A Generalized Wick Transform for Gravity

Abhay Ashtekar

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A Generalized Wick Transform for Gravity

Abhay Ashtekar

General Relativity and Quantum Cosmology · Submitted 30 Nov 1995

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The authors' main claim Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources.

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What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.10 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.02 · compares with prior results 0.23 · mentions code or data availability 0.02.

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arXiv listing abstract v2. Results and the main claim are underlined; show every role.

Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue within ``connection-dynamics'' where one can work, throughout, only with real variables. The resulting quantum theory would then be free of complicated reality conditions. Ramifications of this development to the canonical quantization program are discussed.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources.	contribution 0.99	0.91	0.42	asserted 1.00
s1	This opens up a new avenue within ``connection-dynamics'' where one can work, throughout, only with real variables.	interpretation 0.95	0.53	0.19	hedged possibility 0.51
s2	The resulting quantum theory would then be free of complicated reality conditions.	interpretation 0.89	0.28	0.24	hedged possibility 0.68
s3	Ramifications of this development to the canonical quantization program are discussed.	interpretation 0.57	0.53	0.07	unclear 0.74

What kind of paper the classifier reports this is: method or tool 0.98 · evidence from proof or derivation 0.74.

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arXiv listing abstract v2

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full text
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T body sentences
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The paper

Original abstract

Using a key observation due to Thiemann, a generalized Wick transform is introduced to map the constraint functionals of Riemannian general relativity to those of the Lorentzian theory, including matter sources. This opens up a new avenue within ``connection-dynamics'' where one can work, throughout, only with real variables. The resulting quantum theory would then be free of complicated reality conditions. Ramifications of this development to the canonical quantization program are discussed.

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References

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Quantum Spin Dynamics (QSD)
gr-qc 1996-06 conditional novelty 8.0 of 10

A finite, diffeomorphism-covariant operator for the Wheeler-DeWitt constraint of Lorentzian gravity is built on spin-network states, with the volume operator absorbing the inverse-metric singularity that normally forc...
QSD V : Quantum Gravity as the Natural Regulator of Matter Quantum Field Theories
gr-qc 1997-05 conditional novelty 6.0 of 10

In loop quantum gravity the volume operator's discrete spectrum absorbs the point-splitting divergences of the Standard Model Hamiltonian, yielding finite operators without renormalization.
Quantum Spin Dynamics (QSD) II
gr-qc 1996-06 conditional novelty 6.0 of 10

A symmetric Wheeler-DeWitt constraint operator is constructed, its Euclidean self-adjoint extensions are proved to exist, and the complete solution space of the earlier non-symmetric operator is classified.

How the literature uses it

4 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

Cites it as background 3 papers

Some effort was devoted to exploit these complex variables (see for instance [ref] ) however the use of real variables allowed finally for important progress [ref] .

An Alternative Canonical Approach to the Ghost Problem in a Complexified Extension of the Pais-Uhlenbeck Oscillator · Introduction · 0.92
Some effort was devoted to exploit these complex variables (see for instance [ref] ) however the use of real variables allowed finally for important progress [ref] .

Coping with the Pais-Uhlenbeck oscillator's ghosts in a canonical approach · Introduction · 0.94
Self-dual Ashtekar variables, reality conditions, Wick rotations and the map $γ→±γ$ for the Barbero-Immirzi parameter (see Tab. [ref] with $ρ=γj$), have played a defining role in the early developments of loop quantum gravity [ref] (see also [ref] ).

Toller matrices and the Feynman $i\varepsilon$ in spinfoams · Discussion · 1.00

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