From classical physics to strings

In summary, the conversation discusses the quantization of a classic Hamiltonian and how it can be done using different methods such as first and second quantization or using a string theory formalism. The approach to this depends on the type of system being described, with different methods being used for relativistic and non-relativistic strings. The process of obtaining the action or Hamiltonian for a string theory formalism from the classic Hamiltonian is known as third quantization and involves making appropriate substitutions for the variables.
  • #1
eljose79
1,518
1
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?..
 
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  • #2
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.
 

1. What is classical physics?

Classical physics is the branch of physics that deals with the behavior of macroscopic objects and systems, using principles such as Newton's laws of motion and thermodynamics. It was the dominant form of physics from the 17th to the early 20th century.

2. What is quantum mechanics?

Quantum mechanics is the branch of physics that deals with the behavior of particles on a microscopic scale, such as atoms and subatomic particles. It describes the fundamental nature of matter and energy and how they interact with each other.

3. What is the connection between classical physics and string theory?

Classical physics and string theory are both theories that attempt to explain the fundamental laws of the universe. String theory is considered to be an extension of classical physics, as it includes and expands upon the principles of classical mechanics and quantum mechanics.

4. How does string theory differ from other theories of physics?

String theory differs from other theories of physics in that it proposes that the fundamental building blocks of the universe are not particles, but rather tiny vibrating strings. It also suggests that there are more than three dimensions in the universe, which is not accounted for in other theories.

5. Is string theory a proven theory?

No, string theory is still a theoretical framework and has not been proven through experimentation. It is still being studied and developed by scientists, and there is much debate and research surrounding its validity as a theory of physics.

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