13,390 research outputs found
Gauge Invariant Geometric Variables For Yang-Mills Theory
In a previous publication [1], local gauge invariant geometric variables were
introduced to describe the physical Hilbert space of Yang-Mills theory. In
these variables, the electric energy involves the inverse of an operator which
can generically have zero modes, and thus its calculation is subtle. In the
present work, we resolve these subtleties by considering a small deformation in
the definition of these variables, which in the end is removed. The case of
spherical configurations of the gauge invariant variables is treated in detail,
as well as the inclusion of infinitely heavy point color sources, and the
expression for the associated electric field is found explicitly. These
spherical geometries are seen to correspond to the spatial components of
instanton configurations. The related geometries corresponding to Wu-Yang
monopoles and merons are also identified.Comment: 21 pp. in plain TeX. Uses harvmac.te
Continuous point symmetries in Group Field Theories
We discuss the notion of symmetries in non-local field theories characterized
by integro-differential equations of motion, from a geometric perspective. We
then focus on Group Field Theory (GFT) models of quantum gravity and provide a
general analysis of their continuous point symmetry transformations, including
the generalized conservation laws following from them
One-dimensional model for QCD at high energy
We propose a stochastic particle model in (1+1)-dimensions, with one
dimension corresponding to rapidity and the other one to the transverse size of
a dipole in QCD, which mimics high-energy evolution and scattering in QCD in
the presence of both saturation and particle-number fluctuations, and hence of
Pomeron loops. The model evolves via non-linear particle splitting, with a
non-local splitting rate which is constrained by boost-invariance and multiple
scattering. The splitting rate saturates at high density, so like the gluon
emission rate in the JIMWLK evolution. In the mean field approximation obtained
by ignoring fluctuations, the model exhibits the hallmarks of the BK equation,
namely a BFKL-like evolution at low density, the formation of a traveling wave,
and geometric scaling. In the full evolution including fluctuations, the
geometric scaling is washed out at high energy and replaced by diffusive
scaling. It is likely that the model belongs to the universality class of the
reaction-diffusion process. The analysis of the model sheds new light on the
Pomeron loops equations in QCD and their possible improvements.Comment: 35 pages, 4 figures, one appendi
Emergent gravitational dynamics from multi-BEC hydrodynamics?
In this paper, we examine the possibility to implement some form of emergent
Newtonian gravity in a generic multi-component Bose--Einstein condensate.
Parallely to what happens for the emergence of low energy Lorentz invariance,
strong requirements have to be imposed on the underlying condensed matter
model. We will show, within a simplified model, that the presence of a global
symmetry alleviates the problems associated to Lorentz violation, allows the
presence of a long range potential, to which the analogue matter fields (the
quasi-particles) are coupled following a weaker form of equivalence principle.Comment: revtex4, 23 page
Towards classical geometrodynamics from Group Field Theory hydrodynamics
We take the first steps towards identifying the hydrodynamics of group field
theories (GFTs) and relating this hydrodynamic regime to classical
geometrodynamics of continuum space. We apply to GFT mean field theory
techniques borrowed from the theory of Bose condensates, alongside standard GFT
and spin foam techniques. The mean field configuration we study is, in turn,
obtained from loop quantum gravity coherent states. We work in the context of
2d and 3d GFT models, in euclidean signature, both ordinary and colored, as
examples of a procedure that has a more general validity. We also extract the
effective dynamics of the system around the mean field configurations, and
discuss the role of GFT symmetries in going from microscopic to effective
dynamics. In the process, we obtain additional insights on the GFT formalism
itself.Comment: revtex4, 32 pages. Contribution submitted to the focus issue of the
New Journal of Physics on "Classical and Quantum Analogues for Gravitational
Phenomena and Related Effects", R. Schuetzhold, U. Leonhardt and C. Maia,
Eds; v2: typos corrected, references updated, to match the published versio
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