Errata to
Quantum Fields - from the Hubble to the Planck Scale
Erratum for the first imprints:
Notations:
- p. ix, add to table: Levi-Civita tensor \(\epsilon_{\mu\nu\rho\sigma}\)
with \(\epsilon_{0123}=-\epsilon^{0123}=1\)
Chapter 1:
- p. 11, in Eq. (1.51): \(1/L\) should be \(m^2/L\).
- p. 13, problem 1.3 b): \(P_1\) should be \(P_1=\frac{\partial L}{\partial\dot q}-\frac{d}{dt}\frac{\partial L}{\partial \ddot q}\).
Chapter 2:
- p. 16, in Eq. (2.3a): \(e^{ipx}\) should be \(e^{ipq}\),
in Eq. (2.3b): \(e^{-ikx}\) should be \(e^{-ipq}\)
Chapter 3:
- p. 46, ERP correlations should be EPR (or better
Einstein-Podolosky-Rosen) correlations.
Chapter 4:
- p. 55, in Eq. (4.18): \({\cal L}+\ln({\cal N})/(VT)\) should be
\({\cal L}-{\rm i}\ln({\cal N})/(VT)\)
- p. 63, footnote: \(L=n-V+1\) should be \(L=I-V+1\)
- p. 66, after Eq. (4.64): \(n=V\geq 0\) should be \(I=V\geq 0\)
- p. 68, in Eq. (4.73b): \(=-\lambda\mu^\epsilon+\ldots\) should be
\(=-\lambda\mu^{2\epsilon}+\ldots\)
- p. 69, above Eq. (4.77): \(\{s_0.t_0,u_0\}\) should be \(\{s_0,t_0,u_0\}\)
- p. 69, in Eq. (4.81): \(s_0^2,t_0^2,u_0^2\) should be \(s_0,t_0,u_0\)
- p. 71, in Eq. (4.89): \(\alpha_1 x_1\cdots\alpha_n x_n\) should be \(\alpha_1 x_1+\ldots+\alpha_n x_n\), in the next line also \(\alpha_i\) and \(x_i\) should be exchanged:
\([x_1(1-\alpha_1)+x_2(\alpha_1-\alpha_2)+\ldots +x_n\alpha_{n-1}]^{-n} \)
- p. 71/72, in Eqs. (4.93,94,96): \(I_0(\omega,\alpha)\) should be \(I(\omega,\alpha)\)
- p. 72, in Eqs. (4.100) and (4.101): \(\frac{(-\pi)^\omega}{(2\pi)^{2\omega}}\) should be \(\frac{(-1)^\alpha}{(4\pi)^{\omega}}\)
Chapter 5:
- p. 79, paragraph after Eq. (5.27): with the changed definition
of the Levi-Civita tensor change to "The other components are
\(S^1=-S_1=J^{23}\), \(S^2=J^{31}\), and \(S^3=J^{12}\)."
Chapter 6:
- p. 85, top of page : change \((0,\ldots,1,0\ldots)\) to
\((0,\ldots,\partial/\partial x^i,0\ldots)\).
- p. 88, Eq. (6.26): change \(\Gamma^\mu_{\;\rho\sigma}\) to
\(\Gamma^\mu_{\;\sigma\rho}\).
- p. 91, Eq. (6.50): change in the middle term \(X^\mu X^\mu\) to
\(X^\mu X^\nu\).
- p. 91, after Eq. (6.51): "Since the Lagrangian of..." should be
"Since the Lagrangian (1.47) of..."
- p. 92, Eq. (6.55): change \(\tilde g,g\) to
\(\tilde g_{\mu\nu},g_{\mu\nu}\).
Chapter 7:
- p. 111, 2.nd line: change "some of the extra dimensions" to
"some of the six extra dimensions" to
\(
\def \slash#1{\centeron{$#1$}{$/$}}
\def\centeron#1#2{{\setbox0=\hbox{#1}\setbox1=\hbox{#2}\ifdim
\wd1>\wd0\kern.5\wd1\kern-.5\wd0\fi
\copy0\kern-.5\wd0\kern-.5\wd1\copy1\ifdim\wd0>\wd1
\kern.5\wd0\kern-.5\wd1\fi}}
\)
Chapter 8:
- p. 123, 1. phrase: change "...and \(E=p^0=|{\mathbf p}|>0\)." to
"...and \(E=p^0=\sqrt{m^2+{\mathbf p}^2}>0\)."
- p. 124, in Eq.(8.56) change "\(u(0,\pm)\)" to "\(u(m,\pm)\)" and
"\(v(0,\pm)\)" to "\(v(m,\pm)\)".
- p. 125, after Eq. (8.60): change "commutes with the Dirac
Hamiltonian" to "commutes with the massless Dirac
Hamiltonian".
- p. 137, in Eq.(8.125) change the sign of "-\(m_D^2\)".
Chapter 9:
- p. 149, between Eq. (9.47) and (9.48): delete the prime on the
spin in \( \bar u(p,s^\prime)\).
- p. 150, Eq. (9.58): \( v_{\rm rel}\) should be
\( v_{\rm M{ø}l}\).
- p. 151, Eq. (9.70b): delete the superfluous bracket in
\( \frac{\cdots}{(1+2\tilde\omega}\) .
- p. 159, last sentence in paragraph \(s>1\):
"no consistent theory \(\ldots\) with spins \(s\geq 2 \)" should be
"no consistent theory \(\ldots\) with spins \(s> 2\)".
- p. 159, Eq. (9.109): \( E'+\omega-E'\) should be
\( E'+\omega-E\).
- p. 161, between Eq. (9.122) and (9.123): change
\( dp_2/dx=\ldots\) to \( dx/dp_2=\ldots\)
- p. 161, in Eq. (9.123): change
\(\frac{p_{\rm cms}^\prime}{M} \) to \( \frac{p_{\rm cms}}{M^2}\)
- p. 162, in Eq. (9.125a): change
\( \lambda(x,y,z)=[ x^2+\ldots]^{1/2}\) to
\( \lambda(x,y,z)= x^2+\ldots\)
- p. 162, in Eq. (9.128a): change
\( \ldots dp_2\) to
\( \ldots p_2^2 dp_2\)
- p. 162, before Eq. (9.130): change
"Performing the angular integral, ..." into
"Performing these substitutions, ...."
- p. 163, in Eq. (9.134): change
\( \ldots =\pm \sqrt{\ldots}\) to
\( \ldots =\pm 2\sqrt{\ldots}\).
In the following paragraph change
"Then the equation with the minus sign becomes
\(E_2=M/2+m_3^2/(4E_1-M)\),
while the equation with the plus sign simplifies to a straight
line \(E_2=-E_1+M/2(1-m_3^2/M^2)\)." to
"Then the equation with the plus sign becomes
\(E_2=M/2+m_3^2/(4E_1-M)\),
while the equation with the minus sign simplifies to a straight
line \(E_2=-E_1+M/2(1-m_3^2/M^2)\).", i.e. exchange the words
plus and minus.
- p. 163, after Eq. (9.135c): add
"where the RHS is valid in the rest-frame of the decaying particle."
- p. 165, Summary: "...spin-2 particle has to couples..."
should be "...spin-2 particle has to couple..."
Chapter 10:
- p. 172, Eq. (10.34): delete the index \(\mu\) in
\(\psi(x+dx^\mu)\).
- p. 174, Eq. (10.45): the index \(a\) in the second term of
the RHS should be an \(\alpha\), and the index \(b\) in the fourth
term of should be a \(\beta\).
- p. 175, Eq. (10.52): \(\cdots=k^2 P_T^{\mu\nu}(k)=k^2(\cdots)\)
should be \(\cdots=-k^2 P_T^{\mu\nu}(k)=-k^2(\cdots)\).
- p. 182, Ex. 10.7 : \(\delta(p_1+p_2+p_2)\)
should be \(\delta(p_1+p_2+p_3)\) .
Chapter 11:
- p. 192, around Eq.~(11.30): "\(\ldots\) and the \(m^0\ell^0\) term
gives, after some work,
\( \gamma^\nu {P'\!\!\!\!/} \gamma^\mu {P\!\!\!\!/}\gamma_\nu \to
2m[\alpha(1-\alpha)+\beta(1-\beta)](p+p')^\mu. \qquad (11.30) \)
Finally, the \(m^0\) term contributes\(\ldots\)" should be
"\(\ldots\) and the \(m^0\ell^0\) term results in
\(
\gamma^\nu {P'\!\!\!\!/} \gamma^\mu {P\!\!\!\!/}\gamma_\nu =
-2m[(1-\beta){p\!\!\!\!/}-\alpha m] \gamma^\mu
[(1-\alpha){p'\!\!\!\!/}-\beta m] ,
\)
where we used also the Dirac equation, \({p\!\!\!/} u(p)=mu(p)\). Repeating
the splitting of this expression into powers of \(m\), the contribution of
the linear term to the anomalous magnetic moment can be rewritten as
\(
\to 2m[\alpha(1-\alpha)+\beta(1-\beta)](p'+p)^\mu ,
\)
while the \(m^0\) term contributes\(\ldots\)"
- p. 196, below Eq. (11.46):
" ... implies that loops with a an odd number of fermion propagator... "
should be
" ... implies that loops with an odd number of fermion propagators... ".
- p. 197, second bullet below Eq. (11.48):
"An example... in \(D=4\) with \([\lambda]=m^0\)."
should be
"An example... in \(d=4\) with \([\lambda]=m\)."
Chapter 12:
- p. 207, after Eq. (12.10): "gives us the number of loops"
should be "determines the number of loops".
- p. 217, in the numerator of Eq. (12.60):
\(\ldots f_{acd} k_\nu \) should be \(\ldots f_{acd} k^\nu \).
- p. 229, Eq. (12.112): \(D\sigma D\phi \) should be
\(D\sigma D\psi \).
Chapter 13:
- p. 237, below Eq. (13.14):
" ... if an internal symmetry is broken,"
should be
" ... if an internal symmetry is broken."
- p. 241, above Eq. (13.31):
" ... a complete sets... "
should be
" ... a complete set... ".
Chapter 14:
- p. 251,
\( L_{CC} = \frac{-i g}{\sqrt{2}}
\left(\begin{array}{cc}\bar\nu_e&\bar e\end{array}\right)_L
(\tau^+ W_\mu^- + \tau^- W_\mu^+) \gamma^\mu
\left(\begin{array}{c}\nu_e\\e\end{array}\right)_L \) should be
\( L_{CC} = \frac{- g}{\sqrt{2}}
\left(\begin{array}{cc}\bar\nu_e&\bar e\end{array}\right)_L
(\tau^+ W_\mu^+ + \tau^- W_\mu^-) \gamma^\mu
\left(\begin{array}{c}\nu_e\\e\end{array}\right)_L \).
- p. 256, in Table 14.1, \(T_3\) should be 0 for the right-handed fields (E,U and D)
- p. 262, "improve our understand" should be "improve our understanding"; "in an higgsless" should be "in a higgless".
- p. 263, above Eq. (14.43): "Frist we use..." should be "First we use..."
Chapter 16:
- p. 283, Fig. 16.2 "from one maxima" should be "from one maximum"
- p. 295, Eq. 16.62 "\(D_\mu\phi^a)^2\)" should be "\(D_i\phi^a)^2\)"
- p. 294-296: In the paragraph on monopoles, only one of the coupling
constants "\(e\)" and "\(g\)" should be used.
- p. 299, problem 16.4: delete the last period.
Chapter 17:
- p. 300, "The only other example" should be "The only other examples"
-
p. 301, Eq. (17.2): "\(...-\partial_\nu V_\nu\)" should be "\(-\partial_\nu V_\mu\)"
-
p. 301, delete the trace in Eq. (17.9).
-
p. 301, Eq. (17.5): "\(\sum_n\phi_x(x)...\)" should be "\(\sum_n\phi_n(x)...\)"
- p. 303, "an one-loop result" should be "a one-loop result"
- p. 306, "an heuristic argument" should be "a heuristic argument"
- p. 307, "contains term linear" should be "contains terms linear";
"absence of triangle diagrams guaranties" should be "absence of
triangle diagrams guarantees".
-
p. 313, a space-time integral is mising in Eq. (17.69): "\({\rm tr}(F\tilde F)\) should be "\(\int {\rm d}^4x\, {\rm tr}(F\tilde F) \)"
Chapter 18:
-
p. 321, after Eq. (18.13): "This the..." should be "This is the...";
"an infinitesimal scale transformations" should be "an infinitesimal scale transformation".
-
p. 322, "5% of the mass of proton" should be "5% of the mass of the proton".
-
p. 326, in the second line of Eq. (18.35): \(\frac{{\rm d}z}{z}\) should be
\( {\rm d}z\) .
-
p. 333, in Eq. (18.60): \(4\pi\alpha^2/2Q^2\) should be
\(4\pi\alpha^2/Q^2\).
-
p. 333, in Eq. (18.62): \(S_{qq} +S_{\bar q \bar q}\) should be
\(S_{q\bar q} +S_{\bar q q}\).
-
p. 333, after Eq. (18.62): "\((1-\cos\beta_q)\)" should be
"\((1-\beta_q\cos\theta)\)". In the next phrase,
"collinear (\(\beta_q\to 0\))" should be "collinear (\(\theta\to 0\))"
-
p. 336, "This also reason" should be "This is also the reason".
-
p. 337, "by a collections" should be "by a collection".
Chapter 21:
-
p. 379, start of the new paragraph: "For CDM with \(x_{\rm f}\ll 3\),..."
should be "For CDM with \(x_{\rm f}\gg 3\),..."
-
p. 387, in Eq (21.24): \(-\frac{sx}{H}\ldots .\) should be
\(-\frac{sx}{H(m)}\ldots,\) ; add directly after the equation
"with \(H(m)\equiv H(x)x^2\ldots\)."
-
p. 387, after Eq (21.25): "with \(\Gamma_{A}=n_{eq}\langle\sigma_{ann}v\rangle\)." should be "with \(\Gamma_{A}=n_{eq}\langle\sigma_{ann}v\rangle\)
and \(H= H(x)\)."
Chapter 23:
-
p. 407, after Eq. (23.25) "...as \(|k|/a\gg H^{-1}\)." should be
"...as \(|k|/a\gg H\)."
-
p. 411, first paragraph of 23.2.2: "spacetimes which approach..."
should be "Spacetimes which approach..."
-
p. 417, before Eq. (23.90) "Expressing the four-acceleration \(\dot u\)..." should be
"Expressing \(\dot u\)..."
-
p. 418, Eq. (23.94) should be
\( t = \frac{1}{a} \, \mathrm e^{a\chi}\sinh(a\xi) \text{ and }
x = \frac{1}{a} \, \mathrm e^{a\chi}\cosh(a\xi) . \)
Chapter 24:
-
p. 426, between (24.14) and (24.15):
\(2L\) should be \(2{\cal L}\).
-
p. 448, "...discussed in chapter 21 ! and 22..." should be "...discussed in chapter 21..."
Chapter 25:
-
p. 469, Fig. 25: "spacetime" should be capitalised.
-
p. 471, in Eq. (25.42)
\(\ldots - \frac{\rho}{r^2+a^2}\mathrm dr^2 - r^2\mathrm d\theta^2\ldots \)
should be
\( - \frac{\rho^2}{r^2+a^2}\mathrm dr^2 - \rho^2\mathrm d\theta^2 \ldots\)
-
p. 472, after Eq. (25.47): "...is given by \(\sqrt{g_2}=g_{\theta\theta}g_{\phi\phi}=2Mr_+\sin\theta\)..." should be "...is given by \(\sqrt{g_2}=\sqrt{g_{\theta\theta}g_{\phi\phi}}=2Mr_+\sin\theta\)..."
-
p. 473, before Eq. (25.54): "...allowed range of values, \(\phi_-\leq \omega\leq \phi_+\),..." should be
"...allowed range of values, \(\dot\phi_-\leq \omega\leq \dot\phi_+\),..."
Chapter 26:
-
p. 485, Eq. (26.16): \(x=\frac{\dot\phi}{\sqrt{48\pi G}H}\)
should be \(x=\sqrt{\frac{4\pi G}{3}}\frac{\dot\phi}{H}\),
\(y=\frac{\sqrt{V}}{\sqrt{24\pi G}H}\)
should be \(x=\sqrt{\frac{8\pi G}{3}}\frac{\sqrt{V}}{H}\).
-
p. 485, before Eq. (26.18a): "Setting also
\(\lambda\equiv-(8\pi G)^{1/2} V_{,\phi}/V\)..."
should be "Setting also
\(\lambda\equiv-V_{,\phi}/[(8\pi G)^{1/2}V]\)..."
-
p. 485, Eq. (26.18a) \(\frac{\mathrm dx}{\mathrm dN}=3x+\ldots\)
should be
\(\frac{\mathrm dx}{\mathrm dN}=-3x+\ldots\)
Appendix:
- p. 498, the Levi-Civita tensor \(\epsilon_{\mu\nu\rho\sigma}\)
should be defined as \(\epsilon_{0123}=-\epsilon^{0123}=1\) to
be consistent with our definition of \(\gamma^5\) and (A.21).
- p. 508, Eq.(B.9): change \(\theta^a\) to \(i\theta^a\).
- p. 509, Eq.(B.13): change the RHS from \(\frac{N^2-1}{2N}\) to
\(\frac{N^2-1}{2N}\delta_{ij}\).
- p. 509, Eqs.(B.15-17): \( T^a T^b\) should be
to \(T^a T^a \).
- p. 511, Eq.(B.27): change \(\tilde\phi_a= S_{ba}\ldots\)
to \(\tilde\phi_b= S_{ba}\ldots\). At the end of the next paragraph,
change "... we can use
\(\delta x^\rho=\omega_\nu^{\;\sigma}x^\sigma=...\)" to
"\(\delta x^\rho=\omega^\rho_{\;\sigma}x^\sigma=...\)".
- p. 511, Eq.(B.31): change \(\ldots\eta^{0\mu}_\nu\ldots\)
to \(\ldots\eta^{0\mu}\ldots\).
- p. 512, Eq.(B.37): change again \(\tilde\phi_a= S_{ba}\ldots\)
to \(\tilde\phi_b= S_{ba}\ldots\).
- p. 512, between Eq.(B.39) and (B.40): change again "Inserting
\(\delta x^\rho=\omega_\nu^{\;\sigma}x^\sigma=...\)" to
"\(\delta x^\rho=\omega^\rho_{\;\sigma}x^\sigma=...\)".
- p. 512, (B.42): replace the two
\(\phi_a\) by \(\phi_L\).