Part III
Green’s Functions

12 Scalar Green’s functions in flat spacetime
 12.1 Green’s equation for a massive scalar field
 12.2 Integration over the source
 12.3 Singular part of g(σ)
 12.4 Smooth part of g(σ )
 12.5 Advanced distributional methods
 12.6 Alternative computation of the Green’s functions
13 Distributions in curved spacetime
 13.1 Invariant Dirac distribution
 13.2 Light-cone distributions
14 Scalar Green’s functions in curved spacetime
 14.1 Green’s equation for a massless scalar field in curved spacetime
 14.2 Hadamard construction of the Green’s functions
 14.3 Reciprocity
 14.4 Kirchhoff representation
 14.5 Singular and regular Green’s functions
 14.6 Example: Cosmological Green’s functions
15 Electromagnetic Green’s functions
 15.1 Equations of electromagnetism
 15.2 Hadamard construction of the Green’s functions
 15.3 Reciprocity and Kirchhoff representation
 15.4 Relation with scalar Green’s functions
 15.5 Singular and regular Green’s functions
16 Gravitational Green’s functions
 16.1 Equations of linearized gravity
 16.2 Hadamard construction of the Green’s functions
 16.3 Reciprocity and Kirchhoff representation
 16.4 Relation with electromagnetic and scalar Green’s functions
 16.5 Singular and regular Green’s functions

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