Efficient simulation of relativistic fermions via vertex models

We have developed an efficient simulation algorithm for strongly interacting relativistic fermions in two-dimensional field theories based on a formulation as a loop gas. The loop models describing the dynamics of the fermions can be mapped to statistical vertex models and our proposal is in fact an efficient simulation algorithm for generic vertex models in arbitrary dimensions. The algorithm essentially eliminates critical slowing down by sampling two-point correlation functions and it allows simulations directly in the massless limit. Moreover, it generates loop configurations with fluctuating topological boundary conditions enabling to simulate fermions with arbitrary periodic or anti-periodic boundary conditions. As illustrative examples, the algorithm is applied to the Gross-Neveu model and to the Schwinger model in the strong coupling limit.Comment: 5 pages, 4 figure

Non-Gaussian wave functionals in Coulomb gauge Yang--Mills theory

A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson--Schwinger techniques, the static Green functions are expressed in terms of the kernels arising in the Taylor expansion of the exponent of the vacuum wave functional. These kernels are then determined by minimizing the vacuum expectation value of the Hamiltonian. The method is applied to Yang--Mills theory in Coulomb gauge, using a vacuum wave functional whose exponent contains up to quartic terms in the gauge field. An estimate of the cubic and quartic interaction kernels is given using as input the gluon and ghost propagators found with a Gaussian wave functional.Comment: 27 pages, 21 figure

Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.Comment: 17 pages, 9 figure

Critical correlators of three-dimensional gauge theories at finite temperature: exact results from universality

According to the Svetitsky-Yaffe conjecture, a three-dimensional gauge theory undergoing a continuous deconfinement transition is in the same universality class as a two-dimensional statistical model with order parameter taking values in the center of the gauge group. This allows us to use conformal field theory techniques to evaluate exactly various correlation functions at the critical point. In particular, we show that the plaquette operator of the gauge theory is mapped into the energy operator of the dimensionally reduced model. The plaquette expectation value in presence of static sources for three-dimensional SU(2) and SU(3) theories at the deconfinement temperature can be exactly evaluated, providing some new insight about the structure of the color flux tube in mesons and baryons.Comment: LATTICE98(hightemp

DRA method: Powerful tool for the calculation of the loop integrals

We review the method of the calculation of multiloop integrals suggested in Ref.\cite{Lee2010}.Comment: 6 pages, contribution to ACAT2011 proceedings, Uxbridge, London, September 5-9, 2011, typos are correcte

Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States

General expressions for quantum electrodynamic corrections to the one-loop self-energy [of order alpha(Zalpha)^6] and for the two-loop Lamb shift [of order alpha^2(Z\alpha)^] are derived. The latter includes all diagrams with closed fermion loops. The general results are valid for arbitrary excited non-S hydrogenic states and for the normalized Lamb shift difference of S states, defined as Delta_n = n^3 DeltaE(nS) - DeltaE(1S). We present numerical results for one-loop and two-loop corrections for excited S, P and D states. In particular, the normalized Lamb shift difference of S states is calculated with an uncertainty of order 0.1 kHz.Comment: 4 pages, RevTe

Survival probability of a diffusing test particle in a system of coagulating and annihilating random walkers

We calculate the survival probability of a diffusing test particle in an environment of diffusing particles that undergo coagulation at rate lambda_c and annihilation at rate lambda_a. The test particle dies at rate lambda' on coming into contact with the other particles. The survival probability decays algebraically with time as t^{-theta}. The exponent theta in d<2 is calculated using the perturbative renormalization group formalism as an expansion in epsilon=2-d. It is shown to be universal, independent of lambda', and to depend only on delta, the ratio of the diffusion constant of test particles to that of the other particles, and on the ratio lambda_a/lambda_c. In two dimensions we calculate the logarithmic corrections to the power law decay of the survival probability. Surprisingly, the log corrections are non-universal. The one loop answer for theta in one dimension obtained by setting epsilon=1 is compared with existing exact solutions for special values of delta and lambda_a/lambda_c. The analytical results for the logarithmic corrections are verified by Monte Carlo simulations.Comment: 8 pages, 8 figure

Collective polarization exchanges in collisions of photon clouds

The one-loop "vacuum" Heisenberg-Euler coupling of four electromagnetic fields can lead to interesting collective effects in the collision of two photon clouds, on a time scale orders of magnitude faster than one estimates from the cross-section and density. We estimate the characteristic time for macroscopic transformation of positive to negative helicity in clouds that are initially totally polarized and for depolarization of a polarized beam traversing an unpolarized cloud.Comment: Recapitulates much that is in hep-ph/0402127, with new results in the last section, and the first section drastically reduced in view of the previous work of Kotkin and Serbo. Typo corrected in eq. 1

A Maximally Symmetric Vector Propagator

We derive the propagator for a massive vector field on a de Sitter background of arbitrary dimension. This propagator is de Sitter invariant and possesses the proper flat spacetime and massless limits. Moreover, the retarded Green's function inferred from it produces the correct classical response to a test source. Our result is expressed in a tensor basis which is convenient for performing quantum field theory computations using dimensional regularization.Comment: 21 pages, no figures, uses LaTeX 2 epsilon, version 2 has an error in eqn (86) corrected and an updated reference lis

Reply to `Can infrared gravitons screen Λ\Lambda?'

We reply to the recent criticism by Garriga and Tanaka of our proposal that quantum gravitational loop corrections may lead to a secular screening of the effective cosmological constant. Their argument rests upon a renormalization scheme in which the composite operator $(R \sqrt{-g} - 4 \Lambda \sqrt{-g} )_{\rm ren}$ is defined to be the trace of the renormalized field equations. Although this is a peculiar prescription, we show that it {\it does not preclude secular screening}. Moreover, we show that a constant Ricci scalar {\it does not even classically} imply a constant expansion rate. Other important points are: (1) the quantity $R_{\rm ren}$ of Garriga and Tanaka is neither a properly defined composite operator, nor is it constant; (2) gauge dependence does not render a Green's function devoid of physical content; (3) scalar models on a non-dynamical de Sitter background (for which there is no gauge issue) can induce arbitrarily large secular contributions to the stress tensor; (4) the same secular corrections appear in observable quantities in quantum gravity; and (5) the prospects seem good for deriving a simple stochastic formulation of quantum gravity in which the leading secular effects can be summed and for which the expectation values of even complicated, gauge invariant operators can be computed at leading order.Comment: 17 pages, no figures, uses LaTeX 2epsilon. Version 2 adds important points about R_ren being neither finite nor constant, and that a constant Ricci scalar is not even classically an indicator of de Sitter expansion. Version 3 corrects some typoes and updates the reference