Little question about string theory

[jostpuur]

If a particle is point like, then point $x\in\mathbb{R}^3$ specifies the particle's spatial configuration, and the quantum mechanical wave function for the particle is

$$\Psi:\mathbb{R}^3\to\mathbb{C}$$

The spatial configuration of a closed string with fixed length L can be specified with a function

$$f:S^1\to\mathbb{R}^3$$

such that the function satisfies

$$\underset{S^1}{\int} du\;|\nabla f(u)| = L$$

Is the idea in string theory to then describe these strings with wave mappings

$$\Psi:\{f\}\to\mathbb{C}?$$

 

[jostpuur]

If this had been normal string theory, somebody would have probably already confirmed it.

Is the situation with this little like with the QFT? It is possible to describe the states of quantum fields with wave functionals, but it is not popular, and everybody wants to do everything with the operators more abstractly without explicit representations.

In string theory everything is done again with operators, although the wave mapping approach could possible work too?

(btw. If everything goes as planned (course on QFT this fall successfully), I'll be taking my first course on string theory on the spring. I'm just warming up here.)