/sci/ - Science & Math

>>11055726
- A classical particle x(t) (maps in R->R^3, time to space) follows a deterministic motion in Newtons theory.
If you got information of the noise characteristic n(t) of such classical particle in motion, you can propagate your loss of information by wrapping it in a stochastic model (Wiener processes, etc.), i.e. the point motion becomes the evolution of a measurable function / distribution p(x, t).
- Quantum mechanics of point particles is similar to this (except not p(x, t) is evolved but the square root, see Fokker-Planck becomes Schrödinger). The stochastic integrals lead to the necessity ito-like calculus (non-commutation relations), but you can solve things analytically
- QFT takes fields already f(x) (maps from R->(R^3->R^n) (time to space to field value), elements in an infinite dimensional vector spaces) and the "stochastification" leads to ill-defined integrals (of which truncated aspects still give experimental information, however)
- String Theory starts with higher dimensional objects, e.g. closed strings (R->(S->R^3), time to embedding in space) and goes QM, the particle excitation are e.g. kinetic energies of S.
The volume of the thing in space time (pic related) looks like nice field theories, e.g. conformal fields, that have nice quantization properties