Two-dimensional quantum dilaton gravity and the quantum cosmological constant

Quantum gravity and the cosmological constant: Lessons from two-dimensional dilaton gravity

“…This choice is not the most intuitive but it has the advantage of providing us with complete control on the single coefficients of each field, so that specific quantum states are easily selected for the purpose of a spectrum analysis 7 . 6 We refer to [5,7] for details. 7 In the simple example of two decoupled systems, A and B, with an Hilbert space basis |n and |m respectively, the easiest way to write a general state has the form |ψg = n,m ψ(n, m)|n |m .…”

“…6 We refer to [5,7] for details. 7 In the simple example of two decoupled systems, A and B, with an Hilbert space basis |n and |m respectively, the easiest way to write a general state has the form |ψg = n,m ψ(n, m)|n |m . Considering factorized states |ψ f (a, b) = n a(n)|n ⊗ m b(m)|m , a sum over different sets of coefficients {a, b} reproduces the general state given the identification ψ(n, m) = a,b a(n)b(m), as in a series expansion.…”

“…The integrals are all Gaussian in the z's, since |ψ| 2 carries a Gaussian factor for each mode. In a generalization of the formulas contained in [7] we can write the quantum constraints (22) as:…”

“…Most of the technical results are contained in [5][6][7]. This paper is organized as follows: in Section II we present a general mechanism that can determine the cosmological constant in a quantum theory of gravity.…”

“…It is interesting to note that such a cancellation occurs only in the presence of a Maxwell field. As discussed in[5,7], if the Maxwell field is not present at the classical level there is no Liouville potential of the Y field. Therefore there is no need to fix a quantum correction to the coupling constant in the Y sector, while quantum corrections to ξ are still allowed.…”