2,941 research outputs found
A Comprehensive Coordinate Space Renormalization of Quantum Electrodynamics to 2-Loop Order
We develop a coordinate space renormalization of massless Quantum
Electrodynamics using the powerful method of differential renormalization. Bare
one-loop amplitudes are finite at non-coincident external points, but do not
accept a Fourier transform into momentum space. The method provides a
systematic procedure to obtain one-loop renormalized amplitudes with finite
Fourier transforms in strictly four dimensions without the appearance of
integrals or the use of a regulator. Higher loops are solved similarly by
renormalizing from the inner singularities outwards to the global one. We
compute all 1- and 2-loop 1PI diagrams, run renormalization group equations on
them and check Ward identities. The method furthermore allows us to discern a
particular pattern of renormalization under which certain amplitudes are seen
not to contain higher-loop leading logarithms. We finally present the
computation of the chiral triangle showing that differential renormalization
emerges as a natural scheme to tackle problems.Comment: 28 pages (figures not included
Ground state entanglement in quantum spin chains
A microscopic calculation of ground state entanglement for the XY and
Heisenberg models shows the emergence of universal scaling behavior at quantum
phase transitions. Entanglement is thus controlled by conformal symmetry. Away
from the critical point, entanglement gets saturated by a mass scale. Results
borrowed from conformal field theory imply irreversibility of entanglement loss
along renormalization group trajectories. Entanglement does not saturate in
higher dimensions which appears to limit the success of the density matrix
renormalization group technique. A possible connection between majorization and
renormalization group irreversibility emerges from our numerical analysis.Comment: 26 pages, 16 figures, added references, minor changes. Final versio
A Generic Renormalization Method in Curved Spaces and at Finite Temperature
Based only on simple principles of renormalization in coordinate space, we
derive closed renormalized amplitudes and renormalization group constants at 1-
and 2-loop orders for scalar field theories in general backgrounds. This is
achieved through a generic renormalization procedure we develop exploiting the
central idea behind differential renormalization, which needs as only inputs
the propagator and the appropriate laplacian for the backgrounds in question.
We work out this generic coordinate space renormalization in some detail, and
subsequently back it up with specific calculations for scalar theories both on
curved backgrounds, manifestly preserving diffeomorphism invariance, and at
finite temperature.Comment: 15pp., REVTeX, UB-ECM-PF 94/1
Differential Renormalization of Massive Quantum Field Theories
We extend the method of differential renormalization to massive quantum field
theories treating in particular \ph4-theory and QED. As in the massless case,
the method proves to be simple and powerful, and we are able to find, in
particular, compact explicit coordinate space expressions for the finite parts
of two notably complicated diagrams, namely, the 2-loop 2-point function in
\ph4 and the 1-loop vertex in QED.Comment: 8 pages(LaTex, no figures
Fine-grained entanglement loss along renormalization group flows
We explore entanglement loss along renormalization group trajectories as a
basic quantum information property underlying their irreversibility. This
analysis is carried out for the quantum Ising chain as a transverse magnetic
field is changed. We consider the ground-state entanglement between a large
block of spins and the rest of the chain. Entanglement loss is seen to follow
from a rigid reordering, satisfying the majorization relation, of the
eigenvalues of the reduced density matrix for the spin block. More generally,
our results indicate that it may be possible to prove the irreversibility along
RG trajectories from the properties of the vacuum only, without need to study
the whole hamiltonian.Comment: 5 pages, 3 figures; minor change
Boundary and impurity effects on entanglement of Heisenberg chains
We study entanglement of a pair of qubits and the bipartite entanglement
between the pair and the rest within open-ended Heisenberg and XY models.
The open boundary condition leads to strong oscillations of entanglements with
a two-site period, and the two kinds of entanglements are 180 degree out of
phase with each other. The mean pairwise entanglement and ground-state energy
per site in the model are found to be proportional to each other. We
study the effects of a single bulk impurity on entanglement, and find that
there exists threshold values of the relative coupling strength between the
impurity and its nearest neighbours, after which the impurity becomes pairwise
entangled with its nearest neighbours.Comment: 6 pages and 6 figure
The Hidden Spatial Geometry of Non-Abelian Gauge Theories
The Gauss law constraint in the Hamiltonian form of the gauge theory
of gluons is satisfied by any functional of the gauge invariant tensor variable
. Arguments are given that the tensor is a more appropriate variable. When the Hamiltonian
is expressed in terms of or , the quantity appears.
The gauge field Bianchi and Ricci identities yield a set of partial
differential equations for in terms of . One can show that
is a metric-compatible connection for with torsion, and that the curvature
tensor of is that of an Einstein space. A curious 3-dimensional
spatial geometry thus underlies the gauge-invariant configuration space of the
theory, although the Hamiltonian is not invariant under spatial coordinate
transformations. Spatial derivative terms in the energy density are singular
when . These singularities are the analogue of the centrifugal
barrier of quantum mechanics, and physical wave-functionals are forced to
vanish in a certain manner near . It is argued that such barriers are
an inevitable result of the projection on the gauge-invariant subspace of the
Hilbert space, and that the barriers are a conspicuous way in which non-abelian
gauge theories differ from scalar field theories.Comment: 19 pages, TeX, CTP #223
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