80,145 research outputs found

### On the Fixed-Point Structure of Scalar Fields

In a recent Letter (K.Halpern and K.Huang, Phys. Rev. Lett. 74 (1995) 3526),
certain properties of the Local Potential Approximation (LPA) to the Wilson
renormalization group were uncovered, which led the authors to conclude that
$D>2$ dimensional scalar field theories endowed with {\sl non-polynomial}
interactions allow for a continuum of renormalization group fixed points, and
that around the Gaussian fixed point, asymptotically free interactions exist.
If true, this could herald very important new physics, particularly for the
Higgs sector of the Standard Model. Continuing work in support of these ideas,
has motivated us to point out that we previously studied the same properties
and showed that they lead to very different conclusions. Indeed, in as much as
the statements in hep-th/9406199 are correct, they point to some deep and
beautiful facts about the LPA and its generalisations, but however no new
physics.Comment: Typos corrected. A Comment - to be published in Phys. Rev. Lett. 1
page, 1 eps figure, uses LaTeX, RevTex and eps

### Elements of the Continuous Renormalization Group

These two lectures cover some of the advances that underpin recent progress
in deriving continuum solutions from the exact renormalization group. We
concentrate on concepts and on exact non-perturbative statements, but in the
process will describe how real non-perturbative calculations can be done,
particularly within derivative expansion approximations. An effort has been
made to keep the lectures pedagogical and self-contained. Topics covered are
the derivation of the flow equations, their equivalence, continuum limits,
perturbation theory, truncations, derivative expansions, identification of
fixed points and eigenoperators, and the role of reparametrization invariance.
Some new material is included, in particular a demonstration of
non-perturbative renormalizability, and a discussion of ultraviolet
renormalons.Comment: Invited lectures at the Yukawa International Seminar '97. 20 pages
including 6 eps figs. LaTeX. PTPTeX style files include

### Manifestations of the Galactic Center Magnetic Field

Several independent lines of evidence reveal that a relatively strong and
highly ordered magnetic field is present throughout the Galaxy's central
molecular zone (CMZ). The field within dense clouds of the central molecular
zone is predominantly parallel to the Galactic plane, probably as a result of
the strong tidal shear in that region. A second magnetic field system is
present outside of clouds, manifested primarily by a population of vertical,
synchrotron-emitting filamentary features aligned with the field. Whether or
not the strong vertical field is uniform throughout the CMZ remains
undetermined, but is a key central issue for the overall energetics and the
impact of the field on the Galactic center arena. The interactions between the
two field systems are considered, as they are likely to drive some of the
activity within the CMZ. As a proxy for other gas-rich galaxies in the local
group and beyond, the Galactic center region reveals that magnetic fields are
likely to be an important diagnostic, if not also a collimator, of the flow of
winds and energetic particles out of the nucleus.Comment: To appear in "LESSONS FROM THE LOCAL GROUP" - A Conference in Honour
of David Block and Bruce Elmegreen, eds: Freeman, K.C., Elmegreen, B.G.,
Block, D.L. & Woolway, M. (SPRINGER: NEW YORK

### Renormalization group properties of the conformal sector: towards perturbatively renormalizable quantum gravity

The Wilsonian renormalization group (RG) requires Euclidean signature. The
conformal factor of the metric then has a wrong-sign kinetic term, which has a
profound effect on its RG properties. Generically for the conformal sector,
complete flows exist only in the reverse direction (i.e. from the infrared to
the ultraviolet). The Gaussian fixed point supports infinite sequences of
composite eigenoperators of increasing infrared relevancy (increasingly
negative mass dimension), which are orthonormal and complete for bare
interactions that are square integrable under the appropriate measure. These
eigenoperators are non-perturbative in $\hbar$ and evanescent. For
$\mathbb{R}^4$ spacetime, each renormalised physical operator exists but only
has support at vanishing field amplitude. In the generic case of infinitely
many non-vanishing couplings, if a complete RG flow exists, it is characterised
in the infrared by a scale $\Lambda_\mathrm{p}>0$, beyond which the field
amplitude is exponentially suppressed. On other spacetimes, of length scale
$L$, the flow ceases to exist once a certain universal measure of inhomogeneity
exceeds $O(1)+2\pi L^2\Lambda^2_\mathrm{p}$. Importantly for cosmology, the
minimum size of the universe is thus tied to the degree of inhomogeneity, with
spacetimes of vanishing size being required to be almost homogeneous. We
initiate a study of this exotic quantum field theory at the interacting level,
and discuss what the full theory of quantum gravity should look like, one which
must thus be perturbatively renormalizable in Newton's constant but
non-perturbative in $\hbar$.Comment: 52 pages, 4 figures; fixed typos; improved explanation of the sign of
V, and the use of Sturm-Liouville theory. To be publ in JHE

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