15 research outputs found
Fermionization, Convergent Perturbation Theory, and Correlations in the Yang-Mills Quantum Field Theory in Four Dimensions
We show that the Yang-Mills quantum field theory with momentum and spacetime
cutoffs in four Euclidean dimensions is equivalent, term by term in an
appropriately resummed perturbation theory, to a Fermionic theory with nonlocal
interaction terms. When a further momentum cutoff is imposed, this Fermionic
theory has a convergent perturbation expansion. To zeroth order in this
perturbation expansion, the correlation function of generic components
of pairs of connections is given by an explicit, finite-dimensional integral
formula, which we conjecture will behave as \noindent for where is a positive integer depending
on the gauge group In the case where we conjecture that \noindent so that the rate
of decay of correlations increases as Comment: Minor corrections of notation, style and arithmetic errors;
correction of minor gap in the proof of Proposition 1.4 (the statement of the
Proposition was correct); further remark and references adde
Renormalization Group and Asymptotic Spin--Charge separation for Chiral Luttinger liquids
The phenomenon of Spin-Charge separation in non-Fermi liquids is well
understood only in certain solvable d=1 fermionic systems. In this paper we
furnish the first example of asymptotic Spin-Charge separation in a d=1 non
solvable model. This goal is achieved using Renormalization Group approach
combined with Ward-Identities and Schwinger-Dyson equations, corrected by the
presence of a bandwidth cut-offs. Such methods, contrary to bosonization, could
be in principle applied also to lattice or higher dimensional systems.Comment: 45 pages, 11 figure
Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations
We calculate exactly matrix elements between states that are not eigenstates
of the quantum XY model for general anisotropy. Such quantities therefore
describe non equilibrium properties of the system; the Hamiltonian does not
contain any time dependence. These matrix elements are expressed as a sum of
Pfaffians. For single particle excitations on the ground state the Pfaffians in
the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of
refs. modifie
Combinatorial Hopf algebras in quantum field theory I
This manuscript stands at the interface between combinatorial Hopf algebra
theory and renormalization theory. Its plan is as follows: Section 1 is the
introduction, and contains as well an elementary invitation to the subject. The
rest of part I, comprising Sections 2-6, is devoted to the basics of Hopf
algebra theory and examples, in ascending level of complexity. Part II turns
around the all-important Faa di Bruno Hopf algebra. Section 7 contains a first,
direct approach to it. Section 8 gives applications of the Faa di Bruno algebra
to quantum field theory and Lagrange reversion. Section 9 rederives the related
Connes-Moscovici algebras. In Part III we turn to the Connes-Kreimer Hopf
algebras of Feynman graphs and, more generally, to incidence bialgebras. In
Section10 we describe the first. Then in Section11 we give a simple derivation
of (the properly combinatorial part of) Zimmermann's cancellation-free method,
in its original diagrammatic form. In Section 12 general incidence algebras are
introduced, and the Faa di Bruno bialgebras are described as incidence
bialgebras. In Section 13, deeper lore on Rota's incidence algebras allows us
to reinterpret Connes-Kreimer algebras in terms of distributive lattices. Next,
the general algebraic-combinatorial proof of the cancellation-free formula for
antipodes is ascertained; this is the heart of the paper. The structure results
for commutative Hopf algebras are found in Sections 14 and 15. An outlook
section very briefly reviews the coalgebraic aspects of quantization and the
Rota-Baxter map in renormalization.Comment: 94 pages, LaTeX figures, precisions made, typos corrected, more
references adde
Dynamics of Entanglement in One-Dimensional Spin Systems
We study the dynamics of quantum correlations in a class of exactly solvable
Ising-type models. We analyze in particular the time evolution of initial Bell
states created in a fully polarized background and on the ground state. We find
that the pairwise entanglement propagates with a velocity proportional to the
reduced interaction for all the four Bell states. Singlet-like states are
favored during the propagation, in the sense that triplet-like states change
their character during the propagation under certain circumstances.
Characteristic for the anisotropic models is the instantaneous creation of
pairwise entanglement from a fully polarized state; furthermore, the
propagation of pairwise entanglement is suppressed in favor of a creation of
different types of entanglement. The ``entanglement wave'' evolving from a Bell
state on the ground state turns out to be very localized in space-time. Further
support to a recently formulated conjecture on entanglement sharing is given.Comment: 25 pages, 21 figures; revte