Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userHamiltonian solutions of the 3-body problem in (2+1)-gravity
197
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We present a full study of the 3-body problem in gravity in flat (2+1)-dimensional space-time, and in the nonrelativistic limit of small velocities. We provide an explicit form of the ADM Hamiltonian in a regular coordinate system and we set up all the ingredients for canonical quantization. We emphasize the role of a U(2) symmetry under which the Hamiltonian is invariant and which should generalize to a U(N-1) symmetry for N bodies. This symmetry seems to stem from a braid group structure in the operations of looping of particles around each other, and guarantees the single-valuedness of the Hamiltonian. Its role for the construction of single-valued energy eigenfunctions is also discussed.
rate research
Read More
In this paper we consider 2+1-dimensional gravity coupled to N point-particles. We introduce a gauge in which the $z$- and $bar{z}$-components of the dreibein field become holomorphic and anti-holomorphic respectively. As a result we can restrict ourselves to the complex plane. Next we show that solving the dreibein-field: $e^a_z(z)$ is equivalent to solving the Riemann-Hilbert problem for the group $SO(2,1)$. We give the explicit solution for 2 particles in terms of hypergeometric functions. In the N-particle case we give a representation in terms of conformal field theory. The dreibeins are expressed as correlators of 2 free fermion fields and twistoperators at the position of the particles.
We study quantum corrections to projectable Horava gravity with $z = 2$ scaling in 2+1 dimensions. Using the background field method, we utilize a non-singular gauge to compute the anomalous dimension of the cosmological constant at one loop, in a normalization adapted to the spatial curvature term.
We consider a point particle coupled to 2+1 gravity, with de Sitter gauge group SO(3,1). We observe that there are two contraction limits of the gauge group: one resulting in the Poincare group, and the second with the gauge group having the form AN(2) ltimes an(2)^*. The former case was thoroughly discussed in the literature, while the latter leads to the deformed particle action with de Sitter momentum space, like in the case of kappa-Poincare particle. However, the construction forces the mass shell constraint to have the form p_0^2 = m^2, so that the effective particle action describes the deformed Carroll particle.
In this note we study the $1+1$ dimensional Jackiw-Teitelboim gravity in Lorentzian signature, explicitly constructing the gauge-invariant classical phase space and the quantum Hilbert space and Hamiltonian. We also semiclassically compute the Hartle-Hawking wave function in two different bases of this Hilbert space. We then use these results to illustrate the gravitational version of the factorization problem of AdS/CFT: the Hilbert space of the two-boundary system tensor-factorizes on the CFT side, which appears to be in tension with the existence of gauge constraints in the bulk. In this model the tension is acute: we argue that JT gravity is a sensible quantum theory, based on a well-defined Lorentzian bulk path integral, which has no CFT dual. In bulk language, it has wormholes but it does not have black hole microstates. It does however give some hint as to what could be added to to rectify these issues, and we give an example of how this works using the SYK model. Finally we suggest that similar comments should apply to pure Einstein gravity in $2+1$ dimensions, which wed then conclude also cannot have a CFT dual, consistent with the results of Maloney and Witten.
We present a canonical formulation of gravity theories whose Lagrangian is an arbitrary function of the Riemann tensor. Our approach allows a unified treatment of various subcases and an easy identification of the degrees of freedom of the theory.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
