A 4d Lorentzian Spin Foam Model With Timelike Surfaces

Quantum Gravity;Spin Foam;Physics

Hnybida, Jeffrey

University of Waterloo

关键词: Quantum Gravity;    Spin Foam;    Physics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/5593/1/Hnybida_Jeffrey.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 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.