×

Real sector of the nonminimally coupled scalar field to self-dual gravity. (English) Zbl 0946.83045

Summary: A scalar field nonminimally coupled to gravity is studied in the canonical framework, using self-dual variables. The corresponding constraints are first class and polynomial. To identify the real sector of the theory, reality conditions are implemented as second class constraints, leading to three real configurational degrees of freedom per space point. Nevertheless, this realization makes nonpolynomial some of the constraints. The original complex symplectic structure reduces to the expected real one, by using the appropriate Dirac brackets. For the sake of preserving the simplicity of the constraints, an alternative method preventing the use of Dirac brackets, is discussed. It consists of converting all second class constraints into first class by adding extra variables. This strategy is implemented for the pure gravity case.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] C. Rovelli, gr-qc archives No. gr-qc/9803024.
[2] DOI: 10.1103/PhysRevLett.69.237 · Zbl 0968.83510
[3] DOI: 10.1103/PhysRevLett.69.237 · Zbl 0968.83510
[4] DOI: 10.1103/PhysRevLett.69.237 · Zbl 0968.83510
[5] DOI: 10.1103/PhysRevLett.69.237 · Zbl 0968.83510
[6] DOI: 10.1016/0370-2693(96)00532-1 · Zbl 0945.83013
[7] DOI: 10.1016/0370-2693(96)00532-1 · Zbl 0945.83013
[8] DOI: 10.1103/PhysRevD.36.1587
[9] DOI: 10.1103/PhysRevD.36.1587
[10] DOI: 10.1088/0264-9381/13/11/009 · Zbl 0863.53064
[11] DOI: 10.1142/S0217751X91001581 · Zbl 0741.58050
[12] DOI: 10.1142/S0217732394003385 · Zbl 1015.81575
[13] DOI: 10.1016/0370-2693(89)90810-1
[14] DOI: 10.1016/0370-1573(94)00111-F
[15] DOI: 10.1103/PhysRevD.46.1450
[16] DOI: 10.1103/PhysRevD.51.5507
[17] DOI: 10.1103/PhysRevD.51.5498
[18] DOI: 10.1103/PhysRevD.51.5498
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.