2,977 research outputs found
Solution to the ghost problem in fourth order derivative theories
We present a solution to the ghost problem in fourth order derivative
theories. In particular we study the Pais-Uhlenbeck fourth order oscillator
model, a model which serves as a prototype for theories which are based on
second plus fourth order derivative actions. Via a Dirac constraint method
quantization we construct the appropriate quantum-mechanical Hamiltonian and
Hilbert space for the system. We find that while the second-quantized Fock
space of the general Pais-Uhlenbeck model does indeed contain the negative norm
energy eigenstates which are characteristic of higher derivative theories, in
the limit in which we switch off the second order action, such ghost states are
found to move off shell, with the spectrum of asymptotic in and out S-matrix
states of the pure fourth order theory which results being found to be
completely devoid of states with either negative energy or negative norm. We
confirm these results by quantizing the Pais-Uhlenbeck theory via path
integration and by constructing the associated first-quantized wave mechanics,
and show that the disappearance of the would-be ghosts from the energy
eigenspectrum in the pure fourth order limit is required by a hidden symmetry
that the pure fourth order theory is unexpectedly found to possess. The
occurrence of on-shell ghosts is thus seen not to be a shortcoming of pure
fourth order theories per se, but rather to be one which only arises when
fourth and second order theories are coupled to each other.Comment: 36 pages, revtex. Prepared for the proceedings of the 2006 Biennial
Meeting of the International Association for Relativistic Dynamics Version 2
contains an expanded discussion of the path integral quantization of the
Pais-Uhlenbeck fourth order oscillator theor
Completeness of non-normalizable modes
We establish the completeness of some characteristic sets of non-normalizable
modes by constructing fully localized square steps out of them, with each such
construction expressly displaying the Gibbs phenomenon associated with trying
to use a complete basis of modes to fit functions with discontinuous edges. As
well as being of interest in and of itself, our study is also of interest to
the recently introduced large extra dimension brane-localized gravity program
of Randall and Sundrum, since the particular non-normalizable mode bases that
we consider (specifically the irregular Bessel functions and the associated
Legendre functions of the second kind) are associated with the tensor
gravitational fluctuations which occur in those specific brane worlds in which
the embedding of a maximally four-symmetric brane in a five-dimensional anti-de
Sitter bulk leads to a warp factor which is divergent. Since the brane-world
massless four-dimensional graviton has a divergent wave function in these
particular cases, its resulting lack of normalizability is thus not seen to be
any impediment to its belonging to a complete basis of modes, and consequently
its lack of normalizability should not be seen as a criterion for not including
it in the spectrum of observable modes. Moreover, because the divergent modes
we consider form complete bases, we can even construct propagators out of them
in which these modes appear as poles with residues which are expressly finite.
Thus even though normalizable modes appear in propagators with residues which
are given as their finite normalization constants, non-normalizable modes can
just as equally appear in propagators with finite residues too -- it is just
that such residues will not be associated with bilinear integrals of the modes.Comment: 34 pages, 6 figures. Revte
Local and global gravity
Our long experience with Newtonian potentials has inured us to the view that
gravity only produces local effects. In this paper we challenge this quite
deeply ingrained notion and explicitly identify some intrinsically global
gravitational effects. In particular we show that the global cosmological
Hubble flow can actually modify the motions of stars and gas within individual
galaxies, and even do so in a way which can apparently eliminate the need for
galactic dark matter. Also we show that a classical light wave acquires an
observable, global, path dependent phase in traversing a gravitational field.
Both of these effects serve to underscore the intrinsic difference between
non-relativistic and relativistic gravity.Comment: LaTeX, 20 pages plus three figures in two postscript files. To appear
in a special issue of Foundations of Physics honoring Professor Lawrence
Horwitz on the occasion of his 65th birthday; A. van der Merwe and S. Raby,
Editors, Plenum Publishing Company, N.Y., 199
Implications of Cosmic Repulsion for Gravitational Theory
In this paper we present a general, model independent analysis of a recently
detected apparent cosmic repulsion, and discuss its potential implications for
gravitational theory. In particular, we show that a negatively spatially curved
universe acts like a diverging refractive medium, to thus naturally cause
galaxies to accelerate away from each other. Additionally, we show that it is
possible for a cosmic acceleration to only be temporary, with some accelerating
universes actually being able to subsequently recontract.Comment: RevTeX, 13 page
Comprehensive Solution to the Cosmological Constant, Zero-Point Energy, and Quantum Gravity Problems
We present a solution to the cosmological constant, the zero-point energy,
and the quantum gravity problems within a single comprehensive framework. We
show that in quantum theories of gravity in which the zero-point energy density
of the gravitational field is well-defined, the cosmological constant and
zero-point energy problems solve each other by mutual cancellation between the
cosmological constant and the matter and gravitational field zero-point energy
densities. Because of this cancellation, regulation of the matter field
zero-point energy density is not needed, and thus does not cause any trace
anomaly to arise. We exhibit our results in two theories of gravity that are
well-defined quantum-mechanically. Both of these theories are locally conformal
invariant, quantum Einstein gravity in two dimensions and Weyl-tensor-based
quantum conformal gravity in four dimensions (a fourth-order derivative quantum
theory of the type that Bender and Mannheim have recently shown to be
ghost-free and unitary). Central to our approach is the requirement that any
and all departures of the geometry from Minkowski are to be brought about by
quantum mechanics alone. Consequently, there have to be no fundamental
classical fields, and all mass scales have to be generated by dynamical
condensates. In such a situation the trace of the matter field energy-momentum
tensor is zero, a constraint that obliges its cosmological constant and
zero-point contributions to cancel each other identically, no matter how large
they might be. Quantization of the gravitational field is caused by its
coupling to quantized matter fields, with the gravitational field not needing
any independent quantization of its own. With there being no a priori classical
curvature, one does not have to make it compatible with quantization.Comment: Final version, to appear in General Relativity and Gravitation (the
final publication is available at http://www.springerlink.com). 58 pages,
revtex4, some additions to text and some added reference
Light deflection in Weyl gravity: critical distances for photon paths
The Weyl gravity appears to be a very peculiar theory. The contribution of
the Weyl linear parameter to the effective geodesic potential is opposite for
massive and nonmassive geodesics. However, photon geodesics do not depend on
the unknown conformal factor, unlike massive geodesics. Hence light deflection
offers an interesting test of the Weyl theory.
In order to investigate light deflection in the setting of Weyl gravity, we
first distinguish between a weak field and a strong field approximation.
Indeed, the Weyl gravity does not turn off asymptotically and becomes even
stronger at larger distances.
We then take full advantage of the conformal invariance of the photon
effective potential to provide the key radial distances in Weyl gravity.
According to those, we analyze the weak and strong field regime for light
deflection. We further show some amazing features of the Weyl theory in the
strong regime.Comment: 20 pages, 9 figures (see published version for a better resolution,
or online version at stacks.iop.org/CQG/21/1897
Open Questions in Classical Gravity
We discuss some outstanding open questions regarding the validity and
uniqueness of the standard second order Newton-Einstein classical gravitational
theory. On the observational side we discuss the degree to which the realm of
validity of Newton's Law of Gravity can actually be extended to distances much
larger than the solar system distance scales on which the law was originally
established. On the theoretical side we identify some commonly accepted but
actually still open to question assumptions which go into the formulating of
the standard second order Einstein theory in the first place. In particular, we
show that while the familiar second order Poisson gravitational equation (and
accordingly its second order covariant Einstein generalization) may be
sufficient to yield Newton's Law of Gravity they are not in fact necessary. The
standard theory thus still awaits the identification of some principle which
would then make it necessary too. We show that current observational
information does not exclusively mandate the standard theory, and that the
conformal invariant fourth order theory of gravity considered recently by
Mannheim and Kazanas is also able to meet the constraints of data, and in fact
to do so without the need for any so far unobserved non-luminous or dark
matter.Comment: UCONN-93-1, plain TeX format, 22 pages (plus 7 figures - send
requests to [email protected]). To appear in a special issue of
Foundations of Physics honoring Professor Fritz Rohrlich on the occasion of
his retirement, L. P. Horwitz and A. van der Merwe Editors, Plenum Publishing
Company, N.Y., Fall 199
On photohadronic processes in astrophysical environments
We discuss the first applications of our newly developed Monte Carlo event
generator SOPHIA to multiparticle photoproduction of relativistic protons with
thermal and power law radiation fields. The measured total cross section is
reproduced in terms of excitation and decay of baryon resonances, direct pion
production, diffractive scattering, and non-diffractive multiparticle
production. Non--diffractive multiparticle production is described using a
string fragmentation model. We demonstrate that the widely used
`--approximation' for the photoproduction cross section is reasonable
only for a restricted set of astrophysical applications. The relevance of this
result for cosmic ray propagation through the microwave background and hadronic
models of active galactic nuclei and gamma-ray bursts is briefly discussed.Comment: 9 pages including 4 embedded figures, submitted to PAS
Dirac Quantization of the Pais-Uhlenbeck Fourth Order Oscillator
As a model, the Pais-Uhlenbeck fourth order oscillator with equation of
motion
is a quantum-mechanical prototype of a field theory containing both second and
fourth order derivative terms. With its dynamical degrees of freedom obeying
constraints due to the presence of higher order time derivatives, the model
cannot be quantized canonically. We thus quantize it using the method of Dirac
constraints to construct the correct quantum-mechanical Hamiltonian for the
system, and find that the Hamiltonian diagonalizes in the positive and negative
norm states that are characteristic of higher derivative field theories.
However, we also find that the oscillator commutation relations become singular
in the limit, a limit which corresponds to a prototype
of a pure fourth order theory. Thus the particle content of the theory cannot be inferred from that of the
theory; and in fact in the limit we find that all of
the negative norm states move off shell, with the
spectrum of asymptotic in and out states of the equal frequency theory being
found to be completely devoid of states with either negative energy or negative
norm. As a byproduct of our work we find a Pais-Uhlenbeck analog of the zero
energy theorem of Boulware, Horowitz and Strominger, and show how in the equal
frequency Pais-Uhlenbeck theory the theorem can be transformed into a positive
energy theorem instead.Comment: RevTeX4, 20 pages. Final version, to appear in Phys. Rev.
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