Abstract
A new framework of loop quantization that assimilates conformal and scale invariance is constructed and is found to be applicable to a large class of physically important theories of gravity and gravity-matter systems. They include general relativity and scale-invariant scalar-tensor and dilaton theories. Consequently, matter to be coupled to such theories is restricted to be conformal or scale invariant. Standard model-type systems naturally fall into this category. The new loop quantization follows from a novel conformally generalized Holst action principle. In contrast to standard loop quantum gravity, the resulting quantum geometry is not beset by the Immirzi ambiguity and has no definitive area gaps within the considered large class of theories of gravitation. As an additional feature, the scale invariance gives rise to a conservedWeyl current and we discuss briefly its possible implication on the problem of time in quantum gravity.
Original language | English |
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Article number | 124041 |
Number of pages | 8 |
Journal | Physical Review D |
Volume | 98 |
Issue number | 12 |
DOIs | |
Publication status | Published - 28 Dec 2018 |
Bibliographical note
C. W. wishes to thank C. J. Isham and J. W. York for encouragement in pursuing the conformal properties of (loop) quantum gravity. The referee’s constructive criticismhas been very helpful in clarifying the presentation of results and their context. For financial support, C. W. and D. R. are grateful to EPSRC, STFC, and Cruickshank Trust (UK) and CNPq (Brazil).