Physics / research
Loop integrals and observable corrections
Perform representative perturbative field-theory calculations with explicit regularization, analytic continuation, divergence identification, and unitarity checks.
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Inside this module
Module 01 research
Loop integrals and observable corrections
Perform representative perturbative field-theory calculations with explicit regularization, analytic continuation, divergence identification, and unitarity checks.
- 01
Wick contractions and diagram symmetry factors
Derive scalar diagram coefficients from explicitly labeled contractions and distinguish combinatorics from coupling powers.
30 min - 02
One-loop scalar self-energy
Evaluate a massive scalar tadpole with an explicit Euclidean cutoff and connect subtraction conditions to propagator poles.
30 min - 03
Feynman parameter combination of denominators
Combine propagators, complete the loop-momentum square, and preserve analytic prescriptions and regulator assumptions.
30 min - 04
Dimensional loop integration
Derive a Euclidean master integral and expand its ultraviolet pole with an explicit scale and subtraction convention.
30 min - 05
Tensor integral reduction
Use rotational identities and external momenta to reduce tensor numerators without discarding dimension-dependent finite terms.
30 min - 06
One-loop four-point amplitudes
Assemble the scalar s, t, and u bubbles, subtract their ultraviolet pole, and check renormalization-scale dependence.
30 min - 07
Branch cuts and threshold discontinuities
Locate the scalar two-particle threshold from parameter space and compute its imaginary part with a fixed causal branch.
30 min - 08
Cutkosky cuts and perturbative unitarity
Match a scalar bubble’s absorptive part to on-shell phase space with explicit state normalization and identical-particle factors.
30 min - 09
Infrared divergences and inclusive observables
Identify soft and collinear limits and state the measurement conditions needed for physical infrared cancellation.
30 min - 10
Real–virtual cancellation in simple processes
Combine regulated endpoint terms into a plus distribution and distinguish universal singular structure from supplied hard matching constants.
30 min