Truncating the Schwinger-Dyson equations: How multiplicative renormalizability and the Ward identity restrict the three-point vertex in QED

1990 ◽  
Vol 42 (12) ◽  
pp. 4165-4169 ◽  
Author(s):  
D. C. Curtis ◽  
M. R. Pennington
Keyword(s):  
Ward Identity ◽  
Point Vertex ◽  
Multiplicative Renormalizability

scholarly journals Covariant phase space and soft factorization in non-Abelian gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Temple He ◽  
Prahar Mitra
Keyword(s):  
Phase Space ◽  
Ward Identity ◽  
Gauge Theories ◽  
Minkowski Spacetime ◽  
Soft Gluon ◽  
Careful Study ◽  
Abelian Gauge ◽  
Gauge Sector ◽  
Vacuum States ◽  
The One

Abstract We perform a careful study of the infrared sector of massless non-abelian gauge theories in four-dimensional Minkowski spacetime using the covariant phase space formalism, taking into account the boundary contributions arising from the gauge sector of the theory. Upon quantization, we show that the boundary contributions lead to an infinite degeneracy of the vacua. The Hilbert space of the vacuum sector is not only shown to be remarkably simple, but also universal. We derive a Ward identity that relates the n-point amplitude between two generic in- and out-vacuum states to the one computed in standard QFT. In addition, we demonstrate that the familiar single soft gluon theorem and multiple consecutive soft gluon theorem are consequences of the Ward identity.

scholarly journals Infinite-dimensional fermionic symmetry in supersymmetric gauge theories

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Thomas T. Dumitrescu ◽  
Temple He ◽  
Prahar Mitra ◽  
Andrew Strominger
Keyword(s):  
Ward Identity ◽  
Gauge Theories ◽  
Soft Photon ◽  
Supersymmetric Gauge Theories ◽  
Null Infinity ◽  
Infinite Dimensional ◽  
Charged Matter ◽  
Gauge Symmetries ◽  
Supersymmetric Gauge

Abstract We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian $$ \mathcal{N} $$ N = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same $$ \mathcal{N} $$ N = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.

scholarly journals Celestial superamplitude in $$ \mathcal{N} $$ = 4 SYM theory

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Hongliang Jiang
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Scattering Amplitudes ◽  
Momentum Space ◽  
Ward Identity ◽  
Yang Mills ◽  
Conformal Field ◽  
New Perspective ◽  
Celestial Sphere

Abstract Celestial amplitude is a new reformulation of momentum space scattering amplitudes and offers a promising way for flat holography. In this paper, we study the celestial amplitudes in $$ \mathcal{N} $$ N = 4 Super-Yang-Mills (SYM) theory aiming at understanding the role of superconformal symmetry in celestial holography. We first construct the superconformal generators acting on the celestial superfield which assembles all the on-shell fields in the multiplet together in terms of celestial variables and Grassmann parameters. These generators satisfy the superconformal algebra of $$ \mathcal{N} $$ N = 4 SYM theory. We also compute the three-point and four-point celestial super-amplitudes explicitly. They can be identified as the conformal correlation functions of the celestial superfields living at the celestial sphere. We further study the soft and collinear limits which give rise to the super-Ward identity and super-OPE on the celestial sphere, respectively. Our results initiate a new perspective of understanding the well-studied $$ \mathcal{N} $$ N = 4 SYM amplitudes via 2D celestial conformal field theory.

QUANTUM LIOUVILLE FIELD THEORY ON A MANIFOLD WITH BOUNDARY

1998 ◽  
Vol 13 (25) ◽  
pp. 2057-2063
Author(s):  
S. A. APIKYAN
Keyword(s):  
Field Theory ◽  
Functional Equations ◽  
Ward Identity ◽  
Semiclassical Approximation ◽  
Boundary Structure ◽  
Manifold With Boundary ◽  
Structure Constants ◽  
Liouville Field Theory

This letter studies the quantum Liouville field theory on a manifold with boundary. The boundary conformal Ward identity (CWI) is written and its semiclassical approximation is analyzed. This establishes a method of finding the accessory parameters of the theory with boundary. The boundary structure constants of the theory are defined and the functional equations which determine them are derived.

Abstract T P75: Vertex Analysis Demonstrates Significant Changes in Contralesional Thalamus 3 Months After Ischemic Stroke

Stroke ◽  
2015 ◽  
Vol 46 (suppl_1) ◽  
Author(s):  
Nawaf Yassi ◽  
Bruce C Campbell ◽  
Andrew Bivard ◽  
Charles Malpas ◽  
Mark W Parsons ◽  
...  
Keyword(s):  
Ischemic Stroke ◽  
Brain Structures ◽  
Recovery Phase ◽  
Subcortical Structures ◽  
Inferior Surface ◽  
Clinical Endpoints ◽  
Point Vertex ◽  
Number Of Patients ◽  
Surface Changes

Objective: Changes in remote brain structures after stroke may correlate with functional outcomes. We sought to investigate contralesional subcortical structural change after stroke. Methods: 15 patients with carotid territory ischemic stroke underwent 3T MRI within 7 days of onset and at 3 months. Imaging involved a 1mm T1 axial MPRAGE. In 6 patients with left hemispheric stroke, scans were inverted across the midline to allow group comparison. FIRST (Part of FSL) was used to segment subcortical structures including thalamus, pallidum, caudate, putamen, hippocampus, accumbens and brainstem. Analysis was restricted to the non-stroke hemisphere due to the confounding effect of stroke lesions and edema in the lesional hemisphere. Change in volume was assessed as percentage change between the time points. A vertex analysis was performed in order to also identify areas of significant surface atrophy. Briefly, a surface mesh is created for each structure at each time point. Vertex wise statistical analysis then allows for the identifications of areas of significant surface atrophy between baseline and follow-up within the group. Results: Mean age was 71y. Median baseline NIHSS was 9. Vertex analysis demonstrated atrophy over the superior and inferior surface of the contralesional thalamus between baseline and 3 months (figure, p<0.05 multiple comparisons corrected). The median overall change in contralesional thalamic volume was -0.96% (IQR -0.11 - -1.98%), but this difference was not statistically significant (p=0.1). No statistically significant changes in other subcortical structures were found. Contralesional thalamus (blue) superior (A) and inferior (B) views with areas of significant atrophy (red) Conclusions: We have described post stroke surface changes in the contralesional thalamus. This may be a result of deafferentation occurring during the recovery phase. An analysis in a larger number of patients may allow correlation with clinical endpoints.

scholarly journals Axions are blind to anomalies

2019 ◽  
Vol 79 (10) ◽  
Author(s):  
Jérémie Quevillon ◽  
Christopher Smith
Keyword(s):  
Ward Identity ◽  
Gauge Theories ◽  
Feynman Diagrams ◽  
Explicit Calculation ◽  
Gauge Bosons ◽  
Vector Gauge

Abstract The axion couplings to SM gauge bosons are derived in various models, and shown to always arise entirely from non-anomalous fermion loops. They are thus independent of the anomaly structure of the model. This fact is without consequence for vector gauge interactions like QCD and QED, but has a major impact for chiral gauge theories. For example, in the DFSZ axion model, the couplings of axions to electroweak gauge bosons do not follow the pattern expected from chiral anomalies, as we prove by an explicit calculation. The reason for this mismatch is traced back to triangle Feynman diagrams sensitive to the anomalous breaking of the vector Ward identity, and is ultimately related to the conservation of baryon and lepton numbers. Though our analyses are entirely done for true axion models, this observation could have important consequences for axion-like particle searches.

scholarly journals Electroweak fermion triangle loop contributions to the muon anomalous magnetic moment revisited

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Ken Sasaki
Keyword(s):  
Magnetic Moment ◽  
Top Quark ◽  
Anomalous Magnetic Moment ◽  
Ward Identity ◽  
Axial Vector ◽  
Goldstone Boson ◽  
Muon Anomalous Magnetic Moment ◽  
Feynman Gauge ◽  
Unitary Gauge ◽  
The One

Abstract The contribution to the muon anomalous magnetic moment from the fermion triangle loop diagrams connected to the muon line by a photon and a $Z$ boson is re-analyzed in both the unitary gauge and the ’t Hooft–Feynman gauge. With use of the anomalous axial-vector Ward identity, it is shown that the calculation in the unitary gauge exactly coincides with the one in the ’t Hooft–Feynman gauge. The part which arises from the ordinary axial-vector Ward identity corresponds to the contribution of the neutral Goldstone boson. For the top-quark contribution, the one-parameter integral form is obtained up to the order of $m_\mu^2/m_Z^2$. The results are compared with those obtained by the asymptotic expansion method.

Sign in / Sign up

Export Citation Format

Share Document