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Further Explorations in SQC N = 1 SUGRA

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Quantum Cosmology - The Supersymmetric Perspective - Vol. 2

Part of the book series: Lecture Notes in Physics ((LNP,volume 804))

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Abstract

In Chap. 5 of Vol. I, we discussed the basic framework and associated results from the methodology followed there (see [1] and also [2,3,4]). Recall that this uses the reduction of canonical quantum N = 1 SUGRA in four spacetime dimensions (see Sects. 4.1 and 4.2 of Vol. I) to a cosmological minisuperspace, with the essential feature that all momenta are represented by differential operators of the canonical conjugate variables [5–7].

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Notes

  1. 1.

    Extrapolating to higher orders, this situation seems to go through without any formal modifications.

  2. 2.

    It was shown in [27] for the case of the gauge group SO(3) \(\sim\) SU(2) that invariance under homogeneity and isotropy as well as gauge transformations require all components of \(\phi\) to be zero. Only for SO(N), \(N>3\), can we have \(\phi\) = (0,0,0, \(\phi_1,\ldots, \phi_{N-3}\)).

  3. 3.

    \(X^a\) ia the Killing vector of the associated Kähler geometry.

  4. 4.

    It is interesting to note that, for the \(\chi,\overline \chi\) fields, no powers of h seem to be needed to establish the equations for the coefficients in \(\varPsi\).

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  1. Depto. Fisica Rua Marquês d’Avila e Bolama, Universidade da Beira Interior, 6200-307, Covilhã, Portugal

    Paulo Vargas Moniz

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Moniz, P.V. (2010). Further Explorations in SQC N = 1 SUGRA. In: Quantum Cosmology - The Supersymmetric Perspective - Vol. 2. Lecture Notes in Physics, vol 804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11570-7_5

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