Specialization of Ashtekar's Formalism to Bianchi Cosmology

Details Specialization of Ashtekar's Formalism to Bianchi Cosmology Specialization of Ashtekar's Formalism to Bianchi Cosmology

Dec 1988

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988pthph..80.1024k&link_type=abstract

Progress of Theoretical Physics, Vol. 80, No. 6, pp. 1024-1040

Physics

73

Scientific paper

Recently Ashtekar found a new canonical formalism of general relativity inwhichi the constraints and the dynamical equations are all written formallyas polynomials of canonical variables. In this paper we apply his formalismto the Bianchi cosmology and write down the constraints and the dynamicalequations explicitly in terms of Ashtekar-type canonical variables whichdepend only on time. In particular we prove that for the vacuum BianchiIX model the gauge freedom is decoupled from the dynamics andthe canonical variables reduce to three diagonal components of the metricand their Ashtekar-type conjugate momentum, preserving the polynomial natureof the equations. Further we discuss the quantization of this model and showthat the quantized hamiltonian constraint takes a quite simple and beautifulform. To illustrate the tractability of this equation, we present anexplicit non-trivial solution to it.

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