- #1
jostpuur
- 2,116
- 19
If a particle is point like, then point [itex]x\in\mathbb{R}^3[/itex] specifies the particle's spatial configuration, and the quantum mechanical wave function for the particle is
[tex]
\Psi:\mathbb{R}^3\to\mathbb{C}
[/tex]
The spatial configuration of a closed string with fixed length L can be specified with a function
[tex]
f:S^1\to\mathbb{R}^3
[/tex]
such that the function satisfies
[tex]
\underset{S^1}{\int} du\;|\nabla f(u)| = L
[/tex]
Is the idea in string theory to then describe these strings with wave mappings
[tex]
\Psi:\{f\}\to\mathbb{C}?
[/tex]
[tex]
\Psi:\mathbb{R}^3\to\mathbb{C}
[/tex]
The spatial configuration of a closed string with fixed length L can be specified with a function
[tex]
f:S^1\to\mathbb{R}^3
[/tex]
such that the function satisfies
[tex]
\underset{S^1}{\int} du\;|\nabla f(u)| = L
[/tex]
Is the idea in string theory to then describe these strings with wave mappings
[tex]
\Psi:\{f\}\to\mathbb{C}?
[/tex]