Real- and imaginary-time field theory at finite temperature and density

We review the theoretical foundations and most important physical applications of the Pinch Technique (PT). This method allows the construction of off-shell Green's functions in non-Abelian gauge theories that are independent of the gauge-fixing parameter and satisfy ghost-free Ward identities. We first present the diagrammatic formulation of the technique in QCD, deriving at one loop the gauge independent gluon self-energy, quark-gluon vertex, and three-gluon vertex, together with their Abelian Ward identities. The generalization to theories with spontaneous symmetry breaking is carried out in detail, and the connection with the optical theorem and the dispersion relations are explained within the electroweak sector of the Standard Model. The equivalence between the PT and the Feynman gauge of the Background Field Method (BFM) is elaborated, and the crucial differences between the two methods are critically scrutinized. The Batalin-Vilkovisky quantization method and the general formalism of algebraic renormalization are introduced, and the all-order generalization of the PT is thoroughly examined. The extension of the PT to the non-perturbative domain of the QCD Schwinger-Dyson equations is presented systematically, and the main advantages of the resulting self-consistent truncation scheme are discussed. A plethora of physical applications relying on the PT are reviewed, such as the definition of gauge-independent off-shell form-factors, the construction of non-Abelian effective charges, the gauge-invariant treatment of resonant transition amplitudes and unstable particles, and the dynamical generation of an effective gluon mass.

Pinch Technique: Theory and Applications

https://digital.csic.es/bitstream/10261/20634/3/0909.2536v1.pdf

The progress in the last decade in perturbative quantum field theory at high temperatures and densities, made possible by the use of effective field theories and hard thermal/dense loop resummations in ultrarelativistic gauge theories, is reviewed. The relevant methods are discussed in field theoretical models from simple scalar theories to non-Abelian gauge theories including gravity. In the simpler models, the aim is to give a pedagogical account of some of the relevant problems and their resolution, while in the more complicated but also more interesting models such as quantum chromodynamics, a summary of the results obtained so far is given together with references to a few of the most recent developments and open problems.

https://iopscience.iop.org/article/10.1088/0034-4885/67/3/R05/pdf

Advances in perturbative thermal field theory

We develop a flow-based sampling algorithm for $\mathrm{SU}(N)$ lattice gauge theories that is gauge invariant by construction. Our key contribution is constructing a class of flows on an $\mathrm{SU}(N)$ variable [or on a $\mathrm{U}(N)$ variable by a simple alternative] that respects matrix conjugation symmetry. We apply this technique to sample distributions of single $\mathrm{SU}(N)$ variables and to construct flow-based samplers for SU(2) and SU(3) lattice gauge theory in two dimensions.

Sampling using SU ( N ) gauge equivariant flows

Sparse matrices are a core component in many numerical simulations, and their efficiency is essential to achieving high performance. Dynamic sparse-matrix allocation (insertion) can benefit a number of problems such as sparse-matrix factorization, sparse-matrix-matrix addition, static analysis (e.g., points-to analysis), computing transitive closure, and other graph algorithms. Existing sparse-matrix formats are poorly designed to handle dynamic updates. The compressed sparse-row (CSR) format is fully compact and must be rebuilt after each new entry. Ellpack (ELL) stores a constant number of entries per row, which allows for efficient insertion and sparse matrix-vector multiplication (SpMV) but is memory inefficient and strictly limits row size. The coordinate (COO) format stores a list of entries and is efficient for both memory use and insertion time; however, it is much less efficient at SpMV. Hybrid ellpack (HYB) compromises by using a combination of ELL and COO but degrades in performance as the COO portion fills up. Rows that use the COO portion require it to be completely traversed during every SpMV operation.

/pdf/dynamic-sparse-matrix-allocation-on-gpus-14yj3gy1bb.pdf

Dynamic Sparse-Matrix Allocation on GPUs

The discontinuous Galerkin (DG) method has very quickly found utility in such diverse applications as computational solid mechanics, fluid mechanics, acoustics, and electromagnetics. The DG methodology merely requires weak constraints on the fluxes between elements. This feature provides a flexibility which is difficult to match with conventional continuous Galerkin methods. However, allowing discontinuity between element interfaces can in turn be problematic during simulation postprocessing, such as in visualization. Consequently, smoothness-increasing accuracy-conserving (SIAC) filters were proposed in [M. Steffen et al., IEEE Trans. Vis. Comput. Graph., 14 (2008), pp. 680--692, D. Walfisch et al., J. Sci. Comput., 38 (2009), pp. 164--184] as a means of introducing continuity at element interfaces while maintaining the order of accuracy of the original input DG solution. Although the DG methodology can be applied to arbitrary triangulations, the typical application of SIAC filters has been to DG solutions obtained over translation invariant meshes such as structured quadrilaterals and triangles. As the assumption of any sort of regularity including the translation invariance of the mesh is a hindrance towards making the SIAC filter applicable to real life simulations, we demonstrate in this paper for the first time the behavior and complexity of the computational extension of this filtering technique to fully unstructured tessellations. We consider different types of unstructured triangulations and show that it is indeed possible to get reduced errors and improved smoothness through a proper choice of kernel scaling. These results are promising, as they pave the way towards a more generalized SIAC filtering technique.

/pdf/smoothness-increasing-accuracy-conserving-filters-for-1g2oyuss06.pdf

Smoothness-Increasing Accuracy-Conserving Filters for Discontinuous Galerkin Solutions over Unstructured Triangular Meshes

Smoothness-increasing accuracy-conserving (SIAC) filtering has demonstrated its effectiveness in raising the convergence rate of discontinuous Galerkin solutions from order $k+\frac{1}{2}$ to order 2k+1 for specific types of translation invariant meshes (Cockburn et al. in Math. Comput. 72:577---606, 2003; Curtis et al. in SIAM J. Sci. Comput. 30(1):272---289, 2007; Mirzaee et al. in SIAM J. Numer. Anal. 49:1899---1920, 2011). Additionally, it improves the weak continuity in the discontinuous Galerkin method to k?1 continuity. Typically this improvement has a positive impact on the error quantity in the sense that it also reduces the absolute errors. However, not enough emphasis has been placed on the difference between superconvergent accuracy and improved errors. This distinction is particularly important when it comes to understanding the interplay introduced through meshing, between geometry and filtering. The underlying mesh over which the DG solution is built is important because the tool used in SIAC filtering--convolution--is scaled by the geometric mesh size. This heavily contributes to the effectiveness of the post-processor. In this paper, we present a study of this mesh scaling and how it factors into the theoretical errors. To accomplish the large volume of post-processing necessary for this study, commodity streaming multiprocessors were used; we demonstrate for structured meshes up to a 50× speed up in the computational time over traditional CPU implementations of the SIAC filter.

/pdf/smoothness-increasing-accuracy-conserving-siac-filtering-for-41rma1ks3w.pdf

Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions: Improved Errors Versus Higher-Order Accuracy

Hidden Spurious Sources in Axial Gauge Propagators

Stencil computations are a common class of operations that appear in many computational scientific and engineering applications Stencil computations often benefit from compile-time analysis, exploiting data-locality, and parallelism Post-processing of discontinuous Galerkin (dG) simulation solutions with B-spline kernels is an example of a numerical method which requires evaluating computationally intensive stencil operations over a mesh Previous work on stencil computations has focused on structured meshes, while giving little attention to unstructured meshes Performing stencil operations over an unstructured mesh requires sampling of heterogeneous elements which often leads to inefficient memory access patterns and limits data locality/reuse In this paper, we present an efficient method for performing stencil computations over unstructured meshes which increases data-locality and cache efficiency, and a scalable approach for stencil tiling and concurrent execution We provide experimental results in the context of post-processing of dG solutions that demonstrate the effectiveness of our approach

/pdf/a-scalable-efficient-scheme-for-evaluation-of-stencil-2bic651g0e.pdf

A scalable, efficient scheme for evaluation of stencil computations over unstructured meshes

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

James King

Author Tools

Chat about Author