scholarly journals Gauge functions and Galilean invariance of Lagrangians

2020 ◽  
Vol 384 (26) ◽  
pp. 126642 ◽  
Author(s):  
Z.E. Musielak ◽  
T.B. Watson
Keyword(s):  
Galilean Invariance ◽  
Gauge Functions

scholarly journals The Yang-Mills heat equation with finite action in three dimensions

2022 ◽  
Vol 275 (1349) ◽  
Author(s):  
Leonard Gross
Keyword(s):  
Heat Equation ◽  
Three Dimensional ◽  
Strong Solutions ◽  
Three Dimensions ◽  
Dimensional Manifold ◽  
Uniqueness Of Solutions ◽  
Reconstruction Procedure ◽  
Content Type ◽  
Yang Mills ◽  
Gauge Functions

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over R 3 \mathbb {R}^3 and over a bounded open convex set in R 3 \mathbb {R}^3 . The initial data is taken to lie in the Sobolev space of order one half, which is the critical Sobolev index for this equation over a three dimensional manifold. The existence is proven by solving first an augmented, strictly parabolic equation and then gauge transforming the solution to a solution of the Yang-Mills heat equation itself. The gauge functions needed to carry out this procedure lie in the critical gauge group of Sobolev regularity three halves, which is a complete topological group in a natural metric but is not a Hilbert Lie group. The nature of this group must be understood in order to carry out the reconstruction procedure. Solutions to the Yang-Mills heat equation are shown to be strong solutions modulo these gauge functions. Energy inequalities and Neumann domination inequalities are used to establish needed initial behavior properties of solutions to the augmented equation.

scholarly journals Filtered lattice Boltzmann collision formulation enforcing isotropy and Galilean invariance

2020 ◽  
Vol 95 (3) ◽  
pp. 034003 ◽  
Author(s):  
Hudong Chen ◽  
Raoyang Zhang ◽  
Pradeep Gopalakrishnan
Keyword(s):  
Lattice Boltzmann ◽  
Galilean Invariance

Galilean invariance of Omega vortex identification method

2019 ◽  
Vol 31 (2) ◽  
pp. 249-255 ◽  
Author(s):  
Jian-ming Liu ◽  
Yi-qian Wang ◽  
Yi-sheng Gao ◽  
Chaoqun Liu
Keyword(s):  
Galilean Invariance ◽  
Vortex Identification ◽  
Identification Method

scholarly journals Lagrangians, Gauge Functions, and Lie Groups for Semigroup of Second-Order Differential Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Z. E. Musielak ◽  
N. Davachi ◽  
M. Rosario-Franco
Keyword(s):  
Differential Equations ◽  
Lie Groups ◽  
Lie Group ◽  
Algebraic Structure ◽  
Second Order ◽  
Lagrangian Formalism ◽  
Group Approach ◽  
Second Order Differential Equations ◽  
Gauge Functions ◽  
The Relationship

A set of linear second-order differential equations is converted into a semigroup, whose algebraic structure is used to generate novel equations. The Lagrangian formalism based on standard, null, and nonstandard Lagrangians is established for all members of the semigroup. For the null Lagrangians, their corresponding gauge functions are derived. The obtained Lagrangians are either new or generalization of those previously known. The previously developed Lie group approach to derive some equations of the semigroup is also described. It is shown that certain equations of the semigroup cannot be factorized, and therefore, their Lie groups cannot be determined. A possible solution of this problem is proposed, and the relationship between the Lagrangian formalism and the Lie group approach is discussed.

Galilean-invariance ambiguity in the nonrelativistic pion-nucleon absorption operator

1974 ◽  
Vol 10 (3) ◽  
pp. 1225-1226 ◽  
Author(s):  
M. Bolsterli ◽  
W. R. Gibbs ◽  
B. F. Gibson ◽  
G. J. Stephenson
Keyword(s):  
Galilean Invariance ◽  
Pion Nucleon
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