Spectral representation of lattice gluon and ghost propagators at zero temperature

We consider the analytic continuation of Euclidean propagator data obtained from 4D simulations to Minkowski space. In order to perform this continuation, the common approach is to first extract the K\"all\'en-Lehmann spectral density of the field. Once this is known, it can be extended to Minkowski space to yield the Minkowski propagator. However, obtaining the K\"all\'en-Lehmann spectral density from propagator data is a well known ill-posed numerical problem. To regularize this problem we implement an appropriate version of Tikhonov regularization supplemented with the Morozov discrepancy principle. We will then apply this to various toy model data to demonstrate the conditions of validity for this method, and finally to zero temperature gluon and ghost lattice QCD data. We carefully explain how to deal with the IR singularity of the massless ghost propagator. We also uncover the numerically different performance when using two ---mathematically equivalent--- versions of the K\"all\'en-Lehmann spectral integral.Comment: 33 pages, 18 figure

Finite temperature gluon propagator in Landau gauge: non-zero Matsubara frequencies and spectral densities

We report on the lattice computation of the Landau gauge gluon propagator at finite temperature, including the non-zero Matsubara frequencies. Moreover, the corresponding K\"all\'en-Lehmann spectral density is computed, using a Tikhonov regularisation together with the Morozov discrepancy principle. Implications for gluon confinement are also discussed.Comment: 5 pages, 5 figures, Lattice 2017 proceeding

From Invariant Decomposition to Spinors

Plane-based Geometric Algebra (PGA) has revealed points in a $d$-dimensional pseudo-Euclidean space $\mathbb{R}_{p,q,1}$ to be represented by $d$-blades rather than vectors. This discovery allows points to be factored into $d$ orthogonal hyperplanes, establishing points as pseudoscalars of a local geometric algebra $\mathbb{R}_{pq}$. Astonishingly, the non-uniqueness of this factorization reveals the existence of a local $\text{Spin}(p,q)$ geometric gauge group at each point. Moreover, a point can alternatively be factored into a product of the elements of the Cartan subalgebra of $\mathfrak{spin}(p,q)$, which are traditionally used to label spinor representations. Therefore, points reveal previously hidden geometric foundations for some of quantum field theory's mysteries. This work outlines the impact of PGA on the study of spinor representations in any number of dimensions, and is the first in a research programme exploring the consequences of this insight.Comment: 19 pages, 6 figures, submitted to the AACA ICCA13 topical collectio

Faddeev-Popov matrix in linear covariant gauge : first results

We discuss a possible definition of the Faddeev-Popov matrix for the minimal linear covariant gauge on the lattice and present first results for the ghost propagator. We consider Yang-Mills theory in four space-time dimensions, for SU(2) and SU(3) gauge groups

Forster resonance energy transfer and protein-induced fluorescence enhancement as synergetic multiscale molecular rulers

Advanced microscopy methods allow obtaining information on (dynamic) conformational changes in biomolecules via measuring a single molecular distance in the structure. It is, however, extremely challenging to capture the full depth of a three-dimensional biochemical state, binding-related structural changes or conformational cross-talk in multi-protein complexes using one-dimensional assays. In this paper we address this fundamental problem by extending the standard molecular ruler based on Forster resonance energy transfer (FRET) into a two-dimensional assay via its combination with protein-induced fluorescence enhancement (PIFE). We show that donor brightness (via PIFE) and energy transfer efficiency (via FRET) can simultaneously report on e.g., the conformational state of double stranded DNA (dsDNA) following its interaction with unlabelled proteins (BamHI, EcoRV, and T7 DNA polymerase gp5/trx). The PIFE-FRET assay uses established labelling protocols and single molecule fluorescence detection schemes (alternating-laser excitation, ALEX). Besides quantitative studies of PIFE and FRET ruler characteristics, we outline possible applications of ALEX-based PIFE-FRET for single-molecule studies with diffusing and immobilized molecules. Finally, we study transcription initiation and scrunching of E. coli RNA-polymerase with PIFE-FRET and provide direct evidence for the physical presence and vicinity of the polymerase that causes structural changes and scrunching of the transcriptional DNA bubble