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PlanetPhysics/Quantum Gravity Programs 2

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Quantum Gravity Programs

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There are several distinct programs aimed at developing a quantum gravity theory. These include--but are not limited to-- the following.

  • The Penrose, twistors programme applied to an open curved space-time (ref. [1]), (which is presumably a globally hyperbolic, relativistic space-time). This may also include the idea of developing a `sheaf cohomology' for twistors (ref. \cite {Hawking and Penrose}) but still needs to justify the assumption in this approach of a charged, fundamental fermion of spin-3/2 of undefined mass and unitary `homogeneity' (which has not been observed so far);
  • The Weinberg, supergravity theory, which is consistent with supersymmetry and superalgebra, and utilizes graded Lie algebras and matter-coupled superfields in the presence of weak gravitational fields;
  • The programs of Hawking and Penrose [1]) in quantum cosmology, concerned with singularities, such as black and `white' holes; S. W. Hawking combines, joins, or `glues' an initially flat Euclidean metric with convex Lorentzian metrics in the expanding, and then contracting, space-times with a very small value of Einstein's cosmological `constant'. Such `Hawking', double-pear shaped, space-times also have an initial Weyl tensor value close to zero and, ultimately, a largely fluctuating Weyl tensor during the `final crunch' of our Universe, presumed to determine the irreversible arrow of time; furthermore, an observer will always be able to access through measurements only a limited part of the global space-times in our universe;
  • The TQFT/ approach that aims at finding the `topological' invariants of a manifold embedded in an abstract vector space related to the statistical mechanics problem of defining extensions of the partition function for many-particle quantum systems;
  • The string and superstring theories/M-theory that `live' in higher dimensional spaces (e.g., , preferred ), and can be considered to be topological representations of physical entities that vibrate, are quantized, interact, and that might also be able to 'predict' fundamental masses relevant to quantum 'particles';
  • The Baez `categorification' programme ([2], [3]) that aims to deal with quantum field and QG problems at the abstract level of categories and functors in what seems to be mostly a global approach;
  • The `monoidal category' and valuation approach initiated by Isham (ref. [4]) to the quantum measurement problem and its possible solution through local-to-global, finite constructions in small categories.

Most of the quantum gravity programs are consistent with the Big-Bang theory, or the theory of a rapidly expanding universe, although none `prove' the necessity of its existence. Several competing and conflicting theories were reported that deal with singularities in spacetime, such as black holes `without hair', evaporating black holes and naked singularities.

All Sources

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[2] [3] [5] [6] [7] [8] [9] [1] [10] [11] [12] [13] [14] [15] [16] [17]

References

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  1. ↑ 1.0 1.1 1.2 S. W. Hawking and R. Penrose. 2000. The Nature of Space and Time . Princeton and Oxford: Princeton University Press.
  2. ↑ 2.0 2.1 J. Baez. 2004. Quantum quandaries : a category theory perspective, in Structural Foundations of Quantum Gravity , (ed. S. French et al.) Oxford Univ. Press.
  3. ↑ 3.0 3.1 J. Baez. 2002. Categorified Gauge Theory. in Proceedings of the Pacific Northwest Geometry Seminar Cascade Topology Seminar,Spring Meeting--May 11 and 12, 2002. University of Washington, Seattle, WA.
  4. ↑ Cite error: Invalid <ref> tag; no text was provided for refs named Isham1
  5. ↑ I.C. Baianu, James Glazebrook, G. Georgescu and Ronald Brown. 2008."Generalized `Topos' Representations of Quantum Space--Time: Linking Quantum  --Valued Logics with Categories and Higher Dimensional Algebra.", (Preprint )
  6. ↑ J. Butterfield and C. J. Isham : A topos perspective on the Kochen--Specker theorem I - IV, Int. J. Theor. Phys , 37 (1998) No 11., 2669--2733 38 (1999) No 3., 827--859, 39 (2000) No 6., 1413--1436, 41 (2002) No 4., 613--639.
  7. ↑ J. Butterfield and C. J. Isham : Some possible roles for topos theory in quantum theory and quantum gravity, Foundations of Physics .
  8. ↑ F.M. Fernandez and E. A. Castro. 1996. (Lie) Algebraic Methods in Quantum Chemistry and Physics. , Boca Raton: CRC Press, Inc.
  9. ↑ Feynman, R. P., 1948, "Space--Time Approach to Non--Relativistic Quantum Mechanics", Reviews of Modern Physics , 20: 367--387. [It is reprinted in (Schwinger 1958).]
  10. ↑ R. J. Plymen and P. L. Robinson: Spinors in Hilbert Space. Cambridge Tracts in Math. 114 , \emph{Cambridge Univ. Press} 1994.
  11. ↑ I. Raptis : Algebraic quantisation of causal sets, \emph{Int. Jour. Theor. Phys.} 39 (2000), 1233.
  12. ↑ I. Raptis : Quantum space-time as a quantum causal set,  .
  13. ↑ J. E. Roberts : More lectures on algebraic quantum field theory (in A. Connes, et al. (Non--commutative Geometry ), Springer (2004).
  14. ↑ C. Rovelli : Loop quantum gravity (1997),  .
  15. ↑ Jan Smit. 2002. Quantum Field Theory on a Lattice .
  16. ↑ S. Weinberg.1995--2000. The Quantum Theory of Fields . Cambridge, New York and Madrid: Cambridge University Press, Vols. 1 to 3.
  17. ↑ Wess and Bagger. 2000. Supergravity. (Weinberg)
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