Ashtekar's formalism in first-order tetrad form

Journal Article · Thu Mar 15 04:00:00 EST 1990 · Physical Review, D (Particles Fields); (USA)

DOI:https://doi.org/10.1103/PhysRevD.41.1885· OSTI ID:7001777

Kamimura, K ^[1]; Fukuyama, T ^[2]

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1. Department of Physics, Toho University, Funabashi 274, Japan (JP)
2. Department of Physics, Ritsumeikan University, Kyoto 603, Japan (JP)

Ashtekar's polynomial constraints for a new canonical gravity are examined in the first-order tetrad formalism. The action is given by the sum of Einstein's action and a complex total divergence term. We find the canonical form of the Hamiltonian explicitly. In the Hamiltonian, the coefficients of Gauss-law constraints are not arbitrary functions but must satisfy nonpolynomial relations. They guarantee the reality condition of canonical variables. In quantum theory an additional measure factor must be required in the inner product of state space.

• OSTI ID: 7001777
• Journal Information: Physical Review, D (Particles Fields); (USA), Journal Name: Physical Review, D (Particles Fields); (USA) Vol. 41:6; ISSN PRVDA; ISSN 0556-2821
• Country of Publication: United States
• Language: English

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ANGULAR MOMENTUM
COSMOLOGY
DIFFERENTIAL EQUATIONS
DIRAC EQUATION
EINSTEIN FIELD EQUATIONS
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LAGRANGIAN FUNCTION
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PARTIAL DIFFERENTIAL EQUATIONS
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QUANTUM GRAVITY
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