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A Note On The Chern-Simons And Kodama Wavefunctions
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Yang-Mills theory in four dimensions formally admits an exact Chern-Simons wavefunction. It is an eigenfunction of the quantum Hamiltonian with zero energy. It is known to be unphysical for a variety of reasons, but it is still interesting to understand what it describes. We show that in expanding around this state, positive helicity gauge bosons have positive energy and negative helicity ones have negative energy. Some of the negative energy states would have negative norm. We also show that the Chern-Simons state is the supersymmetric partner of the naive fermion vacuum in which one does not fill the fermi sea. Finally, we give a sort of explanation of ``why'' this state exists. Similar properties can be expected for the analogous Kodama wavefunction of gravity.
Forward citations
Cited by 3 Pith papers
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The paper asserts a unified scenario of preon supersymmetry, no-boundary cosmology, and Chern-Simons gravity without providing new derivations or quantitative predictions.
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Chern-Simons States in $SO(1,n)$ Yang-Mills Gauge Theory of Quantum Gravity
The paper claims Einstein gravity emerges from an SO(1,4) Yang-Mills theory at one loop, but the derivation requires dropping the Yang-Mills term and fixing the coupling to match Newton's constant.
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