1,720,971 research outputs found
Spin-raising operators and spin-3/2 potentials in quantum cosmology
No full textLocal boundary conditions involving field strengths and the normal to the boundary,
originally studied in anti-de Sitter spacetime, have been recently considered in one-loop quanhun
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 caa only be imposed in a flat Euclidean background, for which the gauge freedom in
the choice of the potentials remains
Twistors in conformally flat Einstein four-manifolds
No full textThis 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
Twistors and spin-3/2 potentials in quantum gravity
No full textLocal 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-lowering and 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. Alternative boundary conditions for supergravity involving the spinor-valued 1-forms for gravitinos and the normal to the boundary are also studied
Boundary terms for massless fermionic fields
No full textLocal supersymmetry leads to boundary conditions
for fermionic fields in one-loop quantum cosmology involving
the Euclidean normal _{e}n_{A}^{; ; A'} to the boundary and a pair
of independent spinor fields psi^{A} and
{widetilde psi}^{A'}. This paper studies the corresponding
classical properties, i.e. the classical boundary-value problem
and boundary terms in the variational problem. If
sqrt{2} ; {_{e}n_{A}^{; ; A'}} ; psi^{A}
mp {widetilde psi}^{A'} equiv Phi^{A'} is set to zero
on a 3-sphere bounding flat Euclidean 4-space, the modes of the
massless spin-1/2 field multiplying harmonics having
positive eigenvalues for the intrinsic 3-dimensional Dirac operator
on S^{3} should vanish on S^{3}. Remarkably, this coincides with
the property of the classical boundary-value problem when spectral
boundary conditions are imposed on S^3 in the massless case.
Moreover, the boundary term in the action functional is proportional
to the integral on the boundary of Phi^{A'} ; {_{e}n_{AA'}}
; psi^{A}
1-loop effective action on the 4-ball
No full textThis paper applies zeta-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, the vacuum Maxwell theory is
studied and the contribution of all perturbative modes to zeta'(0)
is derived: transverse, longitudinal
and normal modes of the electromagnetic potential, jointly with ghost modes. The analysis is
performed by 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 zeta'(0)
resulting from longitudinal, normal and ghost modes
Noncovariant Gauges in Simple Supergravity
No full textA gauge-averaging functional of the axial type is studied for
simple supergravity at one loop about flat Euclidean four-space
bounded by a three-sphere, or two
concentric three-spheres. This is
a generalization of recent work on the axial gauge in quantum
supergravity on manifolds with boundary. Ghost modes obey
nonlocal boundary conditions of the spectral type, in that
half of them obey Dirichlet or Neumann conditions at the boundary.
In both cases, they give a vanishing contribution to the
one-loop divergence. The admissibility of noncovariant gauges
at the classical level is also proved
Lorenz gauge in quantum cosmology
No full textIn a path-integral approach to quantum cosmology, the Lorenz gauge-averaging term is studied for Euclidean Maxwell theory on a portion of flat four-space bounded by two concentric three-spheres, but with arbitrary values of the gauge parameter. The resulting set of eigenvalue equations for normal and longitudinal modes of the electromagnetic potential cannot be decoupled, and is here studied with a Green-function method. This means that an equivalent equation for longitudinal modes is obtained which has integro-differential nature, after inverting a differential operator in the original coupled system. A complete calculational scheme is therefore obtained for the one-loop semiclassical evaluation of the wave function of the universe in the presence of gauge fields. This might also lead to a better understanding of how gauge independence is actually achieved on manifolds with boundary, whose consideration cannot be avoided in a quantum theory ofthe universe
Euclidean Maxwell theory in the presence of boundaries. II
No full textzeta-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 flaf 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
Gravitons in one-loop quantum cosmology: correspondence between covariant and noncovariant formalisms
No full textThe discrepancy between the results of
covariant and noncovariant one-loop calculations for higher-spin
fields in quantum cosmology is analyzed.
A detailed mode-by-mode study of perturbative quantum gravity
about a flat Euclidean background bounded by two concentric
three-spheres, including nonphysical degrees of freedom and
ghost modes, leads to one-loop amplitudes in agreement with
the covariant Schwinger-DeWitt method. This calculation provides
the generalization of a previous analysis of fermionic fields
and electromagnetic fields at one-loop about flat Euclidean
backgrounds admitting a well-defined 3+1 decomposition
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