69,252 research outputs found

### The action of neutrino ponderomotive force on supernova dynamics

Collective interactions of a beam of neutrinos/antineutrinos traversing a
dense magnetized plasma of electrons/positrons, protons and neutrons are
studied with particular reference to the case of a Supernova. We find that the
ponderomotive force exerted by neutrinos gives, contrary to expectations, a
negligible contribution to the revival of the shock for a successful Supernova
explosion, although new types of convection and plasma cooling processes
induced by the ponderomotive force could be, in principle, relevant for the
dynamics itself.Comment: latex, 14 pages; numerical error corrected, conclusions changed; to
be published in Mod. Phys. Lett.

### Linear Form of Canonical Gravity

Recent work in the literature has shown that general relativity can be
formulated in terms of a jet bundle which, in local coordinates, has five
entries: local coordinates on Lorentzian space-time, tetrads, connection
one-forms, multivelocities corresponding to the tetrads and multivelocities
corresponding to the connection one-forms. The derivatives of the Lagrangian
with respect to the latter class of multivelocities give rise to a set of
multimomenta which naturally occur in the constraint equations. Interestingly,
all the constraint equations of general relativity are linear in terms of this
class of multimomenta. This construction has been then extended to complex
general relativity, where Lorentzian space-time is replaced by a
four-complex-dimensional complex-Riemannian manifold. One then finds a
holomorphic theory where the familiar constraint equations are replaced by a
set of equations linear in the holomorphic multimomenta, providing such
multimomenta vanish on a family of two-complex-dimensional surfaces. In quantum
gravity, the problem arises to quantize a real or a holomorphic theory on the
extended space where the multimomenta can be defined.Comment: 5 pages, plain-te

### Essential self-adjointness in one-loop quantum cosmology

The quantization of closed cosmologies makes it necessary to study squared
Dirac operators on closed intervals and the corresponding quantum amplitudes.
This paper proves self-adjointness of these second-order elliptic operators.Comment: 14 pages, plain Tex. An Erratum has been added to the end, which
corrects section

### Quantized Maxwell Theory in a Conformally Invariant Gauge

Maxwell theory can be studied in a gauge which is invariant under conformal
rescalings of the metric, and first proposed by Eastwood and Singer. This paper
studies the corresponding quantization in flat Euclidean 4-space. The resulting
ghost operator is a fourth-order elliptic operator, while the operator P on
perturbations of the potential is a sixth-order elliptic operator. The operator
P may be reduced to a second-order non-minimal operator if a dimensionless
gauge parameter tends to infinity. Gauge-invariant boundary conditions are
obtained by setting to zero at the boundary the whole set of perturbations of
the potential, jointly with ghost perturbations and their normal derivative.
This is made possible by the fourth-order nature of the ghost operator. An
analytic representation of the ghost basis functions is also obtained.Comment: 8 pages, plain Tex. In this revised version, the calculation of ghost
basis functions has been amended, and the presentation has been improve

### Majorana and the path-integral approach to Quantum Mechanics

We give, for the first time, the English translation of a manuscript by
Ettore Majorana, which probably corresponds to the text for a seminar delivered
at the University of Naples in 1938, where he lectured on Theoretical Physics.
Some passages reveal a physical interpretation of the Quantum Mechanics which
anticipates of several years the Feynman approach in terms of path integrals,
independently of the underlying mathematical formulation.Comment: revtex, 9 pages, 2 figures; a contribution in the centenary of the
birth of Ettore Majoran

### Quantization of Field Theories in the Presence of Boundaries

This paper reviews the progress made over the last five years in studying
boundary conditions and semiclassical properties of quantum fields about
4-real-dimensional Riemannian backgrounds. For massless spin-${1\over 2}$
fields one has a choice of spectral or supersymmetric boundary conditions, and
the corresponding conformal anomalies have been evaluated by using
zeta-function regularization. For Euclidean Maxwell theory in vacuum, the
mode-by-mode analysis of BRST-covariant Faddeev-Popov amplitudes has been
performed for relativistic and non-relativistic gauge conditions. For massless
spin-${3\over 2}$ fields, the contribution of physical degrees of freedom to
one-loop amplitudes, and the 2-spinor analysis of Dirac and Rarita-Schwinger
potentials, have been obtained. In linearized gravity, gauge modes and ghost
modes in the de Donder gauge have been studied in detail. This program may lead
to a deeper understanding of different quantization techniques for gauge fields
and gravitation, to a new vision of gauge invariance, and to new points of view
in twistor theory.Comment: 11 pages, plain-tex, to appear in Proceedings of the XI Italian
Conference on General Relativity and Gravitational Physics, Trieste (Italy),
September 26-30, 1994; 1995 World Scientific Publishing Compan

### Complex Parameters in Quantum Mechanics

The Schrodinger equation for stationary states in a central potential is
studied in an arbitrary number of spatial dimensions, say q. After
transformation into an equivalent equation, where the coefficient of the first
derivative vanishes, it is shown that in such equation the coefficient of the
second inverse power of r is an even function of a parameter, say lambda,
depending on a linear combination of q and of the angular momentum quantum
number, say l. Thus, the case of complex values of lambda, which is useful in
scattering theory, involves, in general, both a complex value of the parameter
originally viewed as the spatial dimension and complex values of the angular
momentum quantum number. The paper ends with a proof of the Levinson theorem in
an arbitrary number of spatial dimensions, when the potential includes a
non-local term which might be useful to understand the interaction between two
nucleons.Comment: 17 pages, plain Tex. The revised version is much longer, and section
5 is entirely ne

### A parametrix for quantum gravity?

In the sixties, DeWitt discovered that the advanced and retarded Green
functions of the wave operator on metric perturbations in the de Donder gauge
make it possible to define classical Poisson brackets on the space of
functionals that are invariant under the action of the full diffeomorphism
group of spacetime. He therefore tried to exploit this property to define
invariant commutators for the quantized gravitational field, but the operator
counterpart of such classical Poisson brackets turned out to be a hard task. On
the other hand, the mathematical literature studies often an approximate
inverse, the parametrix, which is, strictly, a distribution. We here suggest
that such a construction might be exploited in canonical quantum gravity. We
begin with the simplest case, i.e. fundamental solution and parametrix for the
linear, scalar wave operator; the next step are tensor wave equations, again
for linear theory, e.g. Maxwell theory in curved spacetime. Last, the nonlinear
Einstein equations are studied, relying upon the well-established
Choquet-Bruhat construction, according to which the fifth derivatives of
solutions of a nonlinear hyperbolic system solve a linear hyperbolic system.
The latter is solved by means of Kirchhoff-type formulas, while the former
fifth-order equations can be solved by means of well-established parametrix
techniques for elliptic operators. But then the metric components that solve
the vacuum Einstein equations can be obtained by convolution of such a
parametrix with Kirchhoff-type formulas. Some basic functional equations for
the parametrix are also obtained, that help in studying classical and quantum
version of the Jacobi identity.Comment: 27 page

### On the Green functions of gravitational radiation theory

Previous work in the literature has studied gravitational radiation in
black-hole collisions at the speed of light. In particular, it had been proved
that the perturbative field equations may all be reduced to equations in only
two independent variables, by virtue of a conformal symmetry at each order in
perturbation theory. The Green function for the perturbative field equations is
here analyzed by studying the corresponding second-order hyperbolic operator
with variable coefficients, instead of using the reduction method from the
retarded flat-space Green function in four dimensions. After reduction to
canonical form of this hyperbolic operator, the integral representation of the
solution in terms of the Riemann function is obtained. The Riemann function
solves a characteristic initial-value problem for which analytic formulae
leading to the numerical solution are derived.Comment: 15 pages, plain Tex. A misprint on the right-hand side of Eqs. (3.5)
and (3.6) has been amende

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