Texts

Nothing to translate No field-theory conventions to compare.

A complex-analysis text: no metric, no regulator, no field-theory conventions at all. Nothing needs translating — the results are used exactly as written.

Nothing to translate No field-theory conventions to compare.

A complex-analysis course: no metric, no regulator, nothing to translate. The only convention worth noticing is where a source puts the branch cut of the logarithm, and this one uses the principal branch, as this course does.

Nothing to translate No field-theory conventions to compare.

A complex-analysis text, used for the foundations only. No field-theory conventions to compare.

Compare directly Same conventions as this course on every axis below.

The book this course took its conventions from. Intermediate expressions can be compared line by line, which is why it is the primary citation almost everywhere.

• Metric signature same locator unconfirmed

  Theirs $g_{\mu\nu} = \mathrm{diag}(+1,-1,-1,-1)$

  ⚠️ ch. 1, where the book fixes its conventions — mostly-minus throughout. Inherited from this repo’s existing record rather than read: P&S is not openable, and it is tracked in ../references/TO-VERIFY.md.

• Dimensional regulator same locator unconfirmed

  Theirs $d = 4 - 2\varepsilon$

  ⚠️ §7.5 proposed, not confirmed — P&S is not openable and this pointer is tracked in ../references/TO-VERIFY.md. Nothing rests on it: the shared convention is pinned by this course’s own engine, not by the chapter number.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

Same signature as this course, so propagators and slashed momenta compare directly. The two places to be careful are both about gauge, and both are naming rather than physics.

• Metric signature same read directly

  Theirs $g_{\mu\nu} = \mathrm{diag}(+1,-1,-1,-1)$

  Same signature as this course — safe to compare term by term.

• Gauge, and the parameter’s name differs read directly

  Theirs $\alpha \text{, with } \alpha = 1 \text{ (Feynman gauge)}$

  §6.2.2, p. 131, Eq. (6.37) for the parameter; Eq. (6.91), p. 142.

  Carrying a result across Read his α as this course’s ξ — the meaning is identical, including which value is Feynman gauge and which is Landau. Only the letter changes, and it collides with the fine-structure constant, which is the reason to notice it at all.

• Where the coupling sits in a gauge transformation differs read directly

  Theirs $\psi \to e^{-ie\lambda}\psi,\quad A_\mu \to A_\mu + \partial_\mu\lambda$

  §6.3.1 “Coupling to Fermions”, pp. 136–137, Eqs. (6.66)–(6.69).

  Carrying a result across Set α = −eλ and the two forms are the same transformation. He keeps the coupling in the phase and this course keeps it in the shift of the potential, so a factor of e appears in different places downstream — every physical result agrees.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

Two independent flips, and you can be caught by either one alone: the opposite metric signature, and a different definition of ε once loops begin. Neither is an error — they are different definitions of the same continuation — but nothing in the notation warns you.

• Metric signature differs read directly

  Theirs $g_{\mu\nu} = \mathrm{diag}(-1,+1,+1,+1)$

  Fixed at the start; on-shell is written k² = −m² throughout.

  Carrying a result across His k² is minus this course’s. Results quoted in Mandelstam variables need nothing done to them — his s, t and u are numerically the same as ours — but every propagator denominator inverts, and anything with an explicit slashed momentum or a bare metric tensor differs by a sign.

• Dimensional regulator differs read directly

  Theirs $d = 4 - \varepsilon$

  §62, just above Eq. (62.17), where he also replaces $e$ with $e\,\tilde\mu^{\varepsilon/2}$.

  Carrying a result across His ε is twice this course’s. Every pole residue in his loop sections therefore differs from this course’s by a factor of two, and his $\tilde\mu^{\varepsilon/2}$ plays the role of this course’s $\mu^{\varepsilon}$. There is no visual tell — both conventions produce formulas of the same shape — so the check has to be made before any coefficient is compared.

• Photon polarization differs read directly

  Theirs $\sum_\lambda \varepsilon^\mu \varepsilon^{*\nu} \to +g^{\mu\nu}$

  §59, Eqs. (59.9)–(59.17) — the polarization sum done from the Coulomb-gauge relation.

  Carrying a result across The sign is the signature’s, not a second decision: flip the metric and the replacement rule flips with it. The argument and every step licensing it are unaffected, so this is one sign to carry, not a different derivation.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

The only Part 3 source that shares this course’s signature AND its ε, so formulas compare character for character — with one real exception: he works in MS-bar and this course absorbs nothing.

• Metric signature same read directly

  Theirs $g_{\mu\nu} = \mathrm{diag}(+1,-1,-1,-1)$

  Eq. (1.32), where the propagator is written 1/(k² − m² + iδ).

• Dimensional regulator same read directly

  Theirs $d = 4 - 2\varepsilon$

  p. 16, stated explicitly — δ is used for the Feynman prescription to avoid colliding with the D = 4 − 2ϵ regulator.

• What the pole carries differs read directly

  Theirs $\tilde\mu = \mu\sqrt{e^{\gamma_E}/4\pi}$

  Eq. (5.196), with the consequence spelled out below Eq. (5.199): using μ instead would leave every formula “cluttered by γ_E and log(4π)”.

  Carrying a result across He absorbs −γ + ln4π into the scale; this course carries it. To compare a finite part, add −γ + ln4π back per power of 1/ε — or equivalently substitute μ̃² → μ² e^{γ_E}/4π. His massless bubble reads 1/ε + 2 where this course’s carries the constant explicitly, and that is the whole of the difference.

Compare directly Same conventions as this course on every axis below.

A source of numbers rather than of formalism, and its numbers are in this course’s units. The thing to check is not a signature but a scheme: the same coupling is α⁻¹ ≈ 137.036 at low energy and 127.930 in MS-bar at the Z mass, so a quoted α means nothing without the scheme and scale beside it.

• Coupling and units of charge same read directly

  Theirs $\alpha = e^2/4\pi$

  Review 10 (Electroweak Model), §10.2.2 “The electromagnetic coupling” — α⁻¹ ≈ 137.036 at the Thomson limit, and $\hat\alpha^{(5)}(M_Z)^{-1} = 127.930 \pm 0.008$ in MS-bar.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

Same signature as this course, so denominators compare directly — and a spinor normalization that differs from every modern text, which is the most instructive difference on this page. It is not the metric, it is not an overall constant, and both books are right.

• Metric signature same not read — bibliographic

  Theirs $g_{\mu\nu} = \mathrm{diag}(+1,-1,-1,-1)$

  ⚠️ Fixed in the notation section; not read here, tracked in ../references/TO-VERIFY.md.

• Spinor normalization differs not read — bibliographic

  Theirs $\bar u u = 1$

  ⚠️ Carried throughout the Dirac-equation chapters, alongside $u^\dagger u = E/m$; not read here, tracked in ../references/TO-VERIFY.md.

  Carrying a result across Their spinor is this course’s divided by $\sqrt{2m}$, so an amplitude picks up $1/\sqrt{2m}$ for every external fermion — and their flux and phase-space factors carry the compensating $2m$, so every cross section agrees exactly. This is the difference worth understanding before any other here: it is not the metric, it is not a constant you can put back at the end, and neither book is wrong. The conversion is implemented in translate.ts and checked against this course’s own spinors.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

The opposite metric signature to this course, and a formalism far enough from a Lagrangian starting point that the signature is the smallest difference a reader will meet. What it settles are questions of principle, and those survive translation intact.

• Metric signature differs not read — bibliographic

  Theirs $\eta_{\mu\nu} = \mathrm{diag}(-1,+1,+1,+1)$

  ⚠️ Fixed in the notation section preceding ch. 1; not read here, tracked in ../references/TO-VERIFY.md.

  Carrying a result across The same translation Srednicki needs, for the same reason: his $p^2$ is minus this course’s, on-shell reads $p^2 = -m^2$, and every propagator denominator inverts. Mandelstam invariants are untouched — translate.ts computes $s$ in both signatures and gets the same number — so a result quoted in $s$, $t$ and $u$ needs nothing done to it.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

Same posture on the scheme as this course — he carries $-\gamma + \ln4\pi$ rather than absorbing it — but a different loop measure. The crossing is one constant, $i/16\pi^2$, with no $\varepsilon$ in it.

• Dimensional regulator same read directly

  Theirs $D \text{ general, with } \tfrac{2}{4-D} = \tfrac{1}{\varepsilon}$

  Eq. (4.22), where Δ is defined as 2/(4−D) − γ_E + ln4π. He keeps D general rather than writing D = 4 − 2ε, but the pole is the same object under a different name.

• What the pole carries same read directly

  Theirs $\Delta = \tfrac{2}{4-D} - \gamma_E + \ln 4\pi \text{, carried}$

  Eq. (4.22). The constant is packaged into a named symbol Δ and carried through every result in §4.3, not folded into a redefined scale — the same posture this course takes, in different notation.

• Loop measure differs read directly

  Theirs $\frac{(2\pi\mu)^{4-D}}{i\pi^2}\int d^Dq$

  Eq. (4.1), the definition of the general one-loop tensor integral.

  Carrying a result across Multiply his function by $i/16\pi^2$ to get the same integral in this course’s measure. The factor is a CONSTANT — there is no $\varepsilon$ in it — because the powers of $2\pi$ cancel between his $(2\pi\mu)^{4-D}$ and this course’s $1/(2\pi)^d$, which is exactly why he wrote $2\pi\mu$ rather than $\mu$. So this crossing, unusually for a loop convention, CAN be done by scaling the answer at the end.

Translate first The physics is the same; the page is not. Each difference below carries its bridge.

Same metric and same $\varepsilon$ as this course, but a loop measure that removes $r_\Gamma$ — so the crossing carries $(4\pi)^\varepsilon r_\Gamma$ and lands in the finite part. ⚠️ It is NOT Denner’s convention either.

• Metric signature same read directly

  Theirs $g_{\mu\nu} = \mathrm{diag}(+1,-1,-1,-1)$

  §2.1, first line — “We work in the Bjorken-Drell metric so that l² = l₀² − l₁² − l₂² − l₃².”

• Dimensional regulator same read directly

  Theirs $D = 4 - 2\varepsilon$

  §2.1, below Eq. (2.1) — “Near four dimensions we use D = 4 − 2ǫ.”

• Loop measure differs read directly

  Theirs $\frac{\mu^{4-D}}{i\pi^{D/2} r_\Gamma}\int d^Dl$

  Eq. (2.1) for the measure and Eq. (2.2) for r_Γ = Γ²(1−ǫ)Γ(1+ǫ)/Γ(1−2ǫ), which they state explicitly as “the overall constant which occurs in D-dimensional integrals” and have removed.

  Carrying a result across Multiply by $\frac{i}{16\pi^2}(4\pi)^\varepsilon r_\Gamma$ to reach this course’s measure. Unlike Denner’s, this factor is $\varepsilon$-DEPENDENT — their $i\pi^{D/2}$ carries the dimension — so it cannot be applied to a finished number: $(4\pi)^\varepsilon r_\Gamma = 1 + \varepsilon(\ln4\pi - \gamma)$, and against a $1/\varepsilon$ pole that leaves $\ln4\pi - \gamma \approx 1.95$ behind in the finite part. Going between the two published tables is the same factor: $T_{\text{Denner}} = (4\pi)^\varepsilon r_\Gamma\, I_{\text{EZ}}$.

• What the pole carries differs read directly

  Theirs $r_\Gamma \text{ divided out, so } -\gamma + \ln4\pi \text{ is gone}$

  Eq. (2.2), and visible in the results: their tadpole Eq. (4.1) reads m²(μ²/m²)^ǫ(1/ǫ + 1), with no γ and no ln4π anywhere in it.

  Carrying a result across Add $-\gamma + \ln4\pi$ back per power of $1/\varepsilon$ before comparing a finite part — the same arithmetic Tancredi’s $\overline{\mathrm{MS}}$ scale needs, reached by a different route. He moves the scale; they divide out a ratio of gamma functions. Both land in the same place, which is worth knowing because it means the ≈1.95 discrepancy has two quite different-looking causes.

Compare directly Same conventions as this course on every axis below.

Same signature as this course. Its loop conventions — which ε it continues in, and whether it absorbs the scheme constant — are the two things to check before comparing any pole coefficient, and neither has been confirmed here.

• Metric signature same not read — bibliographic

  Theirs $g_{\mu\nu} = \mathrm{diag}(+1,-1,-1,-1)$

  ⚠️ Appendix A, “Conventions” — the appendix is confirmed to exist and to be where the book fixes them, but its contents were not read. Tracked in ../references/TO-VERIFY.md.