Is there a classical counterpart to quantum string theory?

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SUMMARY

Classical string theory serves as the foundation for quantum string theory, beginning with the Lagrangian of a vibrating string, similar to classical Newtonian dynamics. The process involves identifying wave oscillation solutions and calculating Fourier coefficients, followed by the application of quantum (anti)commutation relations. This establishes a direct pathway from classical to quantum frameworks in string theory.

PREREQUISITES
  • Understanding of classical mechanics and Newtonian dynamics
  • Familiarity with Lagrangian mechanics
  • Knowledge of wave oscillation and Fourier analysis
  • Basic concepts of quantum mechanics and (anti)commutation relations
NEXT STEPS
  • Study classical mechanics with a focus on Lagrangian dynamics
  • Learn about wave oscillations and Fourier series
  • Explore the principles of quantum mechanics, particularly (anti)commutation relations
  • Investigate the foundational concepts of string theory and its mathematical framework
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Students and researchers in theoretical physics, particularly those interested in the transition from classical to quantum theories, as well as anyone looking to understand the fundamentals of string theory.

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Standard quantum field theories start so that there is a classical field theory, and then the field is quantized. Is there also a classical string theory, that is quantized to give quantum mechanical theory of strings?

(I don't know anything about string theory yet. I'm just asking things, before I start studying it.)
 
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Yes there is.
 
To expand on Coal's answer, string theory starts classically by considering the Lagrangian of a vibrating string, as is common place in classical Newtonian dynamics. The wave oscillation solutions are found, the Fourier coefficents computed and then you apply quantum (anti)commutation relations to them.
 

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