YITP-96-41 gr-qc/9609052 Partition Function for (2+1)-Dimensional Einstein Gravity
نویسنده
چکیده
Taking (2+1)-dimensional pure Einstein gravity for arbitrary genus g 1 as a model, we investigate the relation between the partition function formally de ned on the entire phase space and the one written in terms of the reduced phase space. The case of g = 1 (torus) is analyzed in detail and it provides us with good lessons for quantum cosmology. We formulate the gaugexing conditions in a form suitable for our purpose. Then the gaugexing procedure is applied to the partition function Z for (2+1)-dimensional gravity, formally de ned on the entire phase space. We show that basically it reduces to a partition function de ned for the reduced system, whose dynamical variables are ( ; pA). [Here the 's are the Teichm uller parameters, and the pA's are their conjugate momenta.] As for the case of g = 1, we nd out that Z is also related with another reduced form, whose dynamical variables are not only ( ; pA), but also (V; ). [Here is a conjugate momentum to the 2-volume (area) V of a spatial section.] A nontrivial factor appears in the measure in terms of this type of reduced form. This factor is understood as a FaddeevPopov determinant associated with the time-reparameterization invariance inherent in this type of formulation. In this manner, the relation between two reduced formulations becomes transparent in the context of quantum theory. As another result for the case of g = 1, one factor originating from the zero-modes of a di erential operator P1 can appear in the path-integral measure in the reduced representation of Z. It depends on how to de ne the path-integral domain for the shift vectors Na in Z: If it is de ned to include kerP1, the nontrivial factor does not appear. On the other hand,
منابع مشابه
General Solutions for Field Equations in Einstein and High Dimensional Gravity
We prove that the Einstein equations can be solved in general form, for any spacetime dimension and various types of energy–momentum tensors following the anholonomic frame method for constructing exact solutions in gravity. In this work, we give proofs and extend to higher dimensions the results for four and five dimensional spacetimes provided in arXiv: 0909.3949 [gr-qc], version 1.
متن کاملar X iv : g r - qc / 9 50 20 02 v 1 1 F eb 1 99 5 YITP / U - 95 - 2 Density fluctuations in Brans - Dicke inflation ∗
Spectrum of density perturbations in the Universe generated from quantumgravitational fluctuations in slow-roll-over inflationary scenarios with the Brans-Dicke gravity is calculated. It is shown that after inflation the isocurvature mode of perturbations may be neglected as compared to the adiabatic mode, and that an amplitude of the latter mode is not significantly different from that in the ...
متن کامل- qc / 0 60 20 10 v 1 2 F eb 2 00 6 Group field theory formulation of 3 d quantum gravity coupled to matter fields
We present a new group field theory describing 3d Riemannian quantum gravity coupled to matter fields for any choice of spin and mass. The perturbative expansion of the partition function produces fat graphs colored with SU(2) algebraic data, from which one can reconstruct at once a 3-dimensional simplicial complex representing spacetime and its geometry, like in the Ponzano-Regge formulation o...
متن کاملUMDGR 96-47, gr-qc/9511022 Multi-Black-Hole Geometries in (2+1)-Dimensional Gravity
Generalizations of the Black Hole geometry of Ba~ nados, Teitelboim and Zanelli (BTZ) are presented. The theory is three-dimensional vacuum Einstein theory with a negative cosmological constant. The n-black-hole solution has n asymptotically anti-de Sitter \exterior" regions that join in one \interior" region. The geometry of each exterior region is identical to that of a BTZ geometry; in parti...
متن کاملar X iv : g r - qc / 0 61 11 00 v 1 1 9 N ov 2 00 6 What is ( not ) wrong with scalar gravity ?
On his way to General Relativity (GR) Einstein gave several arguments as to why a special relativistic theory of gravity based on a massless scalar field could be ruled out merely on grounds of theoretical considerations. We re-investigate his two main arguments, which relate to energy conservation and some form of the principle of the universality of free fall. We find that such a theory-based...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996