# Can we apply 'Quantization' only from motion equation ?

1. Jul 30, 2007

### Klaus_Hoffmann

Can we apply 'Quantization' only from motion equation ??

Supposing you have the equation of motion (in terms of momenta and position)

$$F(\dot p_{a} , q_{a})=0$$

then can you obtain the 'Quantum analogue' without the intervention of the Lagrangian ???

and another question could we regard the expression

$$\int \mathcal D[q(t)] e^{-\int_{a}^{b}dt \mathcal L (q, \dot q , t)}$$

as a 'Zeta function' of something evaluated at a point s=1 where

$$\int_{a}^{b}dt \mathcal L (q, \dot q , t)} =logM[q(t)]$$

being M another functional, so the problems involving Functional integration (if not all many of them) could be sovled by Zeta regularization.

Last edited: Jul 30, 2007
2. Jul 31, 2007