Quantum Field Theory
In QFT we need such objects as functionals \(\psi[A,\Psi]\), path integrals and such like.There is also the operator formalism.
We also have the Feynman propagators \(\Delta_F(x,y)\) and time evolution functions \(K_t[\phi_{in},\phi_{out}] = \int e^{i\int_0^t \mathcal{L}[\phi]dt }D\phi \).
Also the vacuum states \(\psi[\phi]_{Vac} = \frac{ e^{-\int_{-\infty}^t \mathcal{L}[\phi]dt } }{\sqrt{ e^{-\int_{-\infty}^{\infty} \mathcal{L}[\phi]dt } } } \) (?)
Also we have dirac delta functions.
We could also do CFT in 1+1D which is a bit simpler.