期刊
JOURNAL OF MATHEMATICAL PHYSICS
卷 56, 期 10, 页码 -出版社
AMER INST PHYSICS
DOI: 10.1063/1.4932967
关键词
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资金
- NSF [DMR-MRSEC 1420709, PHY 12-02718]
- DOE [DE-FG02-13ER41958]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1202718] Funding Source: National Science Foundation
There is significant recent work on coupling matter to Newton-Cartan spacetimes with the aim of investigating certain condensed matter phenomena. To this end, one needs to have a completely general spacetime consistent with local non-relativistic symmetries which supports massive matter fields. In particular, one cannot impose a priori restrictions on the geometric data if one wants to analyze matter response to a perturbed geometry. In this paper, we construct such a Bargmann spacetime in complete generality without any prior restrictions on the fields specifying the geometry. The resulting spacetime structure includes the familiar Newton-Cartan structure with an additional gauge field which couples to mass. We illustrate the matter coupling with a few examples. The general spacetime we construct also includes as a special case the covariant description of Newtonian gravity, which has been thoroughly investigated in previous works. We also show how our Bargmann spacetimes arise from a suitable non-relativistic limit of Lorentzian spacetimes. In a companion paper [M. Geracie et al., e-print arXiv:1503.02680], we use this Bargmann spacetime structure to investigate the details of matter couplings, including the Noether-Ward identities, and transport phenomena and thermodynamics of non-relativistic fluids. (C) 2015 AIP Publishing LLC.
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