From classical physics to strings

[eljose79]

in fact if we have a classic hamiltonian.

H=p**2/2m+V(x) to quantize it we would do..

p=-ihd/dx and H=ihd/dt (1st quantization)


Or p=(a+)-(a) and x=(a+)+(a) in terms of creation and anhinilation operators (second quantization).

But..if we would like to write it in a string theory formalism..what would be the sustitutions made?...can we obtain our action S or Hamiltonian for our string theory formalism from the classic hamiltonian...?...is that the so-called third quantization ..how is it made?..

 

[Aaron Bex]

The approach to this question depends on the type of system you are trying to describe. For example, if you are trying to describe a relativistic string then the Hamiltonian is already written in a string theory formalism and there is no need to quantize it further. However, if you are looking to describe a non-relativistic string then you would have to use the quantization methods outlined above. You could also use the path integral formalism or some other approach to quantize the system. In terms of obtaining the action or Hamiltonian for your string theory formalism from the classic Hamiltonian, this is typically done by making appropriate substitutions for the classic Hamiltonian variables in terms of the string theory variables. This is usually done using a Lagrangian approach but can also be done using a Hamiltonian approach. This process is known as third quantization.