Loop Quantum Gravity

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Loop Quantum Gravity

• A presentation by J. F. Wong
• Department of Physics

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Why Quantizing Gravity?

• General Relativity and Standard Model have been
  great success in explaining the 4 fundamental
  interactions.
• Is it really necessary to quantize gravitational
  interaction?

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The most compelling reason

• We have been always wanting a grand unified
  theory.

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Can we quantize gravity with QFT?

• Conceptual problem.
• gab ?ab hab higher order terms
• ?ab is the Minkowski metric

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• We apply quantum field theory to general
  relativity.
• gt Our theory is a quantum field theory.
• Conclusion Causality is defined in terms of ?ab

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• We apply quantum field theory to general
  relativity.
• gt Our theory is a quantum field theory.
• Conclusion Causality is defined in terms of ?ab
• We apply quantum field theory to general
  relativity.
• gt Our theory is generally relativistic.
• Conclusion Causality is defined in terms of gab.
• We have a conflict.

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Background Space-time

• We observe that, in QFT, there is a flat
  background space-time in which particles move.
• This tradition of using a fixed, non-dynamical,
  background space-time was already established in
  Newtons time.
• F m d2x/dt2

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Lesson from General Relativity

• The geometry of space-time is provided by the
  distribution of matter in it!
• Its not fixed, Its dynamical, it does not exist
  on its own!

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Background Independence

• Since the existence of space-time is a
  consequence of matter,
• can we eliminate the unnecessary assumption
  i.e. pre-existence of background space-time in
  physics theory?
• Background Independence is a postulate of Loop
  Quantum Gravity.

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Conclusion

• We want to quantize gravity because we would like
  a grand unified theory.
• We cant use QFT to do the job due to its
  background dependence.
• QG has to be background independent, this
  motivates the development of LQG.

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Reference

• 1 Alejandro Perez, Introduction to Loop Quantum
  Gravity and Spin Foams.
• (Proceedings of the II International
  Conference on Fundamental Interactions Pedra
  Azul, Brazil, June 2004)
• http//xxx.lanl.gov/