70 research outputs found
RPA Green's Functions of the Anisotropic Heisenberg Model
We solve in random-phase approximation the anisotropic Heisenberg model,
including nearest and next-nearest neighbour interactions by calculating all
Green's functions and pair correlation functions in a cumulant decoupling
scheme. The general exposition is pedagogic in tone and is intended to be
accessible to any graduate student or physicist who is not an expert in the
field.Comment: 26 pages, 4 figure
Convergence of density expansions of correlation functions and the Ornstein-Zernike equation
We prove absolute convergence of the multi-body correlation functions as a power series in the density uniformly in their arguments. This is done by working in the context of the cluster expansion in the canonical ensemble and by expressing the correlation functions as the derivative of the logarithm of an appropriately extended partition function. In the thermodynamic limit, due to combinatorial cancellations, we show that the coeffi- cients of the above series are expressed by sums over some class of two-connected graphs. Furthermore, we prove the convergence of the density expansion of the “direct correlation function” which is based on a completely different approach and it is valid only for some inte- gral norm. Precisely, this integral norm is suitable to derive the Ornstein-Zernike equation. As a further outcome, we obtain a rigorous quantification of the error in the Percus-Yevick approximation
Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions
In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C* boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C* boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in this setup in a fully consistent fashion, without relying on gauge fixing. We argue that this class of states covers most of the interesting phenomenological applications in the framework of numerical simulations. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED
Central Exclusive Production in QCD
We investigate the theoretical description of the central exclusive
production process, h1+h2 -> h1+X+h2. Taking Higgs production as an example, we
sum logarithmically enhanced corrections appearing in the perturbation series
to all orders in the strong coupling. Our results agree with those originally
presented by Khoze, Martin and Ryskin except that the scale appearing in the
Sudakov factor, mu=0.62 \sqrt{\hat{s}}, should be replaced with
mu=\sqrt{\hat{s}}, where \sqrt{\hat{s}} is the invariant mass of the centrally
produced system. We confirm this result using a fixed-order calculation and
show that the replacement leads to approximately a factor 2 suppression in the
cross-section for central system masses in the range 100-500 GeV.Comment: 41 pages, 19 figures; minor typos fixed; version published in JHE
Theorems for asymptotic safety of gauge theories
We classify the weakly interacting fixed points of general gauge theories coupled to matter and explain how the competition between gauge and matter fluctuations gives rise to a rich spectrum of high- and low-energy fixed points. The pivotal role played by Yukawa couplings is emphasised. Necessary and sufficient conditions for asymptotic safety of gauge theories are also derived, in conjunction with strict no go theorems. Implications for phase diagrams of gauge theories and physics beyond the Standard Model are indicated
One-loop divergences in non-Abelian supersymmetric theories regularized by BRST-invariant version of the higher derivative regularization
- …