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4 Green’s Functions

 4.1 Scalar Green’s functions in flat spacetime
  4.1.1 Green’s equation for a massive scalar field
  4.1.2 Integration over the source
  4.1.3 Singular part of g(σ)
  4.1.4 Smooth part of g(σ)
  4.1.5 Advanced distributional methods
  4.1.6 Alternative computation of the Green’s functions
 4.2 Distributions in curved spacetime
  4.2.1 Invariant Dirac distribution
  4.2.2 Light-cone distributions
 4.3 Scalar Green’s functions in curved spacetime
  4.3.1 Green’s equation for a massless scalar field in curved spacetime
  4.3.2 Hadamard construction of the Green’s functions
  4.3.3 Reciprocity
  4.3.4 Kirchhoff representation
  4.3.5 Singular and radiative Green’s functions
  4.3.6 Example: Cosmological Green’s functions
 4.4 Electromagnetic Green’s functions
  4.4.1 Equations of electromagnetism
  4.4.2 Hadamard construction of the Green’s functions
  4.4.3 Reciprocity and Kirchhoff representation
  4.4.4 Singular and radiative Green’s functions
 4.5 Gravitational Green’s functions
  4.5.1 Equations of linearized gravity
  4.5.2 Hadamard construction of the Green’s functions
  4.5.3 Reciprocity and Kirchhoff representation
  4.5.4 Singular and radiative Green’s functions

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