Anti-deSitter Space and Confinement

Stability at a local maximum in higher dimensional anti-deSitter space and applications to supergravity

Annals of Physics ◽

10.1016/0003-4916(85)90150-2 ◽

1985 ◽

Vol 160 (2) ◽

pp. 406-419 ◽

Cited By ~ 126

Author(s):

L Mezincescu ◽

P.K Townsend

Keyword(s):

Local Maximum ◽

Higher Dimensional ◽

Desitter Space

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Protecting the Conformal Symmetry via Bulk Renormalization on Anti deSitter Space

Communications in Mathematical Physics ◽

10.1007/s00220-011-1311-0 ◽

2011 ◽

Vol 307 (2) ◽

pp. 315-350 ◽

Cited By ~ 1

Author(s):

Michael Dütsch ◽

Karl-Henning Rehren

Keyword(s):

Conformal Symmetry ◽

Desitter Space

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deSitter space-time and rotation

Pramana ◽

10.1007/bf02847227 ◽

1985 ◽

Vol 25 (5) ◽

pp. 513-518 ◽

Cited By ~ 2

Author(s):

P C Vaidya

Keyword(s):

Space Time ◽

Desitter Space

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Coupling of quantum gravitational field with Riemann and Ricci curvature tensors

The European Physical Journal C ◽

10.1140/epjc/s10052-021-09343-x ◽

2021 ◽

Vol 81 (6) ◽

Author(s):

Claudio Cremaschini ◽

Massimo Tessarotto

Keyword(s):

Gravitational Field ◽

Harmonic Oscillator ◽

Variational Principles ◽

Theoretical Problem ◽

Mathematical Framework ◽

Variational Theory ◽

Field Equations ◽

Covariant Quantum ◽

Desitter Space ◽

Curvature Tensors

AbstractThe theoretical problem of establishing the coupling properties existing between the classical and quantum gravitational field with the Ricci and Riemann curvature tensors of General Relativity is addressed. The mathematical framework is provided by synchronous Hamilton variational principles and the validity of classical and quantum canonical Hamiltonian structures for the gravitational field dynamics. It is shown that, for the classical variational theory, manifestly-covariant Hamiltonian functions expressed by either the Ricci or Riemann tensors are both admitted, which yield the correct form of Einstein field equations. On the other hand, the corresponding realization of manifestly-covariant quantum gravity theories is not equivalent. The requirement imposed is that the Hamiltonian potential should represent a positive-definite quadratic form when performing a quadratic expansion around the equilibrium solution. This condition in fact warrants the existence of positive eigenvalues of the quantum Hamiltonian in the harmonic-oscillator representation, to be related to the graviton mass. Accordingly, it is shown that in the background of the deSitter space-time, only the Ricci tensor coupling is physically admitted. In contrast, the coupling of quantum gravitational field with the Riemann tensor generally prevents the possibility of achieving a Hamiltonian potential appropriate for the implementation of the quantum harmonic-oscillator solution.

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