1,605 research outputs found
Infinite reduction of couplings in non-renormalizable quantum field theory
I study the problem of renormalizing a non-renormalizable theory with a
reduced, eventually finite, set of independent couplings. The idea is to look
for special relations that express the coefficients of the irrelevant terms as
unique functions of a reduced set of independent couplings lambda, such that
the divergences are removed by means of field redefinitions plus
renormalization constants for the lambda's. I consider non-renormalizable
theories whose renormalizable subsector R is interacting and does not contain
relevant parameters. The "infinite" reduction is determined by i) perturbative
meromorphy around the free-field limit of R, or ii) analyticity around the
interacting fixed point of R. In general, prescriptions i) and ii) mutually
exclude each other. When the reduction is formulated using i), the number of
independent couplings remains finite or slowly grows together with the order of
the expansion. The growth is slow in the sense that a reasonably small set of
parameters is sufficient to make predictions up to very high orders. Instead,
in case ii) the number of couplings generically remains finite. The infinite
reduction is a tool to classify the irrelevant interactions and address the
problem of their physical selection.Comment: 40 pages; v2: more explanatory comments; appeared in JHE
Deformed dimensional regularization for odd (and even) dimensional theories
I formulate a deformation of the dimensional-regularization technique that is
useful for theories where the common dimensional regularization does not apply.
The Dirac algebra is not dimensionally continued, to avoid inconsistencies with
the trace of an odd product of gamma matrices in odd dimensions. The
regularization is completed with an evanescent higher-derivative deformation,
which proves to be efficient in practical computations. This technique is
particularly convenient in three dimensions for Chern-Simons gauge fields,
two-component fermions and four-fermion models in the large N limit, eventually
coupled with quantum gravity. Differently from even dimensions, in odd
dimensions it is not always possible to have propagators with fully Lorentz
invariant denominators. The main features of the deformed technique are
illustrated in a set of sample calculations. The regularization is universal,
local, manifestly gauge-invariant and Lorentz invariant in the physical sector
of spacetime. In flat space power-like divergences are set to zero by default.
Infinitely many evanescent operators are automatically dropped.Comment: 27 pages, 3 figures; v2: expanded presentation of some arguments,
IJMP
On field theory quantization around instantons
With the perspective of looking for experimentally detectable physical
applications of the so-called topological embedding, a procedure recently
proposed by the author for quantizing a field theory around a non-discrete
space of classical minima (instantons, for example), the physical implications
are discussed in a ``theoretical'' framework, the ideas are collected in a
simple logical scheme and the topological version of the Ginzburg-Landau theory
of superconductivity is solved in the intermediate situation between type I and
type II superconductors.Comment: 27 pages, 5 figures, LaTe
Renormalizable acausal theories of classical gravity coupled with interacting quantum fields
We prove the renormalizability of various theories of classical gravity
coupled with interacting quantum fields. The models contain vertices with
dimensionality greater than four, a finite number of matter operators and a
finite or reduced number of independent couplings. An interesting class of
models is obtained from ordinary power-counting renormalizable theories,
letting the couplings depend on the scalar curvature R of spacetime. The
divergences are removed without introducing higher-derivative kinetic terms in
the gravitational sector. The metric tensor has a non-trivial running, even if
it is not quantized. The results are proved applying a certain map that
converts classical instabilities, due to higher derivatives, into classical
violations of causality, whose effects become observable at sufficiently high
energies. We study acausal Einstein-Yang-Mills theory with an R-dependent gauge
coupling in detail. We derive all-order formulas for the beta functions of the
dimensionality-six gravitational vertices induced by renormalization. Such beta
functions are related to the trace-anomaly coefficients of the matter
subsector.Comment: 36 pages; v2: CQG proof-corrected versio
A review of the role of ultrasound biomicroscopy in glaucoma associated with rare diseases of the anterior segment
Ultrasound biomicroscopy is a non-invasive imaging technique, which allows high-resolution evaluation of the anatomical features of the anterior segment of the eye regardless of optical media transparency. This technique provides diagnostically significant information in vivo for the cornea, anterior chamber, chamber angle, iris, posterior chamber, zonules, ciliary body, and lens, and is of great value in assessment of the mechanisms of glaucoma onset. The purpose of this paper is to review the use of ultrasound biomicroscopy in the diagnosis and management of rare diseases of the anterior segment such as mesodermal dysgenesis of the neural crest, iridocorneal endothelial syndrome, phakomatoses, and metabolic disorders
Lorentz violating kinematics: Threshold theorems
Recent tentative experimental indications, and the subsequent theoretical
speculations, regarding possible violations of Lorentz invariance have
attracted a vast amount of attention. An important technical issue that
considerably complicates detailed calculations in any such scenario, is that
once one violates Lorentz invariance the analysis of thresholds in both
scattering and decay processes becomes extremely subtle, with many new and
naively unexpected effects. In the current article we develop several extremely
general threshold theorems that depend only on the existence of some energy
momentum relation E(p), eschewing even assumptions of isotropy or monotonicity.
We shall argue that there are physically interesting situations where such a
level of generality is called for, and that existing (partial) results in the
literature make unnecessary technical assumptions. Even in this most general of
settings, we show that at threshold all final state particles move with the
same 3-velocity, while initial state particles must have 3-velocities
parallel/anti-parallel to the final state particles. In contrast the various
3-momenta can behave in a complicated and counter-intuitive manner.Comment: V1: 32 pages, 6 figures, 3 tables. V2: 5 references adde
Search for flow invariants in even and odd dimensions
A flow invariant in quantum field theory is a quantity that does not depend
on the flow connecting the UV and IR conformal fixed points. We study the flow
invariance of the most general sum rule with correlators of the trace Theta of
the stress tensor. In even (four and six) dimensions we recover the results
known from the gravitational embedding. We derive the sum rules for the trace
anomalies a and a' in six dimensions. In three dimensions, where the
gravitational embedding is more difficult to use, we find a non-trivial
vanishing relation for the flow integrals of the three- and four-point
functions of Theta. Within a class of sum rules containing finitely many terms,
we do not find a non-vanishing flow invariant of type a in odd dimensions. We
comment on the implications of our results.Comment: 21 pages, v2: expanded introduction, published in NJ
More on the Subtraction Algorithm
We go on in the program of investigating the removal of divergences of a
generical quantum gauge field theory, in the context of the Batalin-Vilkovisky
formalism. We extend to open gauge-algebrae a recently formulated algorithm,
based on redefinitions of the parameters of the
classical Lagrangian and canonical transformations, by generalizing a well-
known conjecture on the form of the divergent terms. We also show that it is
possible to reach a complete control on the effects of the subtraction
algorithm on the space of the gauge-fixing parameters. A
principal fiber bundle with a connection
is defined, such that the canonical transformations are gauge
transformations for . This provides an intuitive geometrical
description of the fact the on shell physical amplitudes cannot depend on
. A geometrical description of the effect of the subtraction
algorithm on the space of the physical parameters is
also proposed. At the end, the full subtraction algorithm can be described as a
series of diffeomorphisms on , orthogonal to
(under which the action transforms as a scalar), and gauge transformations on
. In this geometrical context, a suitable concept of predictivity is
formulated. We give some examples of (unphysical) toy models that satisfy this
requirement, though being neither power counting renormalizable, nor finite.Comment: LaTeX file, 37 pages, preprint SISSA/ISAS 90/94/E
The Gravity dual of the Non-Perturbative SUSY Yang-Mills Theory
The anomalous Ward identity is derived for SUSY Yang-Mills theories,
which is resulted out of Wrapping of branes on Supersymmetric two cycles.
From the Ward identity One obtains the Witten-Dijkgraaf-Verlinde-Verlinde
equation and hence can solve for the pre-potential. This way one avoids the
problem of enhancon which maligns the non-perturbative behaviour of the
Yang-Mills theory resulted out of Wrapped branes.Comment: 4 pages, LaTeX. Talk given at the IXth International Symposium on
Particles, Strings and Cosmology PASCOS '03, Mumbai-India, January 3-8 2003.
v2:some reference adde
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