26 research outputs found
Twistors in conformally flat Einstein four-manifolds
This paper studies the two-component spinor form of massive spin-3/2 potentials in conformally flat Einstein four-manifolds. Following earlier work in the literature, a non-vanishing cosmological constant makes it necessary to introduce a supercovariant derivative operator. The analysis of supergauge transformations of primary and secondary potentials for spin 3/2 shows that the gauge freedom for massive spin-3/2 potentials is generated by solutions of the supertwistor equations. The supercovariant form of a partial connection on a non-linear bundle is then obtained, and the basic equation of massive secondary potentials is shown to be the integrability condition on super beta-surfaces of a differential operator on a vector bundle of rank three. Moreover, in the presence of boundaries, a simple algebraic relation among some spinor fields is found to ensure the gauge invariance of locally supersymmetric boundary conditions relevant for quantum cosmology and supergravity
Rarita-Schwinger Potentials in Quantum Cosmology
This paper studies the two-spinor form of the Rarita-Schwinger potentials
subject to local boundary conditions compatible with local supersymmetry. The
massless Rarita-Schwinger field equations are studied in four-real-dimensional
Riemannian backgrounds with boundary. Gauge transformations on the potentials
are shown to be compatible with the field equations providing the background is
Ricci-flat, in agreement with previous results in the literature. However, the
preservation of boundary conditions under such gauge transformations leads to a
restriction of the gauge freedom. The recent construction by Penrose of
secondary potentials which supplement the Rarita-Schwinger potentials is then
applied. The equations for the secondary potentials, jointly with the boundary
conditions, imply that the background four-geometry is further restricted to be
totally flat.Comment: 23 pages, plain TeX, no figures. The paper has been completely
revise
Quantum Fluctuations in Open Pre-Big Bang Cosmology
We solve exactly the (linear order) equations for tensor and scalar
perturbations over the homogeneous, isotropic, open pre-big bang model recently
discussed by several authors. We find that the parametric amplification of
vacuum fluctuations (i.e. particle production) remains negligible throughout
the perturbative pre-big bang phase.Comment: 12 pages, ReVTeX, Discussion of relation to Ref.[8] modifie
Spin-3/2 potentials in backgrounds with boundary
This paper studies the two-spinor form of the Rarita-Schwinger potentials subject to local boundary conditions compatible with local supersymmetry. The massless Rarita-Schwinger field equations are studied in four-real-dimensional Riemannian backgrounds with boundary. Gauge transformations on the potentials are shown to be compatible with the field equations providing the background is Ricci-flat, in agreement with previous results in the literature. However, the preservation of boundary conditions under such gauge transformations leads to a restriction of the gauge freedom. The recent construction by Penrose of secondary potentials which supplement the Rarita-Schwinger potentials is then applied. The equations for the secondary potentials, jointly with the boundary conditions, imply that the background four-geometry is further restricted to be totally flat. The analysis of other gauge transformations confirms that, in the massless case, the only admissible class of Riemannian backgrounds with boundary is totally flat
Euclidean Maxwell Theory in the Presence of Boundaries. II
Zeta-function regularization is applied to complete a recent analysis of the
quantized electromagnetic field in the presence of boundaries. The quantum
theory is studied by setting to zero on the boundary the magnetic field, the
gauge-averaging functional and hence the Faddeev-Popov ghost field. Electric
boundary conditions are also studied. On considering two gauge functionals
which involve covariant derivatives of the 4-vector potential, a series of
detailed calculations shows that, in the case of flat Euclidean 4-space bounded
by two concentric 3-spheres, one-loop quantum amplitudes are gauge independent
and their mode-by-mode evaluation agrees with the covariant formulae for such
amplitudes and coincides for magnetic or electric boundary conditions. By
contrast, if a single 3-sphere boundary is studied, one finds some
inconsistencies, i.e. gauge dependence of the amplitudes.Comment: 24 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, pages 2939-2950, December 1994. The authors apologize for
the delay in circulating the file, due to technical problems now fixe
Pre-Big Bang Cosmology and Quantum Fluctuations
The quantum fluctuations of a homogeneous, isotropic, open pre-big bang model
are discussed. By solving exactly the equations for tensor and scalar
perturbations we find that particle production is negligible during the
perturbative Pre-Big Bang phase.Comment: 4 pages, use esprc2.sty. Talk given at the 3rd Meeting on Constrained
Dynamics and Quantum Gravity (QG 99), Villasimius, Sardinia, Italy, 14-18 Sep
199
One-Loop Effective Action on the Four-Ball
This paper applies -function regularization to evaluate the 1-loop
effective action for scalar field theories and Euclidean Maxwell theory in the
presence of boundaries. After a comparison of two techniques developed in the
recent literature, vacuum Maxwell theory is studied and the contribution of all
perturbative modes to is derived: transverse, longitudinal and
normal modes of the electromagnetic potential, jointly with ghost modes. The
analysis is performed on imposing magnetic boundary conditions, when the
Faddeev-Popov Euclidean action contains the particular gauge-averaging term
which leads to a complete decoupling of all perturbative modes. It is shown
that there is no cancellation of the contributions to resulting
from longitudinal, normal and ghost modes.Comment: 25 pages, plain Te
Spin-Raising Operators and Spin-3/2 Potentials in Quantum Cosmology
Local boundary conditions involving field strengths and the normal to the
boundary, originally studied in anti-de Sitter space-time, have been recently
considered in one-loop quantum cosmology. This paper derives the conditions
under which spin-raising operators preserve these local boundary conditions on
a 3-sphere for fields of spin 0,1/2,1,3/2 and 2. Moreover, the two-component
spinor analysis of the four potentials of the totally symmetric and independent
field strengths for spin 3/2 is applied to the case of a 3-sphere boundary. It
is shown that such boundary conditions can only be imposed in a flat Euclidean
background, for which the gauge freedom in the choice of the potentials
remains.Comment: 13 pages, plain-tex, recently appearing in Classical and Quantum
Gravity, volume 11, April 1994, pages 897-903. Apologies for the delay in
circulating the file, due to technical problems now fixe