1,603 research outputs found
Quantum Gravity in Large Dimensions
Quantum gravity is investigated in the limit of a large number of space-time
dimensions, using as an ultraviolet regularization the simplicial lattice path
integral formulation. In the weak field limit the appropriate expansion
parameter is determined to be . For the case of a simplicial lattice dual
to a hypercube, the critical point is found at (with ) separating a weak coupling from a strong coupling phase, and with degenerate zero modes at . The strong coupling, large , phase is
then investigated by analyzing the general structure of the strong coupling
expansion in the large limit. Dominant contributions to the curvature
correlation functions are described by large closed random polygonal surfaces,
for which excluded volume effects can be neglected at large , and whose
geometry we argue can be approximated by unconstrained random surfaces in this
limit. In large dimensions the gravitational correlation length is then found
to behave as , implying for the universal
gravitational critical exponent the value at .Comment: 47 pages, 2 figure
Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
We show how Feynman amplitudes of standard QFT on flat and homogeneous space
can naturally be recast as the evaluation of observables for a specific spin
foam model, which provides dynamics for the background geometry. We identify
the symmetries of this Feynman graph spin foam model and give the gauge-fixing
prescriptions. We also show that the gauge-fixed partition function is
invariant under Pachner moves of the triangulation, and thus defines an
invariant of four-dimensional manifolds. Finally, we investigate the algebraic
structure of the model, and discuss its relation with a quantization of 4d
gravity in the limit where the Newton constant goes to zero.Comment: 28 pages (RevTeX4), 7 figures, references adde
Graviton propagator in loop quantum gravity
We compute some components of the graviton propagator in loop quantum
gravity, using the spinfoam formalism, up to some second order terms in the
expansion parameter.Comment: 41 pages, 6 figure
Recognizing Graph Theoretic Properties with Polynomial Ideals
Many hard combinatorial problems can be modeled by a system of polynomial
equations. N. Alon coined the term polynomial method to describe the use of
nonlinear polynomials when solving combinatorial problems. We continue the
exploration of the polynomial method and show how the algorithmic theory of
polynomial ideals can be used to detect k-colorability, unique Hamiltonicity,
and automorphism rigidity of graphs. Our techniques are diverse and involve
Nullstellensatz certificates, linear algebra over finite fields, Groebner
bases, toric algebra, convex programming, and real algebraic geometry.Comment: 20 pages, 3 figure
- …