Applicablilty of the Wheeler-DeWitt equation

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SUMMARY

The Wheeler-DeWitt equation, as discussed in Carlo Rovelli's "Quantum Gravity," is not limited to the quantization of gravity but may also apply to other quantum field theories (QFTs). Rovelli suggests that the equation can represent the equations of motion for various field theories, expressed as H(xα, δ/δxα, φ, δ/δφ)Ψ=0. This indicates a broader applicability of the Wheeler-DeWitt equation beyond its traditional context. Hartle and Hawking's work on the wave function of the universe further supports its relevance in theoretical physics.

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  • Understanding of the Wheeler-DeWitt equation
  • Familiarity with quantum field theory (QFT)
  • Knowledge of quantum gravity concepts
  • Basic grasp of functional derivatives in physics
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The discussion is beneficial for theoretical physicists, researchers in quantum gravity, and students of quantum field theory seeking to understand the broader implications of the Wheeler-DeWitt equation.

jfy4
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Hi,

Throughout much of Carlo Rovelli's book "Quantum Gravity", he continually refers to the Wheeler DeWitt equation, but not always in the context of quantizing gravity. In his section on normal (quantum) field theory, he does a significant portion of the work around the Wheeler DeWitt equation with no reference to quantum gravity in the section. Is the Wheeler DeWitt equation applicable to other QFTs besides quantum gravity?

Let me be even more specific, it seems to me that Rovelli implies that every equation of motion for any field theory can be written
<br /> H\left( x^\alpha, \frac{\delta}{\delta x^\alpha}, \phi, \frac{\delta}{\delta \phi}\right)\Psi=0<br />

Thanks,
 
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