5,203 research outputs found
Quantum geometry from phase space reduction
In this work we give an explicit isomorphism between the usual spin network
basis and the direct quantization of the reduced phase space of tetrahedra. The
main outcome is a formula that describes the space of SU(2) invariant states by
an integral over coherent states satisfying the closure constraint exactly, or
equivalently, as an integral over the space of classical tetrahedra. This
provides an explicit realization of theorems by Guillemin--Sternberg and Hall
that describe the commutation of quantization and reduction. In the final part
of the paper, we use our result to express the FK spin foam model as an
integral over classical tetrahedra and the asymptotics of the vertex amplitude
is determined.Comment: 33 pages, 1 figur
Scalar Asymptotic Charges and Dual Large Gauge Transformations
In recent years soft factorization theorems in scattering amplitudes have
been reinterpreted as conservation laws of asymptotic charges. In gauge,
gravity, and higher spin theories the asymptotic charges can be understood as
canonical generators of large gauge symmetries. Such a symmetry interpretation
has been so far missing for scalar soft theorems. We remedy this situation by
treating the massless scalar field in terms of a dual two-form gauge field. We
show that the asymptotic charges associated to the scalar soft theorem can be
understood as generators of large gauge transformations of the dual two-form
field.
The dual picture introduces two new puzzles: the charges have very unexpected
Poisson brackets with the fields, and the monopole term does not always have a
dual gauge transformation interpretation. We find analogs of these two
properties in the Kramers-Wannier duality on a finite lattice, indicating that
the free scalar theory has new edge modes at infinity that canonically commute
with all the bulk degrees of freedom.Comment: 16 pages, 2 figure
The Relativistic Particle: Dirac observables and Feynman propagator
We analyze the algebra of Dirac observables of the relativistic particle in
four space-time dimensions. We show that the position observables become
non-commutative and the commutation relations lead to a structure very similar
to the non-commutative geometry of Deformed Special Relativity (DSR). In this
framework, it appears natural to consider the 4d relativistic particle as a
five dimensional massless particle. We study its quantization in terms of wave
functions on the 5d light cone. We introduce the corresponding five-dimensional
action principle and analyze how it reproduces the physics of the 4d
relativistic particle. The formalism is naturally subject to divergences and we
show that DSR arises as a natural regularization: the 5d light cone is
regularized as the de Sitter space. We interpret the fifth coordinate as the
particle's proper time while the fifth moment can be understood as the mass.
Finally, we show how to formulate the Feynman propagator and the Feynman
amplitudes of quantum field theory in this context in terms of Dirac
observables. This provides new insights for the construction of observables and
scattering amplitudes in DSR.Comment: 14 pages, Revtex
- …