Exploring the Quantum Formulation of String Theory

[Topolfractal]

String theory is what I'm currently studying. The dominant form is the action formulation of it. A classical string Lagrangian is submitted and quantized to produce the equations of motion of a string. Is there a purely quantum formulation of string theory that doesn't start with a classical lagrangian?

 

[Orodruin]

What do you mean by "pure quantum"? Specifying a Lagrangian and quanising is the standard also in normal quantum mechanics.

 

[haushofer]

AFAIK such a formulation doesn't exist, but Witten mentions this issue briefly in this talk,



probably somewhere at the end.

ps for future topics you could make your topictitle a bit more specific ;)

 

[Topolfractal]

I mean by pure quantum the traditional style of quantum mechanics. The use of operators and wave functions to do calculations. Now my question is ; Is there a formulation that doesn't start in classical mechanics, but purely in the quantum realm? Now the reason why I'm asking is this formulation ,puts quantum mechanics at a less than fundamental role in calculations. Also I do agree the formulation is a large part of traditional quantum mechanics to and all of quantum field theory. My ideas behind such a quantum formulation are that the wave functions are changed into quaternion functionals, that gradients are converted into total derivatives ect. This adaptation to standard quantum mechanics makes it applicable to vibrating strings.

 

[Topolfractal]

The talk was very enlightening and is exactly what I was aiming for in my question. The thoughts listed in my last message are a long way from a self consistent model of quantum gravity, but possibly in the direction of Edward Witten's talk.

 

[Topolfractal]

As Witten said it could very well lead to a new meaning of quantum mechanics.

 

[haushofer]

Yes, but i don't know how to reconcile this with the correspondence principle.

 

[Topolfractal]

What do you mean?

Yes, but i don't know how to reconcile this with the correspondence principle.

 

[haushofer]

Well, somehow you expect that such a formulation should be able to reproduce known theories in certain limits, say h --> 0 ( or alpha' --> 0, if you want to obtain point particle results ). This is the correspondence principle. So I would expect then that one would be able to obtain such a formulation also by quantizing a classical theory.

 

[Topolfractal]

But that's precisely why we need another formulation to describe h and alpha deformations simultaneously.