32,298 research outputs found
Differential Regularization of a Non-relativistic Anyon Model
Differential regularization is applied to a field theory of a
non-relativistic charged boson field with
self-interaction and coupling to a statistics-changing Chern-Simons
gauge field. Renormalized configuration-space amplitudes for all diagrams
contributing to the 4-point function, which
is the only primitively divergent Green's function, are obtained up to 3-loop
order. The renormalization group equations are explicitly checked, and the
scheme dependence of the -function is investigated. If the
renormalization scheme is fixed to agree with a previous 1-loop calculation,
the 2- and 3-loop contributions to vanish, and
itself vanishes when the ``self-dual'' condition relating
to the gauge coupling is imposed.Comment: 22 pages in ReVTEX (with a plaintext PostScript figure appended at
end), MIT CTP #221
Natural renormalization
A careful analysis of differential renormalization shows that a distinguished
choice of renormalization constants allows for a mathematically more
fundamental interpretation of the scheme. With this set of a priori fixed
integration constants differential renormalization is most closely related to
the theory of generalized functions. The special properties of this scheme are
illustrated by application to the toy example of a free massive bosonic theory.
Then we apply the scheme to the phi^4-theory. The two-point function is
calculated up to five loops. The renormalization group is analyzed, the
beta-function and the anomalous dimension are calculated up to fourth and fifth
order, respectively.Comment: 23 pages, LaTeX, AMSsymbols, epsf style, 3 PostScript figure
Quantum structure of the non-Abelian Weizsacker-Williams field for a very large nucleus
We consider the McLerran-Venugopalan model for calculation of the small-
part of the gluon distribution function for a very large ultrarelativistic
nucleus at weak coupling. We construct the Feynman diagrams which correspond to
the classical Weizs\"{a}cker-Williams field found previously [Yu. V. Kovchegov,
Phys. Rev. D 54, 5463 (1996)] as a solution of the classical equations of
motion for the gluon field in the light-cone gauge. Analyzing these diagrams we
obtain a limit for the McLerran-Venugopalan model. We show that as long as this
limit is not violated a classical field can be used for calculation of
scattering amplitudes.Comment: 13 pages, REVTeX, 9 figure
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
The rise of graph-structured data such as social networks, regulatory
networks, citation graphs, and functional brain networks, in combination with
resounding success of deep learning in various applications, has brought the
interest in generalizing deep learning models to non-Euclidean domains. In this
paper, we introduce a new spectral domain convolutional architecture for deep
learning on graphs. The core ingredient of our model is a new class of
parametric rational complex functions (Cayley polynomials) allowing to
efficiently compute spectral filters on graphs that specialize on frequency
bands of interest. Our model generates rich spectral filters that are localized
in space, scales linearly with the size of the input data for
sparsely-connected graphs, and can handle different constructions of Laplacian
operators. Extensive experimental results show the superior performance of our
approach, in comparison to other spectral domain convolutional architectures,
on spectral image classification, community detection, vertex classification
and matrix completion tasks
The critical Z-invariant Ising model via dimers: the periodic case
We study a large class of critical two-dimensional Ising models namely
critical Z-invariant Ising models on periodic graphs, example of which are the
classical square, triangular and honeycomb lattice at the critical temperature.
Fisher introduced a correspondence between the Ising model and the dimer model
on a decorated graph, thus setting dimer techniques as a powerful tool for
understanding the Ising model. In this paper, we give a full description of the
dimer model corresponding to the critical Z-invariant Ising model. We prove
that the dimer characteristic polynomial is equal (up to a constant) to the
critical Laplacian characteristic polynomial, and defines a Harnack curve of
genus 0. We prove an explicit expression for the free energy, and for the Gibbs
measure obtained as weak limit of Boltzmann measures.Comment: 35 pages, 8 figure
Coherent states in quantum gravity: a construction based on the flux representation of LQG
As part of a wider study of coherent states in (loop) quantum gravity, we
introduce a modification to the standard construction, based on the recently
introduced (non-commutative) flux representation. The resulting quantum states
have some welcomed features, in particular concerning peakedness properties,
when compared to other coherent states in the literature.Comment: 24 pages, 2 figures; Revised version to match the published one. Some
references added. Discussion of the resolution of the identity include
Double hard scattering without double counting
Double parton scattering in proton-proton collisions includes kinematic
regions in which two partons inside a proton originate from the perturbative
splitting of a single parton. This leads to a double counting problem between
single and double hard scattering. We present a solution to this problem, which
allows for the definition of double parton distributions as operator matrix
elements in a proton, and which can be used at higher orders in perturbation
theory. We show how the evaluation of double hard scattering in this framework
can provide a rough estimate for the size of the higher-order contributions to
single hard scattering that are affected by double counting. In a numeric
study, we identify situations in which these higher-order contributions must be
explicitly calculated and included if one wants to attain an accuracy at which
double hard scattering becomes relevant, and other situations where such
contributions may be neglected.Comment: 80 pages, 20 figures. v2: clarifications in section 4, extended
section 8, small changes elsewher
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