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It is not the case that The canonical formulation of general relativity must employ the method of constrained Hamiltonian systems.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Lagrangian formulations of general relativity, such as the covariant path-integral approach, are mathematically rigorous without invoking Hamiltonian constraints.
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2.
A canonical formulation is one possible representational choice, not a necessity imposed by the theory's physical content.
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3.
The existence of gauge symmetries underdetermines the formalism required, since equivalent physical predictions can be derived through gauge-fixed Lagrangian methods alone.
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Reason for 2 of 2
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1.
Kuchař and Torre demonstrated that the problem of time in canonical quantum gravity may arise from Hamiltonian constraint quantization itself, not from GR's physical structure.
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2.
If the canonical constrained Hamiltonian method generates artifacts absent in the covariant formulation, it cannot be the uniquely mandatory representational framework.
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Reasons Against
1 perspective
Reason against
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1.
General relativity, like Maxwell's theory of electromagnetism, possesses gauge symmetries.
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2.
Theories with gauge symmetries are constrained theories.
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