| Page | Position | Replace | by | Thanks go to |
|---|---|---|---|---|
| 15 | Eq. (1.33) | (P⇒Q) ∧ (Q⇒R) (P⇒R) | (P⇒Q) ∧ (Q⇒R) (P⇒R) | Viktor Skorniakov, Vilnius University |
| 22 | Table in Eq. (2.17), 2nd row | T T T T T | T F F F F | Viktor Skorniakov, Vilnius University |
| 25 | Eq. (2.26) | f(G) = {y ∈ Y | ∃ x: f(x)=y} | f(G) = {y ∈ Y | ∃ x f(x)=y} | Viktor Skorniakov, Vilnius University |
| 28 | Example 3 | Matrix multiplication is a binary operation on the said set. Matrix addition is a binary operation on the set of all n×n matrices. | Viktor Skorniakov, Vilnius University | |
| 39 | Eq. (3.4) | The expression on the right side should be placed under a square root sign. | Viktor Skorniakov, Vilnius University | |
| 51 | Next to last sentence in the proof of Theorem 3.10 | Now, one can write an arbitrary combination of a and b as ax + by = | Now, one can write an arbitrary combination of a and b as ax + by = | Viktor Skorniakov, Vilnius University |
| 69 | 2nd line after Eq. (4.7) | something that is more commonly denoted by | something that is more commonly denoted by | Viktor Skorniakov, Vilnius University |
| 70 | Example 2 | The example given is a valid example of a linear map, which is an element in the dual space. It does not describe the full dual space. There are other maps, of course. | Charanjit Singh Aulakh, IISER Mohali | |
| 73 | Eq. (4.22), right side | xi2 | |xi|p | |
| 98 | Eq. (5.60) | e'(j) = ∑k (S-1)ik e(i) | e'(k) = ∑i (S-1)ik e(i) | Charanjit Singh Aulakh, IISER Mohali |
| 104 | After Eq. (5.98) | The proof of the Cayley-Hamilton theorem is not trivial. The result is an operator relation, as given in Eq. (5.98), and cannot be inferred from Eq. (5.95) which is a determinant equation. The proof mentioned in the book is often called the bogus proof of the theorem. Just ignore the "proof". The theorem has been rightly applied in what follows immediately, and elsewhere. | Charanjit Singh Aulakh, IISER Mohali | |
| 124 | Eq. (5.222) | U = ∑i , V = ∑i . | U = ∑i , V = ∑i . | Charanjit Singh Aulakh, IISER Mohali |
| 176 | Th. 7.16 | The theorem, as stated, is wrong. It is best to disregard the statement as well as the proof. | Charanjit Singh Aulakh, IISER Mohali | |
| 185 | Eq. 7.100 | img(fk) = ker(fk+1) | img(fk-1) = ker(fk) | Charanjit Singh Aulakh, IISER Mohali |
| 207 | 2nd line after Eq. (8.77) | imply b=a | imply b=a | |
| 229 | Eq. (9.5), 1st line | U†Ai†Ai | U†Ai†Ai | Trinesh Sana, Calcutta University |
| 265 | just before Eq. (9.155) | classes of | classes of | Luis Odin Estrada Ramos, UNAM, Mexico |
| 296 | End of 6th line after Eq. (10.50) | and = 1 + 1 + 2 = 4. | and = 1 + 1 + 2 = 4. | |
| 301, 302 | Eqs. (10.73), (10.74) | The arguments of all sin and cos functions should be 2πk/M; there should not be any factor of i. | Charanjit Singh Aulakh, IISER Mohali | |
| 316 | Heading of Section 11.3 | The group denoted by in the heading has been called within the text. The notations with and without the comma mean the same thing. | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta | |
| 334 | 1st paragraph |
There are two different uses of the word "semisimple", as applied to
algebras. In this paragraph, the word "semisimple" has been used in
the exclusive sense, i.e., these are algebras which are neither
simple, nor do they have any abelian ideal. Beginning from the next
paragraph, the same word has been used in an inclusive sense, i.e.,
by simply demanding that they do not have any abelian ideal. In the
latter sense, simple algebras also fall in the class of semisimple
algebras. One should interpret Theorem 12.2 in this way, as well
as Theorems 12.7 and 12.8 later in the chapter. Alternatively, one can use the inclusive definition throughout by making the following changes in this paragraph: | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta | |
| If an algebra is non-simple but not in this trivial way, i.e., not by the presence of any U(1) generator that commutes with every generator, then it is called a semisimple algebra. We will see in Chapter 15 that SO(4), the algebra of the group of 4×4 orthogonal matrices, is semisimple. | If an algebra is not non-simple in this trivial way, i.e., if an algebra does not have any U(1) ideal, then it is called a semisimple algebra. The definition therefore includes simple algebras which do not have any non-trivial ideal at all, as well as other algebras which have non-trival ideals which are all non-abelian. We will see in Chapter 15 that SO(4), the algebra of the group of 4×4 orthogonal matrices, is of this last kind, i.e., is semisimple but not simple. | |||
| 337 | midway in the 2nd paragraph | But the total exponent must be Hermitian so that R(ξ) is unitary, which means that the exponent must also contain the Hermitian conjugate of −iξX, which is +iξ*X†. | But the total exponent must be of the form of the imaginary unit i times a Hermitian operator so that R(ξ) is unitary, which means that the terms involving ξ in the exponent must be of the form −i(ξX + ξ*X†). | Charanjit Singh Aulakh, IISER Mohali |
| 338 | Eq. (12.35), right side | KI | aIKI | Charanjit Singh Aulakh, IISER Mohali |
| 339 | Eq. (12.45), second line | [A,[B,C]+] + [B,[C,A]]+ − [C,[A,B]]+ = 0 | [A,[B,C]+] + [B,[C,A]]+ − [C,[A,B]]+ = 0 | Trinesh Sana, Calcutta University |
| 350 | Eq. (12.95), last term on the right side | Ta†(2) ⊗ Tb(1) | Tb(1) ⊗ Ta†(2) | Charanjit Singh Aulakh, IISER Mohali |
| 351 | Eq. (12.98), 3rd term on the left side | (2⁄d(ad)) tr (Ta†(1)) tr (Ta(2)) | (1⁄d(ad)) [ tr (Ta†(1)) tr (Ta(2)) + tr (Ta(1)) tr (Ta†(2)) ] | Charanjit Singh Aulakh, IISER Mohali |
| 356 | Section 12.10.4 |
The entire argument, leading to Eq. (12.124), can be taken as an
argument for the normalization constant of a representation of a
direct product group, replacing C2 by K.
For the Casimir invariant, the factors of the dimensions of the
representations should be omitted in all three equations of this
section. It means that the final formula should be
C2(R,R') = C2(R) + C2(R'), with appropriate changes in the two earlier equations. The dimensions are important only to the extent that the unit matrix is d(R)d(R')-dimensional in these earlier equations. | Charanjit Singh Aulakh, IISER Mohali | |
| 383 | Eq. (13.162), under the square root sign | s(s + 1) m(m 1) | s(s + 1) m(m 1) | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 422 | 2nd line after Eq. (15.16) | if is | if is | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 426 | Eq. (15.31) | There should not be a minus sign on the right side of this equation. | Trinesh Sana, Calcutta University | |
| 439 | line after Eq. (15.80) | Recalling that | Recalling that | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 474 | first line of text | denote by a matrix | denote by a matrix | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 482 | 2nd line of Eq. (17.57), left side | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta | ||
| 498 | Eq. (17.143) | The right sides of Eqs. (17.143b) and (17.143d) should have overall negative signs. | Amitabha Lahiri, S N Bose Centre for Basic Sciences | |
| 577 | Eq. (19.148) | xi → x'i + εi(x) | xi → x'i = xi + εi(x) | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 587 | Eq. (19.211) | In the expression for h(t), the sum should be over n. | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta | |
| 589 | Eq. (19.221), the first set of nested brackets | [Tam, [Tbn, ]] | [Tam, [Tbn, ]] | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 589 | Eq. (19.222) | fabd δdc 𝜙(m + n) + fbcd δda 𝜙(n + p) fcad δdb 𝜙(p + m) | fabd δdc 𝜙(m + n) + fbcd δda 𝜙(n + p) fcad δdb 𝜙(p + m) | |
| 604 | 3rd line before Eq. (20.19) | For the open G in Y, we find | For the open G in Y, we find | Viktor Skorniakov, Vilnius University |
| 616 | 1st line of text | the rectangle marked 'B' is (185)× | the rectangle marked 'B' is (185)× | Viktor Skorniakov, Vilnius University |
| 617 | Eq. (21.23) | {G ∩ S ∀G ∈ T} | {G ∩ S ∀G ∈ T} | Viktor Skorniakov, Vilnius University |
| 619 | Eq. (21.31) | UY | UY | Viktor Skorniakov, Vilnius University |
| 620 | Eq. (21.38) | Subset UY | Subset UY | Viktor Skorniakov, Vilnius University |
| 626 | Definition (21.18) | there exist non-empty subsets | there exist non-empty subsets | Viktor Skorniakov, Vilnius University |
| 637 | Eq. (22.23) | In the last line of the defintion of H(s,t), the function should be f̅ instead of f. | Viktor Skorniakov, Vilnius University | |
| 655 | Definition (23.2) | is a map | is a map | Viktor Skorniakov, Vilnius University |
| 662 | Text before Eq. (23.30) | The most general element of C1(X) is given already in Eq. . | The most general element of C1(X) is given already in Eq. . | Viktor Skorniakov, Vilnius University |
| 662 | Text before Eq. (23.34) | calculated through the definition of Eq. | calculated through the definition of Eq. | Viktor Skorniakov, Vilnius University |
| 684 | Answer of Ex. 14.8 | 8, 10, 10, 6 | 8, 15, 15, 6 | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| Page | Where | Replace | by | Thanks go to |
|---|---|---|---|---|
| 16 | line before Eq. (2.7) | assume the statement is true all values | assume the statement is true all values | Viktor Skorniakov, Vilnius University |
| 19 | line before Eq. (2.7) | means the | means the | Viktor Skorniakov, Vilnius University |
| 25 | 3rd line of the penultimate paragraph | consists elements | consists elements | Viktor Skorniakov, Vilnius University |
| 28 | 1st sentence of Sec. 2.2.3 | structures. | structures. | Viktor Skorniakov, Vilnius University |
| 48 | 1st sentence of 2nd paragraph | all integers are also inegers. | all integers are also inegers. | Viktor Skorniakov, Vilnius University |
| 50 | Ex. 3.12, 2nd line | a ring. | a ring. | Viktor Skorniakov, Vilnius University |
| 54 | 4th line above Eq. (3.54) | scalars | scalars | Viktor Skorniakov, Vilnius University |
| 69 | 2nd paragraph, 3rd line | and also linearly independent | and also linearly independent | Viktor Skorniakov, Vilnius University |
| 115 | Line after Eq. (5.166) | are obviously Hermitian. | are obviously Hermitian. | Viktor Skorniakov, Vilnius University |
| 164 | 1st line of text | rpresentation | rpresentation | Augniva Ray, Saha Institute of Nuclear Physics, Calcutta |
| 211 | 3rd line in Section 8.8 | ABCD a permutation | ABCD a permutation | |
| 237 | Section 9.5.1, end of 1st paragraph | the matrices URiU† the same | the matrices URiU† the same | |
| 319 | The sentence leading to Eq. (11.40) | A closely related group groups of transformations | A closely related group groups of transformations | Viktor Skorniakov, Vilnius University |
| 320 | second line before Eq. (11.45) | given in | given in | |
| 341 | last paragraph of the inset | symmetry properties of Eq. (12.52) | symmetry properties of Eq. (12.52) | Viktor Skorniakov, Vilnius University |
| 349 | 4th line after Eq. (12.89) | this information is (12.52) | this information is (12.52) | Viktor Skorniakov, Vilnius University |
| 388 | last line | the reduced d- | the reduced d- | Viktor Skorniakov, Vilnius University |
| 402 | line after Eq. (14.51) | assignnt | assignnt | |
| 667 | 3rd line in the paragraph after the definition | Similarly, a 2- | Similarly, a 2- | Viktor Skorniakov, Vilnius University |