NONPERTURBATIVE 2D QUANTUM GRAVITY VIA SUPERSYMMETRIC STRING

1990 ◽  
Vol 05 (30) ◽  
pp. 2565-2572 ◽  
Author(s):  
MAREK KARLINER ◽  
SASHA MIGDAL
Keyword(s):  
Quantum Gravity ◽  
Ground State ◽  
Scaling Limit ◽  
Linear Ordinary Differential Equation ◽  
Third Order ◽  
Quantum Oscillations ◽  
The Third ◽  
Nonperturbative Solution ◽  
Distribution Of Eigenvalues ◽  
Double Scaling Limit

The Parisi-Marinari suggestion to treat 2d quantum gravity as ground state of the 1d supersymmetric string is elaborated in some detail. The third order linear ordinary differential equation describing in the double scaling limit the distribution of eigenvalues of the random matrix (i.e., the Liouville field) is derived and studied numerically. Unlike the Painlevé equation, our equation leads to continuous spectrum; however, the nonperturbative effects display themselves as quantum oscillations on top of smooth WKB distribution. Nonperturbative solution is free of any ambiguities.

Perturbation treatment of the Hartree–Fock equations for the ground states of the boron-like ions

1969 ◽  
Vol 47 (7) ◽  
pp. 699-705 ◽  
Author(s):  
C. S. Sharma ◽  
R. G. Wilson
Keyword(s):  
Ground State ◽  
Atomic System ◽  
Ground States ◽  
Great Accuracy ◽  
Second Order ◽  
Expectation Values ◽  
Third Order ◽  
First Order ◽  
Hartree Fock ◽  
The Third

The first-order Hartree–Fock and unrestricted Hartree–Fock equations for the ground state of a five electron atomic system are solved exactly. The solutions are used to evaluate the corresponding second-order energies exactly and the third-order energies with great accuracy. The first-order terms in the expectation values of 1/r, r, r2, and δ(r) are also calculated.

scholarly journals REGGE GRAVITY FROM SPINFOAMS

2013 ◽  
Vol 22 (02) ◽  
pp. 1350001 ◽  
Author(s):  
ELENA MAGLIARO ◽  
CLAUDIO PERINI
Keyword(s):  
Fine Structure ◽  
Quantum Gravity ◽  
Scaling Limit ◽  
Einstein Equations ◽  
Quantum Corrections ◽  
Semiclassical Regime ◽  
Double Scaling Limit

We consider spinfoam quantum gravity in the flipped limit, which is the double scaling limit γ → 0, j → ∞ with γj = const. , where γ is the Immirzi parameter, j is the spin and γj gives the physical area in Planck units. In this regime the amplitude for a 2-complex becomes effectively an integral over Regge-like metrics and seems to enforce Einstein equations in the semiclassical regime. The Immirzi parameter must be considered as dynamical in the sense that it runs to zero when the fine structure of the foam is averaged. In addition to quantum corrections which vanish for ℏ → 0, we find new corrections due to the discreteness of geometric spectra.

Random tensor models—the U(N)D-invariant model

2021 ◽  
pp. 178-208
Author(s):  
Adrian Tanasa
Keyword(s):  
Scaling Limit ◽  
Point Function ◽  
Invariant Model ◽  
Invariant Tensor ◽  
The Third ◽  
Tensor Models ◽  
Random Tensor ◽  
Combinatorial Methods ◽  
Double Scaling Limit ◽  
The Way

In the first section we give a briefly presentation of the U(N)D-invariant tensor models (N being again the size of the tensor, and D being the dimension). The next section is then dedicated to the analysis of the Dyson–Schwinger equations (DSE) in the large N limit. These results are essential to implement the double scaling limit mechanism of the DSEs, which is done in the third section. The main result of this chapter is the doubly-scaled 2-point function for a model with generic melonic interactions. However, several assumptions on the large N scaling of cumulants are made along the way. They are proved using various combinatorial methods.

On well-posedness of the third-order nonlinear Schrödinger equation with time-dependent coefficients

2015 ◽  
Vol 17 (04) ◽  
pp. 1450031 ◽  
Author(s):  
Xavier Carvajal ◽  
Mahendra Panthee ◽  
Marcia Scialom
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Scaling Limit ◽  
Nonlinear Schrodinger Equation ◽  
Time Dependent ◽  
Well Posedness ◽  
Third Order ◽  
Nonlinear Schrödinger ◽  
The Third

We consider the Cauchy problem associated to the third-order nonlinear Schrödinger equation with time-dependent coefficients. Depending on the nature of the coefficients, we prove local as well as global well-posedness results for given data in L2-based Sobolev spaces. We also address the scaling limit to fast dispersion management and prove that it converges in H1to the solution of the averaged equation.

Rotational Structure in the (2,0) Band of the C2 Δ3/2–X2 Π1/2 Subsystem of SbO

1974 ◽  
Vol 52 (7) ◽  
pp. 592-598 ◽  
Author(s):  
S. B. Rai ◽  
B. Rai ◽  
D. K. Rai
Keyword(s):  
Excited State ◽  
Ground State ◽  
Rotational Structure ◽  
Third Order ◽  
Rotational Constants ◽  
The Third ◽  
Concave Grating ◽  
Combining States

The rotational structure in (2,0) band of C2Δ3/2–X2Π1/2 subsystem of SbO molecule has been photographed in the third order of a 35 ft concave grating spectrograph, and the rotational constants of the two combining states have been determined. It is found that the new rotational constants for the ground state are in agreement with those reported by Rai et al., but the constants for the excited state differ appreciably from those reported earlier by Rao and Rao. A small λ-type doubling (≈4.0 × 10−6 cm−1) is observed in the excited state. The isotopic lines due to 123SbO have also been observed.

UNIVERSALITY OF THE MATRIX MODEL APPROACH TO TWO-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (15) ◽  
pp. 1387-1396
Author(s):  
FREDDY PERMANA ZEN
Keyword(s):  
Quantum Gravity ◽  
Matrix Model ◽  
Scaling Limit ◽  
Numerical Calculations ◽  
Two Dimensional ◽  
Coupled Equations ◽  
The Matrix ◽  
Pure Gravity ◽  
Double Scaling Limit ◽  
Model Approach

Universality with respect to triangulations is investigated in the Hermitian one-matrix model approach to 2-D quantum gravity for a potential containing both even and odd terms, [Formula: see text]. With the use of analytical and numerical calculations, I find that the universality holds and the model describes pure gravity, which leads in the double scaling limit to coupled equations of Painlevé type.

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