TY - JOUR

T1 - Affine group representation formalism for four-dimensional, Lorentzian, quantum gravity

AU - Chou, Ching Yi

AU - Ita, Eyo E.

AU - Soo, Chopin

PY - 2013/3/21

Y1 - 2013/3/21

N2 - Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure general relativity with cosmological constant, Λ, is re-expressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, Q, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant, and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or the Wheeler-DeWitt equation as an affine algebra requires a non-vanishing cosmological constant, and a fundamental uncertainty relation of the form (wherein V is the total volume) may apply to all physical states of quantum gravity.

AB - Within the context of the Ashtekar variables, the Hamiltonian constraint of four-dimensional pure general relativity with cosmological constant, Λ, is re-expressed as an affine algebra with the commutator of the imaginary part of the Chern-Simons functional, Q, and the positive-definite volume element. This demonstrates that the affine algebra quantization program of Klauder can indeed be applicable to the full Lorentzian signature theory of quantum gravity with non-vanishing cosmological constant, and it facilitates the construction of solutions to all of the constraints. Unitary, irreducible representations of the affine group exhibit a natural Hilbert space structure, and coherent states and other physical states can be generated from a fiducial state. It is also intriguing that formulation of the Hamiltonian constraint or the Wheeler-DeWitt equation as an affine algebra requires a non-vanishing cosmological constant, and a fundamental uncertainty relation of the form (wherein V is the total volume) may apply to all physical states of quantum gravity.

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U2 - 10.1088/0264-9381/30/6/065013

DO - 10.1088/0264-9381/30/6/065013

M3 - Article

AN - SCOPUS:84874963145

VL - 30

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

SN - 0264-9381

IS - 6

M1 - 065013

ER -