A 4d Lorentzian Spin Foam Model With Timelike Surfaces

[摘要] We construct a 4d Lorentzian spin foam model capable of describing both spacelike andtimelike surfaces. To do so we use a coherent state approach inspired by the RiemannianFK model. Using the coherent state method we reproduce the results of the EPRL modelfor Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. Thecoherent states of spacelike/timelike triangles are found to correspond to elements of thediscrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelikeand timelike surfaces is quantized. A path integral for the quantum theory is definedas a product of vertex amplitudes. The states corresponding to timelike triangles areconstructed in a basis diagonalised with respect to a noncompact generator. A derivationof the matrix elements of the generators of SL(2,C) in this basis is provided.

[发布机构] University of Waterloo

[效力级别] Spin Foam

[关键词] Quantum Gravity;Spin Foam;Physics