1,467 research outputs found
Fully extended BV-BFV description of General Relativity in three dimensions
We compute the extension of the BV theory for three-dimensional General
Relativity to all higher-codimension strata - boundaries, corners and vertices
- in the BV-BFV framework. Moreover, we show that such extension is strongly
equivalent to (nondegenerate) BF theory at all codimensions.Comment: 33 pages. Version 2: Improved readability, corrected typo
Geometry of mixed states for a q-bit and the quantum Fisher information tensor
After a review of the pure state case, we discuss from a geometrical point of
view the meaning of the quantum Fisher metric in the case of mixed states for a
two-level system, i.e. for a q-bit, by examining the structure of the fiber
bundle of states, whose base space can be identified with a co-adjoint orbit of
the unitary group. We show that the Fisher Information metric coincides with
the one induced by the metric of the manifold of SU(2), i.e. the 3-dimensional
sphere , when the mixing coefficients are varied. We define the notion of
Fisher Tensor and show that its anti-symmetric part is intrinsically related to
the Kostant Kirillov Souriau symplectic form that is naturally defined on
co-adjoint orbits, while the symmetric part is nontrivially again represented
by the Fubini Study metric on the space of mixed states, weighted by the mixing
coefficients.Comment: 20 pages; Abstract and Introduction modified, references added. Final
published versio
A general construction for monoid-based knapsack protocols
We present a generalized version of the knapsack protocol proposed by D.
Naccache and J. Stern at the Proceedings of Eurocrypt (1997). Our new framework
will allow the construction of other knapsack protocols having similar security
features. We will outline a very concrete example of a new protocol using
extension fields of a finite field of small characteristic instead of the prime
field Z/pZ, but more efficient in terms of computational costs for
asymptotically equal information rate and similar key size.Comment: 18 pages, to appear on Advances in Mathematics of Communication
The reduced phase space of Palatini-Cartan-Holst theory
General relativity in four dimensions can be reformulated as a gauge theory,
referred to as Palatini-Cartan-Holst theory. This paper describes its reduced
phase space using a geometric method due to Kijowski and Tulczyjew and its
relation to that of the Einstein-Hilbert approach.Comment: Revised version comprising new results, a correction of Th 4.22 and
the arguments leading to it. Manuscript accepted for publication in AHP. 31
page
On time
This note describes the restoration of time in one-dimensional
parameterization-invariant (hence timeless) models, namely the
classically-equivalent Jacobi action and gravity coupled to matter. It also
serves as a timely introduction by examples to the classical and quantum BV-BFV
formalism as well as to the AKSZ method.Comment: 36 pages. Improved exposition. To appear in Lett. Math. Phy
BV-BFV approach to General Relativity: Palatini-Cartan-Holst action
We show that the Palatini--Cartan--Holst formulation of General Relativity in
tetrad variables must be complemented with additional requirements on the
fields when boundaries are taken into account for the associated BV theory to
induce a compatible BFV theory on the boundary.Comment: 22 pages. Corrected typos in some formulae. Minor aesthetic fixe
BV-equivalence between triadic gravity and BF theory in three dimensions
The triadic description of General Relativity in three dimensions is known to
be a BF theory. Diffeomorphisms, as symmetries, are easily re- covered on shell
from the symmetries of BF theory. This note describes an explicit off-shell BV
symplectomorphism between the BV versions of the two theories, each endowed
with their natural symmetries
BV-BFV approach to General Relativity, Einstein-Hilbert action
The present paper shows that general relativity in the Arnowitt-Deser-Misner
formalism admits a BV-BFV formulation. More precisely, for any
(pseudo-) Riemannian manifold M with space-like or time-like boundary
components, the BV data on the bulk induces compatible BFV data on the
boundary. As a byproduct, the usual canonical formulation of general relativity
is recovered in a straightforward way.Comment: 16 page
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
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