报告题目:Self dual Ashtekar gravity coupled to matter in symmetry reduced models: anomaly-free algebra of constraints with holonomy corrections
报告人：Antonino Marciano博士
报告时间：下午 2:00-3:00
报告地点： 理学楼报告厅A101
报告题目： Self dual Ashtekar gravity coupled to matter in symmetry reduced models: anomaly-free algebra of constraints with holonomy corrections
报告人：复旦大学 Antonino Marciano博士
报告地点： 理学楼报告厅A101
报告时间： 11.21 周一下午 2:00-3:00
报告摘要： We review a series of works on the analysis of the algebra of constraints cast in terms of the self dual Ashtekar variables, starting form the investigation (at the effective level) the spherically symmetry reduced model of loop quantum gravity, both in vacuum and when coupled to a scalar field. Within the real Ashtekar-Barbero formulation, the system scalar field coupled to spherically symmetric gravity is known to possess a non closed (quantum) algebra of constraints once holonomy corrections are introduced, which forbids the loop quantization of the model. Moreover, the vacuum case, while not anomalous, introduces modifications which are usually interpreted as an effective signature change of the metric in the deep quantum region. I show that both those complications disappear when working with self dual Ashtekar variables, both in the vacuum case and in the case of gravity minimally coupled to a scalar field. In this framework, the algebra of the holonomy corrected constraints is anomaly free and reproduces the classical hypersurface deformation algebra without any deformations.
I then revisit scalar cosmological perturbations in loop quantum cosmology (LQC) in a covariant manner, using self dual Ashtekar variables, and show that working with self dual variables lead again to an undeformed algebra of hypersurface deformations, even after including holonomy corrections in the effective constraints. As a necessary consequence, the diffeomorphism constraint picks up non-perturbative quantum corrections thus hinting at a modification of the underlying space-time structure, a novel ingredient compared to the usual treatment of (spatial) diffeomorphisms in LQG. Contrary to the same approach worked out using the real Ashtekar- Barbero variables where the algebra is deformed, the self dual model is free from the signature change phenomenon, giving rise to an inequivalent quantum effective theory, leading potentially to different predictions concerning the CMB power spectrum. Using a Hamilton-Jacobi inspired approach, I also show the derivation of the gauge invariant Mukhanov-Sasaki scalar variable as well as their equation of motion modified by the effective quantum corrections. Because we are dealing with self dual perturbed variables, our gauge invariant variable turns out to be complex. Interestingly, it provides a non trivial but tractable case where the reality conditions can be solved.
Finally I show how to incorporate putative quantum corrections coming from loop quantum gravity in deriving modified dispersion relations for particles on a deformed Minkowski spacetime. Fundamental quantum gravity theories are known to be notoriously difficult to extract viable testable predictions out of. I show how different choices of the Immirzi parameter can, in some cases, serendipitously lead to different outcomes for such modifications, depending on the quantization scheme chosen. This allows one to differentiate between these quantization choices via testable phenomenological predictions.
报告人简介：Antonino Marcianò博士，复旦大学副教授。2008年于意大利罗马大学获得博士学位；其后分别在法国理论物理中心（2007-2010）、意大利罗马大学（2010）、美国哈弗福德学院（2010-2012）、 美国普林斯顿大学（2011-2012）、美国达特茅斯大学（2012-2013）从事博士后研究工作；2014年1月至今任复旦大学副教授。研究领域包括早期宇宙、暴涨、暗能量、量子宇宙学与量子引力、以及量子引力唯像学，发表论文40余篇。
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