scholarly journals On the optimal local regularity for the Yang-Mills equations in $\mathbb {R}^{4+1}$

1999 ◽  
Vol 12 (1) ◽  
pp. 93-116 ◽  
Author(s):  
Sergiu Klainerman ◽  
Daniel Tataru
Keyword(s):  
Local Regularity ◽  
Yang Mills

scholarly journals Local Regularity for the Harmonic Map and Yang–Mills Heat Flows

2021 ◽  
Author(s):  
Ahmad Afuni
Keyword(s):  
Riemannian Manifolds ◽  
Harmonic Map ◽  
Local Regularity ◽  
Yang Mills ◽  
Heat Flows ◽  
Singular Sets ◽  
Regularity Results ◽  
Local Monotonicity ◽  
Partial Differ ◽  
Singular Time

AbstractWe establish new local regularity results for the harmonic map and Yang–Mills heat flows on Riemannian manifolds of dimension greater than 2 and 4, respectively, obtaining criteria for the smooth local extensibility of these flows. As a corollary, we obtain new characterisations of singularity formation and use this to obtain a local estimate on the Hausdorff measure of the singular sets of these flows at the first singular time. Finally, we show that smooth blow-ups at rapidly forming singularities of these flows are necessarily nontrivial and admit a positive lower bound on their heat ball energies. These results crucially depend on some local monotonicity formulæ for these flows recently established by Ecker (Calc Var Partial Differ Equ 23(1):67–81, 2005) and the Afuni (Calc Var 555(1):1–14, 2016; Adv Calc Var 12(2):135–156, 2019).

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

scholarly journals Wave packet dynamics in Yang-Mills theory

1995 ◽  
Vol 52 (4) ◽  
pp. 2402-2411 ◽  
Author(s):  
C. R. Hu ◽  
S. G. Matinyan ◽  
B. Müller ◽  
A. Trayanov ◽  
T. M. Gould ◽  
...  
Keyword(s):  
Wave Packet ◽  
Yang Mills ◽  
Wave Packet Dynamics

scholarly journals Proof of ultraviolet finiteness for a planar non-supersymmetric Yang–Mills theory

2007 ◽  
Vol 783 (3) ◽  
pp. 227-237 ◽  
Author(s):  
Sudarshan Ananth ◽  
Stefano Kovacs ◽  
Hidehiko Shimada
Keyword(s):  
Yang Mills
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