B
Summary of Important Formulas
This appendix summarizes formulas that appear in the book or are needed but
assumed to be known to the reader (such as formulas from QFT and general
relativity).
B.1
Complex Analysis
The Cauchy–Riemann formula is
C z
dw
2π i
f (w)
(w − z) n =
f (n−1) (z)
(n − 1)!
,
(B.1)
where f (z) is a holomorphic function.
One has
¯
∂
1
z
= 2π δ
(2) (z).
(B.2)
B.2
QFT, Curved Spaces and Gravity
The Green function G of a differential operator D is defined by
D x G(x, y) =
δ(x − y)
√ g
− P (x, y),
(B.3)
where P is the projector on the zero-modes of D.
© Springer Nature Switzerland AG 2021
H. Erbin, String Field Theory, Lecture Notes in Physics 980,
https://doi.org/10.1007/978-3-030-65321-7
381
Summary of Important Formulas
This appendix summarizes formulas that appear in the book or are needed but
assumed to be known to the reader (such as formulas from QFT and general
relativity).
B.1
Complex Analysis
The Cauchy–Riemann formula is
C z
dw
2π i
f (w)
(w − z) n =
f (n−1) (z)
(n − 1)!
,
(B.1)
where f (z) is a holomorphic function.
One has
¯
∂
1
z
= 2π δ
(2) (z).
(B.2)
B.2
QFT, Curved Spaces and Gravity
The Green function G of a differential operator D is defined by
D x G(x, y) =
δ(x − y)
√ g
− P (x, y),
(B.3)
where P is the projector on the zero-modes of D.
© Springer Nature Switzerland AG 2021
H. Erbin, String Field Theory, Lecture Notes in Physics 980,
https://doi.org/10.1007/978-3-030-65321-7
381