50 research outputs found
Radiative corrections to the EPRL-FK spinfoam graviton
I study the corrections engendered by the insertion of a "melon" graph in the
bulk of the first-order spinfoam used for the graviton propagator. I find that
these corrections are highly non-trivial and, in particular, that they concern
those terms which disappear in the Bojowald-Bianchi-Magliaro-Perini limit of
vanishing Barbero-Immirzi parameter at fixed area. This fact is the first
realization of the often cited idea that the spinfoam amplitude receives higher
order corrections under the refinement of the underlying two-complex.Comment: 13 pages, 4 figure
Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity
We calculate the most divergent contribution to the non-degenerate sector of
the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK
Spin Foam model of Quantum Gravity. We find that such a contribution is
logarithmically divergent in the cut-off over the SU(2)-representation spins
when one chooses the face amplitude guaranteeing the face-splitting invariance
of the foam.We also find that the dependence on the boundary data is different
from that of the bare propagator. This fact has its origin in the
non-commutativity of the EPRL-FK Y-map with the projector onto
SL(2,C)-invariant states. In the course of the paper, we discuss in detail the
approximations used during the calculations, its geometrical interpretation as
well as the physical consequences of our result.Comment: 58 pages, 8 figures. Corrections about the degenerate sector
(suppression of a paragraph, introduction of a new appendix), plus minor
corrections and improvements in the introduction and in the conclusion
A unified geometric framework for boundary charges and dressings: non-Abelian theory and matter
Boundaries in gauge theories are a delicate issue. Arbitrary boundary choices
enter the calculation of charges via Noether's second theorem, obstructing the
assignment of unambiguous physical charges to local gauge symmetries. Replacing
the arbitrary boundary choice with new degrees of freedom suggests itself. But,
concretely, such boundary degrees of freedom are spurious---i.e. they are not
part of the original field content of the theory---and have to disappear upon
gluing. How should we fit them into what we know about field-theory? We resolve
these issues in a unified and geometric manner, by introducing a connection
1-form, , in the field-space of Yang-Mills theory. Using this geometric
tool, a modified version of symplectic geometry---here called `horizontal'---is
possible. Independently of boundary conditions, this formalism bestows to each
region a physical notion of charge: the horizontal Noether charge. The
horizontal gauge charges always vanish, while global charges still arise for
reducible configurations characterized by global symmetries. The field-content
itself is used as a reference frame to distinguish `gauge' and `physical'; no
new degrees of freedom, such as group-valued edge modes, are required.
Different choices of reference fields give different 's, which are
cousins of gauge-fixing like the Higgs-unitary and Coulomb gauges. But the
formalism extends well beyond gauge-fixings, for instance by avoiding the
Gribov problem. For one choice of , would-be Goldstone modes arising
from the condensation of matter degrees of freedom play precisely the role of
the known group-valued edge modes, but here they arise as preferred coordinates
in field space, rather than new fields. For another choice, in the Abelian
case, recovers the Dirac dressing of the electron.Comment: 71 pages, 3 appendices, 9 figures. Summary of the results at the
beginning of the paper. v2: numerous improvements in the presentation, and
introduction of new references, taking colleague feedback into accoun
Null Hamiltonian Yang-Mills theory. Soft symmetries and memory as superselection
Soft symmetries for Yang-Mills theory are shown to correspond to the residual
Hamiltonian action of the gauge group on the Ashtekar-Streubel phase space,
which is the result of a partial symplectic reduction. The associated momentum
map is the electromagnetic memory in the abelian theory, or a nonlinear,
gauge-equivariant, generalization thereof in the nonabelian case.
This result follows from an application of Hamiltonian reduction by stages,
enabled by the existence of a natural normal subgroup of the gauge group on a
null codimension-1 submanifold with boundaries. The first stage is coisotropic
reduction of the Gauss constraint, and it yields a symplectic extension of the
Ashtekar-Streubel phase space (up to a covering). Hamiltonian reduction of the
residual gauge action leads to the fully-reduced phase space of the theory.
This is a Poisson manifold, whose symplectic leaves, called superselection
sectors, are labelled by the (gauge classes of the generalized) electric flux
across the boundary.
In this framework, the Ashtekar-Streubel phase space arises as an
intermediate reduction stage that enforces the superselection of the electric
flux at only one of the two boundary components. These results provide a
natural, purely Hamiltonian, explanation of the existence of soft symmetries as
a byproduct of partial symplectic reduction, as well as a motivation for the
expected decomposition of the quantum Hilbert space of states into irreducible
representations labelled by the Casimirs of the Poisson structure on the
reduced phase space.Comment: 52 pages + Appendices. New on v3 (submitted version): significant
restructuring and streamlining with improvements throughout, especially in
sections 1 (introduction), 2 (theoretical framework), and 7 (asymptotic
symmetries); one appendix removed from v2. arXiv admin note: text overlap
with arXiv:1703.05448 by other author