TY - JOUR

T1 - Quantum gravity of a brane-like Universe

AU - Davidson, Aharon

AU - Karasik, David

N1 - Funding Information:
∗This essay received an \honorable mention" from the Gravity Research Foundation, 1998 | Ed. yE-mail: davidson@bgumail.bgu.ac.il zE-mail: karasik@bgumail.bgu.ac.il

PY - 1998/9/7

Y1 - 1998/9/7

N2 - Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism, parametrized by the coordinates yA (t, xi), is governed by some ρAB(y, y′, y″). Invoking a novel Lagrange multiplier λ, accompanying the lapse function N and the shift vector Ni, we derive the quadratic Hamiltonian script H sign = 1/2 N [PA((ρ - λI)-1)AB PB + λ] + Niy,AiPA. The inclusion of matter resembles minimal coupling. Setting PA = -i(δ/δyA), we derive a bifurcated Wheeler-Dewitt-like equation. Einstein gravity, associated with λ being a certain fourfold degenerate eigenvalue of ρAB, is characterized by a vanishing center-of-mass momentum ∫ PA d3x = 0. Troublesome (ρ - λI)-1 is then replaced by regular M-1, such that M-1 (ρ - λI) defines a projection operator, modifying the Hamiltonian accordingly.

AB - Quantum gravity of a brane-like Universe is formulated, and its Einstein limit is approached. Regge-Teitelboim embedding of Arnowitt-Deser-Misner formalism, parametrized by the coordinates yA (t, xi), is governed by some ρAB(y, y′, y″). Invoking a novel Lagrange multiplier λ, accompanying the lapse function N and the shift vector Ni, we derive the quadratic Hamiltonian script H sign = 1/2 N [PA((ρ - λI)-1)AB PB + λ] + Niy,AiPA. The inclusion of matter resembles minimal coupling. Setting PA = -i(δ/δyA), we derive a bifurcated Wheeler-Dewitt-like equation. Einstein gravity, associated with λ being a certain fourfold degenerate eigenvalue of ρAB, is characterized by a vanishing center-of-mass momentum ∫ PA d3x = 0. Troublesome (ρ - λI)-1 is then replaced by regular M-1, such that M-1 (ρ - λI) defines a projection operator, modifying the Hamiltonian accordingly.

UR - http://www.scopus.com/inward/record.url?scp=0000407856&partnerID=8YFLogxK

U2 - 10.1142/S0217732398002321

DO - 10.1142/S0217732398002321

M3 - Article

AN - SCOPUS:0000407856

VL - 13

SP - 2187

EP - 2192

JO - Modern Physics Letters A

JF - Modern Physics Letters A

SN - 0217-7323

IS - 27

ER -