Actually, the FullingDaviesUnruh effect is not related to the 1/2 quanta, the higher order corrections, nor the 3 virtual particle bubbles, but to a more advanced concept in QFT related to time dependent Hamiltonians. Finding it in an experiment would not really be a proof of zero point energy in the usual 1/2 quanta sense. 

384 
15 
May 8, 2017 
I have recently realized that cutoff regularization has a more obvious reason for why it doesn’t work. It is not Lorentz invariant, as the upper limit on our integral (max energy) is not Lorentz invariant (energy for the same object changes as seen in different frames). The other three regularization methods discussed are all Lorentz invariant, and they all produce the correct result. 

480 
17 
May 8, 2017 
(17175): the numerators should all have a “ + m” in them. 
Zhang Juenjie 
231 
8 
Jan 16, 2017 
3rd line after (879): Change “denotes antiparticles.” to is sometimes used in Feynman diagrams for virtual antiparticles. It is just a symbol. The overbar here is not related to adjoint fields. 
Vasudev Godbole 
211 
7 
Nov 11, 2016 
(7109): The first three terms on the second line should have the N_{c} operator in front of them. (7110). The last term in the top row should have the N_{c} operator in front. 
Tom Bartholet 
186 
7 
Oct 27, 2016 
(719): Comparing with (716), one might wonder about the change in order of the QFT field operators (photon and fermion) after the equal sign. The order here is not important, as fields associated with different types of particles commute. A_{mu} commutes with psi here. 
Tom Bartholet 
76 
3 
Sept 29, 2016 
The line after (3140). It is correct as is, but maybe easier to understand if we change “the route” to which route (loop)  

198 
7 
Sept 22, 2016 
Sentence just above Sect 7.5.2, change “(762)” to  (763) . 
Tom Bartholet 
176 
6 
Aug 22, 2016 
Eq (641). The first minus sign (before N_b) should be a plus sign. 
Tom Bartholet 
169 
6 
July 7, 2016 
Eq. (614). The arguments for the vector and tensor on the RHS of their respective equal signs should not have a Lambda^alpha_beta before the x^beta. Two places. (And it might look neater to change the beta on the x to an alpha, but not essential.) 
Tom Bartholet 
184 
7 
June 22, 2016 
Eq. (78). The minus sign in front of “e” should be a plus. 

73 
3 
June 16, 2016 
1^{st} line after (3122). The first “factor” in (3122) is GF of (3120). The second “factor” in (3122) is HF of (3120). In teaching a QFT course, I was asked by a student “where did the GF and HF of (3120) go?” 
Lou Biegeleisen 
142 
5 
June 16, 2016 
(535) top row. This is correct as it is, since dummy indices can be used interchangeably. However, it can be easier to understand if the mu and nu superscripts on the epsilons on the RHS of each equal signed are switched. 
Tom Bartholet 
142 
5 
June 16, 2016 
(536). The r’s after the second equal sign should be underlined, as there is no sum. 
Tom Bartholet 
147 
5 
June 16, 2016 
(550). The summations should only be over r, not k. The integral is over the range of k. 
Tom Bartholet 
247 
8 
June 16, 2016 
2^{nd} paragraph up from bottom of page. At end of sentence, add or to interactions that can be renormalized away (not treated in this text). 

274 
10 
June 16, 2016 
(108), top row. Don’t hold up your study of QFT by spending much time on this fairly advanced material. Someday I may rewrite this section with these changes. Each 1/2, should be multiplied by a delta(0), i.e., a Dirac delta function with argument zero. This also applies to every relation on the next 23 pages with a 1/2 term. See links on book website for Continuous Solutions for reasons why. From that one could also see why comments in this part of the text for single 1/2 quanta particle wave packet in “all space” should refer to “unit volume”. 

281283 
10 
June 16, 2016 
WhCh 102. Wherever there is a continuous solutions form with 1/2 inside the integral, it should be a multiplied by a factor delta(0), i.e., a Dirac delta function with argument zero. See links on book website for Continuous Solutions for reasons why. 

111 
4 
May 16, 2016 
Sect. 4.6.3, last sentence. Change “d_r dagger” to d_r  . Change “annihilates that state” to results in the vacuum 0 >  
Tom Bartholet 
127 
4 
May 16, 2016 
2^{nd} paragraph of Conclusion #1: Insert at beginning of paragraph: For Fig. 45(b), . After “Changing v”, insert (without aligning it with S) After “Therefore,”, insert in Fig. 45(b)  
Tom Bartholet 
158 
5 
May 16, 2016 
Wholeness Chart 54, 4^{th} row, 2^{nd} column on page. Put a bar over rho. Two places. (rho is an expectation value not an operator here.) 
Tom Bartholet 
159 
5 
May 16, 2016 
Wholeness Chart 54, 2^{nd} row up from bottom on page: After “two commutators” insert  /anticommutators  
Tom Bartholet 
160 
5 
May 16, 2016 
Wholeness Chart 54, top row on page: After “two commutators” insert  /anticommutators  
Tom Bartholet 
27 
2 
Apr 6, 2016 
Eq (237). Some further explanation plus some changes related to (237) are in order. See Comments on (237). 
Tom Bartholet 
79 
3 
Apr 1, 2016 
In (3150), change partial time derivative to total derivative. In next line, after “field,” insert with the aid of Box 2.1, pg. 22, 
Tom Bartholet 
74 
3 
Mar 2, 2016 
Last line on page: After the comma, insert we have the Cauchy integral formula  
Tom Bartholet 
54 
3 
Aug 17, 2015 
The k’s in the numerators (two places) in the second line of (352) should have superscripts, not subscripts. (352) as written, strictly speaking, is still correct, as there are two k's with subscript i multiplied, which equal two k's with superscript i multiplied. But this correction should eliminate confusion. 
Steffen Leger 
11 
2 
Aug 6, 2015 
Sect. 2.1.1, point 2. After “mass”, insert  at rest  
Michael Heiss 
23 
2 
Aug 6, 2015 
Box 22. My purpose in this box was to give a derivation of (B22.3) that was much simpler than that in other books. There are some subtleties involved, but it is best not to worry about them until after you have mastered QFT. If at that time, you feel up to it, check out Box2_2_comments 

30 
2 
Aug 6, 2015 
For versions prior to July 2015, this was OK. For the July 2015 version, equations (242) and (243). The “i” subscript on delta would be better as a superscript. Ultimately, it doesn’t really matter, but it helps the parallel with (244) if “i” is superscripted. 

Minor Corrections (should not impact learning process)


Pg 
Chap 
Date Posted 
Minor Correction 
Reported by 
379 
15 
Jan 15, 2018 
(1529): The derivatives in the top row should be enclosed in parentheses, so the epsilon = 0 does not apply to the factors of epsilon and epsilon square. 
Tom Bartholet 
382 
15 
Jan 15, 2018 
(1548) to (1549): We considered the first two terms in the second line of (1548) negligible. In the newly added (not in text, online) appendix used to go from (1544) to (1545), we showed these terms equal i pi/6 5/18. 
Tom Bartholet 
385 
15 
Jan 15, 2018 
2^{nd} line below (1557): put a minus sign in front of Lambda squared. 
Tom Bartholet 
394 
15 
Jan 15, 2018 
2^{nd} line below (15111): Change “electrons” to fermions . (For time upward, Fig. 152 would show an electron and a positron.) Also change “are” to approach and equal signs to approximately equal signs. 
Tom Bartholet 
399 
15 
Jan 15, 2018 
2^{nd} line after (15133): after “each”, insert integral . 
Tom Bartholet 
340 
14 
Dec 7, 2017 
4^{th} line down below Fig 141 title: change “second” to  third row  
Tom Bartholet 
340 
14 
Dec 7, 2017 
Eq (141): The factor in front of the integral needs to be divided by (2pi)^{4}. 
Tom Bartholet 
343 
14 
Dec 7, 2017 
Sect. 14.2.1, Step VI), first line: Delete “the Taylor expansion of the”. This is not wrong, but one reader thought it confusing. 
Tom Bartholet 
369 
14 
Dec 7, 2017 
Wholeness Chart 145, column (IV), 2^{nd} row: change comma to nonsubscript so it can be seen. 
Tom Bartholet 
373 
14 
Dec 7, 2017 
Probs. 3 and 4: In “e^{0 }”, the superscript zero should be a subscript. 
Tom Bartholet 
45 
3 
Oct 25, 2017 
Just above (B31.7): after “probability current”, insert (density)  
Qingzhong Wu 
61 
3 
Oct 25, 2017 addition to May 8, 2017 note 
Normal ordering is also commonly used for another (more complicated) matter, as discussed in pgs. 208209. I discuss an alternative way to handle that issue in those pages. 

403 
16 
Oct 25, 2017 
5th line up from bottom: Change “.)” to  ).  
John Davidson 
414 
16 
Oct 25, 2017 
2^{nd} line above (1648): underlining on mu mu subscripts should be raised. 
John Davidson 
457 
17 
Oct 25, 2017 
(1760): bold p’ in underbracket should have “1” subscript inside the absolute value sign 
John Davidson 
524 
Index 
Oct 25, 2017 
“Lorentz gauge” should be Lorenz gauge  
John Davidson 
324 
13 
Oct 13, 2017 
2^{nd} paragraph after (139): Argument k for Pi_c should be k^{2} 
Tom Bartholet 
328 
13 
Oct 13, 2017 
1^{st} line after “End of Proof”; change “photon loop” to  fermion loop  
Tom Bartholet 
329 
13 
Oct 13, 2017 
(1336): each denominator should have a “+ epsilon” added 
Tom Bartholet 
330 
13 
Oct 13, 2017 
Paragraph after (1340): After “typically)”, insert  , in the sense that it gives rise to a corresponding vertex in a Feynman diagram  
Tom Bartholet 
331 
13 
Oct 13, 2017 
2^{nd} line after (1342): before “photon” insert external  
Tom Bartholet 
332 
13 
Oct 13, 2017 
(1349): Right near end of equation, for Sigma_c, the p argument should have a slash through it. 
Tom Bartholet 
334 
13 
Oct 13, 2017 
1^{st} line after (1356) In the expression right after “Also,”, delete the  i . 
Tom Bartholet 
337 
13 
Oct 13, 2017 
(1378), 4^{th} line down: operator adagger_r” needs an argument (k”). 
Tom Bartholet 
414 
16 
Oct 13, 2017 
(1648) next row up from bottom: Superscript “30” should be  20  
John Lynch 
515 
19 
Aug14, 2017 
3^{rd} line up from bottom re Cutoff Regularization: after “gauge invariance” insert and is not Lorentz invariant . Delete “a” and insert s  after “underpinning. 

285b 
10 
May 24, 2017 
Prob. 1, 2^{nd} line: The quantity inside the bra should not be the complex conjugate of the quantity inside the ket, but the same thing. The bra notation implies the quantity shown inside, when expressed mathematically, has the complex conjugate taken. 
Tom Bartholet 
282 
10 
May 24, 2017 
Last row, 2^{nd} column: The quantity inside the bra should not be the complex conjugate of the quantity inside the ket, but the same thing. The bra notation implies the quantity shown inside, when expressed mathematically, has the complex conjugate taken. 
Tom Bartholet 
285 
10 
May 24, 2017 
Section 10.12, Appendix E: It is clearer if whenever the term “delta function“ is used, it is replaced with “Dirac delta function” (so as not to confuse with the Kronecker delta). 
Tom Bartholet 
256 
9 
May 12, 2017 
Fig. 91, RHS: Reverse the arrow on the lower line to make it a positron. 
Tom Bartholet 
258 
9 
May 12, 2017 
Box 91, 3^{rd} paragraph up from bottom, 2^{nd} line: After “x_{1}x_{3}x_{2}”, insert  in (B91.3)  
Tom Bartholet 
259 
9 
May 12, 2017 
(97): It may be easier to follow if the S_{F}(p) gamma^mu were moved to after the gamma^nu. Given that these factors are inside the trace, it doesn’t really matter, but the whole thing tracks Fig. 95 better if it is done this way. 
Tom Bartholet 
261 
9 
May 12, 2017 
(913): Put a factor of 1/(2 pi)^{2} after the equal sign. 
Tom Bartholet 
262 
9 
May 12, 2017 
Line above (916): After “natural” insert  and HeavisideLorentz  
Tom Bartholet 
524 
Index 
May 12, 2017 
After “Normal ordering, 60”, insert  112113, 208209  

221 
8 
May 9, 2017 
(824): “Bhabba” should be “Bhabha” 
Tom Bartholet 
224 
8 
May 9, 2017 
(842), “r” subscript of “ν” should be primed 
Tom Bartholet 
225 
8 
May 9, 2017 
Fig. 83 would probably be better with the first vertex on each side labeled x_{2} and the second x_{1}, as it would track the text better. But it is common to not write in the coordinate labels at each vertex in Feynman diagrams, so the reader needs to get accustomed to the practice. 
Tom Bartholet 
231 
8 
May 9, 2017 
(876) and (878): D_{mu nu} should be D_{F mu nu} 
Tom Bartholet 
235 
8 
May 9, 2017 
End of 1^{st} paragraph in Sect 8.5, change “delta function” to “Dirac delta function”. 
Tom Bartholet 
236 
8 
May 9, 2017 
3^{rd} Feynman rule: iS_{F} should be iS_{F }(p) 
Tom Bartholet 
241 
8 
May 9, 2017 
First margin note should refer to Chap. 16, not Chap. 17. 
Tom Bartholet 
219 
8 
Dec 8, 2016 
This is not a correction, but an added problem. Box 81. At the end of the box, add “Do Prob. 18 for more insight on this.” Then, add, at the end of the chapter. Prob. 18. Draw the mass shell for a photon. Suppress the k^{2} and k^{3} dimensions, to make it easier. That is, plot E vs k^{1}. Does it touch the origin? Are the sides of the shell, for a photon, straight lines? Does the mass shell for a massive particle like that shown in Box 81 approach that of a photon asymptotically for very high E (speed approaching c)? 
Tom Bartholet 
199 
7 
Nov 7, 2016 
Sect. 7.5.3, 2^{nd} paragraph, beginning: After “Fig. 71” insert  and Wholeness Chart 72  
Tom Bartholet 
43 
3 
Oct 11, 2016 
Eq (39). May be good to insert “This is a solution given E_{n}^{2}  p_{n}^{2} = m^{2}”. 
Jeroen Spandaw 
x 

Sept 30, 2016 
Acknowledgements for 2n Ed, end of first paragraph. Move comma after “them” to after “thank” 

2 
1 
Sept 30, 2016 
2^{nd} line above (11), delete comma at end of the line 

127 
4 
Sept 30, 2016 
mid page. bold 1/2 before ket should be not bold 

131 
4 
Sept 30, 2016 
In title of Sect 4.14.5, “The” should not be capitalized 

264 
9 
Sept 30, 2016 
Next to last bullet near bottom of page: delete space after “Compton” 

144 
5 
Sept 23, 2016 
(542). It will be better here if we take A^mu to be A_mu. It doesn’t matter which we use, but later in Chap 7 we do it with a subscript mu, not a superscript. So we change it here to be consistent 
Tom Bartholet 
184 
7 
Sept 22, 2016 
Margin note for eq (76) should be  gauge  instead of “gage” 
Tom Bartholet 
177 
6 
Aug 22, 2016 
In the third line of Sext 6.6.1, it is better to have the page range for 135141 rather than 138141. 
Tom Bartholet 
177 
6 
June 22, 2016 
Top line on page: After “this means” insert  using the LHS of (639)  . 

491 
18 
June 22, 2016 
Paragraph to the right of Fig. 181, 3^{rd} line: The underline marks in the argument of the delta function should just be spaces. 

88 
4 
June 21, 2016 
2^{nd} paragraph up from bottom, first sentence. Exponent +/ kx should be =+/ ikx. 
Lou Biegeleisen 
520 
19 
June 21, 2016 
Footnote 1. The year should be 2010, not 2002. 

23 
2 
June 16, 2016 
Box 22. Eq (B22.3) number not aligned. 

143 
5 
June 16, 2016 
Footnote paragraph is indented and shouldn’t be. 

127 
4 
May 16, 2016 
2^{nd} paragraph, 2n line of Conclusion #1: Make “1/2” not bold. 

50 
3 
Mar 23, 2016 
Eq. (337). Delete extra RH parenthesis on eq number. 
Juan José Bigeón 
87 
4 
Jan 25, 2016 
3^{rd} line from bottom of page: change “one the” to one of the  
Pavel Fadeev 
147 
5 
Jan 25, 2016 
Sect. 5.3.1, change “pg. 155” to ‘ pg. 156  
Pavel Fadeev 
xi 
Preface 
Oct 19, 2015 
7^{th} line: after “orthodox” insert (pedagogically)  

170 
6 
Oct 7, 2015 
First margin note on page: eliminate underline on e’. 
Michael Koren 
51 
3 
Sept 10, 2015 
Sect. 3.2.4, 1^{st} line: change “of this and” to of this chapter and 
Tom Bartholet 
20 
2 
Sept 1, 2015 
Wholeness Chart 22, left column, 4^{th} row up from bottom: Change “Hamiltonian’s Equations of Motion” to Hamilton’s Equations of Motion”  
Tom Bartholet 
65 
3 
Aug 6, 2015 
Mid page, Note on Nomenclature line: “solution” should have an  s  on the end. 

79 
3 
Aug 6, 2015 
Mid page, Odds and Ends section: After “31” insert  (pg. 65) . After “32”, insert  (pg. 68) . 

96 
4 
Aug 6, 2015 
4^{th} margin note: subscript 1 on u should not be italic 

107 
4 
Aug 6, 2015 
Box 43. Equation numbers not aligned. 

160 
5 
Aug 6, 2015 
4^{th} row down in the wholeness chart, last line: Delete open parenthesis at beginning of the line. 

166 
6 
Aug 6, 2015 
6^{th} line down: Change “functional” to  the function . 

188 
7 
Aug 6, 2015 
Wholeness Chart 71. 4^{th} row up from bottom, Operators column. Superscript S is wrong font. 

211 
7 
Aug 6, 2015 
1^{st} line above (7110): insert a comma after “them”. 

211 
7 
Aug 6, 2015 
(7110), 2^{nd} line: Boxes with 8, 9, and 10 in them should be above the terms, rather than below them. 

463 
17 
Aug 6, 2015 
(1799). “1/4” font size too big. 

371 
14 
Aug 6, 2015 
Page heading should be “Section 14.9 Chapter Summary”. Heading as shown should have “mu” instead of a box (2 places). Computer glitch in 2^{nd} ed. Not in 1^{st}. 

508 
18 
Aug 6, 2015 
Wholeness Chart 186. Title needs to be centered 
