quantum gravity programs
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. [8]), (which is presumably a globally hyperbolic, relativistic space-time). This may also include the idea of developing a `sheaf cohomology' for twistors (ref. [8]) 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 [8]) 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 ([1], [2]) 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. []) 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.
- 1
-
J. Baez. 2004. Quantum quandaries : a category theory perspective, in Structural Foundations of Quantum Gravity, (ed. S. French et al.) Oxford Univ. Press.
- 2
-
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.
- 3
-
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)
- 4
-
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.
- 5
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J. Butterfield and C. J. Isham : Some possible roles for topos theory in quantum theory and quantum gravity, Foundations of Physics.
- 6
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F.M. Fernandez and E. A. Castro. 1996. (Lie) Algebraic Methods in Quantum Chemistry and Physics., Boca Raton: CRC Press, Inc.
- 7
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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).]
- 8
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S. W. Hawking and R. Penrose. 2000. The Nature of Space and Time. Princeton and Oxford: Princeton University Press.
- 9
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R. J. Plymen and P. L. Robinson: Spinors in Hilbert Space.
Cambridge Tracts in Math. 114, Cambridge
Univ. Press 1994.
- 10
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I. Raptis : Algebraic quantisation of causal sets, Int.
Jour. Theor. Phys. 39 (2000), 1233.
- 11
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I. Raptis : Quantum space-time as a quantum causal set,
.
- 12
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J. E. Roberts : More lectures on algebraic quantum field theory
(in A. Connes, et al. (Non-commutative Geometry), Springer (2004).
- 13
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C. Rovelli : Loop quantum gravity (1997),
.
- 14
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Jan Smit. 2002. Quantum Field Theory on a Lattice.
- 15
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S. Weinberg.1995-2000. The Quantum Theory of Fields. Cambridge, New York and Madrid: Cambridge University Press, Vols. 1 to 3.
- 16
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Wess and Bagger. 2000. Supergravity. (Weinberg)
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