Exploring the Quantum Formulation of String Theory

In summary: Quantizing a classical theory is not the same as obtaining a purely quantum theory.Quantizing a classical theory is not the same as obtaining a purely quantum theory.Yes, but what if the classical theory is not quantizable?In that case, one could still quantize the theory by using a suitable functional, but one would get results that don't agree with those obtained by quantizing the classical theory.That's definitely a problem.Quantizing a classical theory is not the same as obtaining a purely quantum theory.
  • #1
Topolfractal
76
7
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?
 
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  • #2
What do you mean by "pure quantum"? Specifying a Lagrangian and quanising is the standard also in normal quantum mechanics.
 
  • #3
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 ;)
 
  • #4
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.
 
  • #5
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.
 
  • #6
As Witten said it could very well lead to a new meaning of quantum mechanics.
 
  • #7
Yes, but i don't know how to reconcile this with the correspondence principle.
 
  • #8
What do you mean?
haushofer said:
Yes, but i don't know how to reconcile this with the correspondence principle.
 
  • #9
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.
 
  • #10
But that's precisely why we need another formulation to describe h and alpha deformations simultaneously.
 

FAQ: Exploring the Quantum Formulation of String Theory

1. What is string theory and why is it important?

String theory is a theoretical framework that attempts to reconcile the theories of quantum mechanics and general relativity. It proposes that the fundamental building blocks of the universe are not particles, but rather tiny, one-dimensional strings. String theory is important because it has the potential to provide a more complete understanding of the universe and address fundamental questions about the nature of reality.

2. How does string theory relate to quantum mechanics?

String theory is built upon the principles of quantum mechanics, such as the uncertainty principle and wave-particle duality. It extends these principles to a higher-dimensional space and proposes that strings can vibrate at different frequencies, giving rise to different types of particles. This allows for the unification of the four fundamental forces of nature.

3. What is the role of extra dimensions in string theory?

String theory requires extra dimensions in order to mathematically describe the behavior of strings. These dimensions are compactified, meaning they are curled up and hidden from our everyday perception. The number of dimensions in string theory ranges from 10 to 26, depending on the specific version of the theory.

4. What is the current status of string theory?

String theory is still a highly active area of research in theoretical physics. While it has shown promise in unifying the fundamental forces and providing a framework for understanding the universe, it has yet to be experimentally verified. Many scientists are working on developing new mathematical tools and techniques to test the predictions of string theory.

5. What are some potential implications of string theory?

If string theory is proven to be correct, it would have significant implications for our understanding of the universe. It could potentially provide a theory of everything, explaining all physical phenomena and bridging the gap between quantum mechanics and general relativity. It could also have practical applications, such as the development of new technologies and insights into the nature of space and time.

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