Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.
Closed formula for the matrix elements of the volume operator in canonical quantum gravity
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abstract
We derive a closed formula for the matrix elements of the volume operator for canonical Lorentzian quantum gravity in four spacetime dimensions in the continuum in a spin-network basis. We also display a new technique of regularization which is state dependent but we are forced to it in order to maintain diffeomorphism covariance and in that sense it is natural. We arrive naturally at the expression for the volume operator as defined by Ashtekar and Lewandowski up to a state independent factor.
fields
gr-qc 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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A matrix free action of the Ashtekar-Lewandowski volume operator of loop quantum gravity
Develops a matrix-free SRQ-based action for the AL volume operator that exactly preserves the kernel and supports large-scale Monte Carlo and spectral estimates without dense matrices.