Generalized LKF transformations for $N$-point fermion correlators in QED
José Nicasio, Christian Schubert, Naser Ahmadiniaz, James P. Edwards
备注：
Prepared for the Proceedings of the 20th Lomonosov Conference on Elementary Particle Physics, held in August 2021, based on a talk given by José Nicasio on the results of arXiv:2012.10536 [hep-th] and arXiv:2010.04160 [hep-th]
Within the worldline approach to quantum electrodynamics (QED), a change of the photon's covariant gauge parameter $ξ$ is investigated to analyse the non-perturbative gauge dependence of the configuration space fermion correlation functions, deriving a generalization of the Landau-Kalatnikov-Fradkin transformations (LKFt). These transformations reveal how the non-perturbative gauge dependence of position space amplitudes can be absorbed into a multiplicative exponential factor.
We examine the non-perturbative gauge dependence of arbitrary configuration space fermion correlators in quantum electrodynamics (QED). First, we study the dressed electron propagator (allowing for emission or absorption of any number of photons along a fermion line) using the first quantised approach to quantum field theory and analyse its gauge transformation properties induced by virtual photon exchange. This is then extended to the $N$-point functions where we derive an exact, generalised version of the fully non-perturbative Landau-Khalatnikov-Fradkin (LKF) transformation for these correl…
The Landau-Khalatnikov-Fradkin transformations (LKFTs) allow to interpolate $n$-point functions between different gauges. We first offer an alternative derivation of these LKFTs for the gauge and fermions field in the Abelian (QED) case when working in the class of linear covariant gauges. Our derivation is based on the introduction of a gauge invariant transversal gauge field, which allows a natural generalization to the non-Abelian (QCD) case of the LKFTs. To our knowledge, within this rigorous formalism, this is the first construction of the LKFTs beyond QED. The renormalizability of our se…
The Landau-Khalatnikov-Fradkin (LKF) transformation is a powerful and elegant transformation allowing to study the gauge dependence of the propagator of charged particles interacting with gauge fields. With the help of this transformation, we derive a non-perturbative identity between massless propagators in two different gauges. From this identity, we find that the corresponding perturbative series can be exactly expressed in terms of a hatted transcendental basis that eliminates all even Euler $ζ$-functions. This explains the mystery of even $ζ$-values observed in multi-loop calculations of …
Conformal symmetry has important consequences for strong interactions at short distances and provides powerful tools for practical calculations. Even if the Lagrangians of Quantum Chromodynamics (QCD) and Electrodynamics (QED) are invariant under conformal transformations, this symmetry is broken by quantum corrections. The signature of the symmetry breaking is encoded in the presence of massless poles in correlators involving stress-energy tensors. We present a general study of the correlation functions $\langle TJJ\rangle$ and $\langle TTJJ\rangle$ of conformal field theory (CFT) in the flat…
Perturbative bosonization from two-point correlation functions
在这里，我们解决的问题玻色化的大规模费米子没有在大规模的$QED_2$和$QED_3$与$ N $费米子口味，包括也Thirring耦合的费米子质量的膨胀。我们从U（1）费米子流和规范场的两点算符出发。从这些玻色子的张量结构出发，我们证明了在D=2和D=3维中，U（1）流在相应的玻色化理论中是拓扑守恒的.我们找到了一个有效的生成功能的玻色子领域，再现这两个点，并从我们获得的拉格朗日密度$\barψ^{r} (i \partial / - m)ψ^{r}$到玻色子在两个维度的映射。这个映射是非定域的，但它是独立的电磁和Thirring耦合，至少在二次近似的费米子行列式。
We apply the conformal bootstrap technique to study the $U(1)$ Dirac spin liquid (i.e. $N_f=4$ QED$_3$) and the newly proposed $N=7$ Stiefel liquid (i.e. a conjectured 3d non-Lagrangian CFT without supersymmetry). For the $N_f=4$ QED$_3$, we focus on the monopole operator and ($SU(4)$ adjoint) fermion bilinear operator. We bootstrap their single correlators as well as the mixed correlators between them. We first discuss the bootstrap kinks from single correlators. Some exponents of these bootstrap kinks are close to the expected values of QED$_3$, but we provide clear evidence that they should…
We present a general study of 3-point functions of conformal field theory in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWI' s), introduced in recent works by Bzowski, McFadden and Skenderis (BMS). We investigate and detail the structure of the CWI's, their non-perturbative solutions and the transition to momentum space, comparing them to perturbation theory by taking QED as an example. We then proceed with an analysis of the $TJJ$ correlator, presenting independent and detailed re-derivations of the conform…
We present a general study of 3-point functions of conformal field theory (CFT) in momentum space, following a reconstruction method for tensor correlators, based on the solution of the conformal Ward identities (CWIs), introduced in recent works. We investigate and detail the structure of the CWIs and their non-perturbative solutions, and compare them to perturbation theory, taking QED and QCD as examples. Exact solutions of CFT's in the flat background limit in momentum space are matched by the perturbative realizations in free field theories, showing that the origin the conformal anomaly is…
We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and $2 + 1$ dimensional QED. Each step in the hierarchy can be considered a large $N$ truncation of an exact, but infinite set of equations relating all $k-$point charge correlators. $N$ is the number of fermion spin components. Each step in the hierarchy sums up an infinite number of large $N$ diagrams, including all diagrams up to some fixed order, for $k$ point functions with $k \leq K$. Higher point functions are replaced with their leading large $N$ behavior. The simplest truncation …
Potential non-relativistic Quantum Electrodynamics and the Keldysh-Schwinger formalism is used to derive Kadanoff-Baym-like equations for two-body field correlators. These cover the out-off-equilibrium dynamics and spectrum of heavy particle-antiparticle pairs under ultra-soft transitions inside a plasma background, whose temperature is much smaller compared to the typical relative pair momentum. It is shown that the dynamical equation for the pair phase-space distribution function, containing recombination and dissociation via the electric dipole interactions, is consistent with the previous …
We study the IR phase of three dimensional quantum electrodynamics (QED$_3$) coupled to $N_f=2$ flavors of two-component Dirac fermions, which has been controversial for decades. This theory has been proposed to be self-dual with symmetry enhancement $(SU(2)_f\times U(1)_t )/\mathbb{Z}_2\rightarrow O(4)$ at the IR fixed point. We focus on the four-point correlator of monopole operators with unit topological charge of $U(1)_t$. We illustrate the $O(4)\rightarrow SU(2)_f\times U(1)_t $ branching rules based on an $O(4)$ symmetric positive structure in the monopole four-point crossing equations. …
Hamiltonian Lattice QED$_3$ with One and Two Flavors of Wilson Fermions: Topological Structure and Response
Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, University of California, Los Angeles（加州大学洛杉矶分校物理与天文学系马尼·L·巴乌米克理论物理研究所）；Transdisciplinary Research Area “Building Blocks of Matter and Fundamental Interactions” (TRA Matter) and Helmholtz Institute for Radiation and Nuclear Physics (HISKP), University of Bonn（波恩大学跨学科研究领域“物质基本组成与基本相互作用”（TRA Matter）及亥姆霍兹辐射与核物理研究所（HISKP））；Deutsches Elektronen-Synchrotron DESY（德国电子同步加速器研究所（DESY））；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）；Computation-Based Science and Technology Research Center, The Cyprus Institute（塞浦路斯研究所计算科学与技术研究中心）；Department of Physics, Tsinghua University（清华大学物理系）
We present the results of a conformal bootstrap study of the presumed unitary IR fixed point of quantum electrodynamics in three dimensions (QED$_3$) coupled to $N_f=4$ two-component Dirac fermions. Specifically, we study the four-point correlators of the $SU(4)$ adjoint fermion bilinear $r$ and the monopole of lowest topological charge $\mathcal{M}_{1/2}$. Most notably, the scaling dimensions of the fermion bilinear $r$ and the monopole $\mathcal{M}_{1/2}$ are found to be constrained into a closed island with a combination of spectrum assumptions inspired by the $1/N_f$ perturbative results a…
