Constraint analysis of two-dimensional quadratic gravity from \({ BF}\) theory

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• 作者：C. E. Valcárcel
• 关键词：Constrained systems ; \({ BF}\) ; theory ; Quadratic gravity
• 刊名：General Relativity and Gravitation
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：49
• 期：1
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Theoretical, Mathematical and Computational Physics; Classical and Quantum Gravitation, Relativity Theory; Differential Geometry; Astronomy, Astrophysics and Cosmology; Quantum Physics;
• 出版者：Springer US
• ISSN：1572-9532
• 卷排序：49

文摘

Quadratic gravity in two dimensions can be formulated as a background field (BF) theory plus an interaction term which is polynomial in both, the gauge and background fields. This formulation is similar to the one given by Freidel and Starodubtsev to obtain MacDowell–Mansouri gravity in four dimensions. In this article we use the Dirac’s Hamiltonian formalism to analyze the constraint structure of the two-dimensional Polynomial BF action. After we obtain the constraints of the theory, we proceed with the Batalin–Fradkin–Vilkovisky procedure to obtain the transition amplitude. We also compare our results with the ones obtained from generalized dilaton gravity.