发表机构
Universidad Complutense de Madrid; Sorbonne Université; CNRS; ENS-Université PSL; Collège de France; Università degli Studi di Padova; INFN, Sezione di Padova（马德里康普顿斯大学; 索邦大学; 法国国家科学研究中心; 巴黎高等师范学院-巴黎文理研究大学; 法兰西公学院; 帕多瓦大学; 意大利国家核物理研究所帕多瓦分部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究在耦合任意n个自由无质量标量场的平直FLRW几何中，建立了区分规范与物理对称性的框架，将单场共形代数结果推广到任意n，明确了艾森哈特-杜瓦尔提升的对称性代数依赖于规范，恢复了约化相空间无法感知的规范不变荷。
AI 中文摘要
在一般协变理论中，坐标时间演化属于规范变换，因此在规范固定表述中显现的对称性未必是物理动力学的对称性。去参数化会消除规范对称性，但可能隐藏物理对称性，尤其是依赖所选物理时钟的那些对称性。我们研究耦合任意n个自由无质量标量场的平直FLRW几何中规范对称性与（隐藏的）物理对称性的关系。我们证明，小超空间度规的共形Killing矢量生成守恒荷，这些荷是狄拉克可观测量（因此是规范不变的），其泊松代数为极大共形代数𝔠𝔬𝔫𝔣(n,1)≅𝔰𝔬(n+1,2)，将此前单场结果推广到任意n。我们随后在一类规范中重新考察艾森哈特-杜瓦尔提升，发现显现的对称性代数依赖于规范：在规范固定小超空间度规变为平直的特殊谐规范中，该代数扩大为薛定谔代数（因此不是物理对称性）。此外，去参数化将提升后的荷映射为规范不变的狄拉克可观测量，这些可观测量始终实现共形代数的子代数，且在谐规范中完全重现该代数。这些结果建立了在小超空间模型中区分规范与物理对称性的框架，恢复了约化相空间表述在结构上无法感知的荷，且在存在势的情况下仍适用。
英文摘要
In generally covariant theories, evolution in coordinate time is a gauge transformation, so that a symmetry made manifest in a gauge-fixed description need not be a symmetry of the physical dynamics. At the same time, deparametrisation removes gauge redundancies but may hide physical symmetries, in particular those that depend on the chosen physical clock. We investigate the relation between gauge and hidden physical symmetries in flat FLRW geometry coupled to an arbitrary number $n$ of free massless scalar fields. We show that conformal Killing vectors of the minisuperspace metric generate conserved charges that are Dirac observables and hence gauge-invariant. Their Poisson algebra realises the maximal conformal algebra $\mathfrak{conf}(n,1)\simeq\mathfrak{so}(n+1,2)$, extending previous single-field results to arbitrary $n$. We then revisit the Eisenhart--Duval lift in a family of gauges and show that the resulting symmetry algebra is gauge dependent. Only in the harmonic gauge does the algebra enlarge to the Schrödinger algebra, which is thus not a physical symmetry. Finally, we show that deparametrisation maps the lifted charges to gauge-invariant Dirac observables, which always realise a subalgebra of $\mathfrak{conf}(n,1)$, recovering it in full in the harmonic gauge. Our results provide a systematic framework for disentangling gauge from physical symmetries in minisuperspace models, recovering charges to which reduced phase-space descriptions are structurally blind, and extending naturally to models with potentials.
Comments25 pages + appendices + references; v2: matches published version
