Symmetries and Conservation Laws

2018 ◽  
pp. 105-133
Author(s):  
Yemima Ben-Menahem
Keyword(s):  
Conservation Laws ◽  
Gauge Theories ◽  
A Priori ◽  
Exclusion Principle ◽  
Gauge Freedom ◽  
Causal Function ◽  
Symmetry Principles ◽  
Conceptual Relation ◽  
Local Symmetries ◽  
Global And Local

This chapter examines how symmetry principles—despite their a priori appearance—function as causal constraints through their conceptual relation with conservation laws. It first provides an overview of how symmetries are linked to causation by focusing on some of their interconnections with other members of the causal family. It then considers an excellent illustration of the causal function of symmetries in physics, Pauli's exclusion principle, before discussing conservation laws in relation to symmetries. The chapter then explains the distinction between active and passive symmetries, and between global and local symmetries (or geometric versus dynamic symmetries, respectively), as well as gauge theories and the notion of gauge freedom. The chapter concludes with an analysis of Curie's principle and how it is intertwined with symmetries.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

scholarly journals A priori estimates for rough PDEs with application to rough conservation laws

2019 ◽  
Vol 276 (12) ◽  
pp. 3577-3645 ◽  
Author(s):  
Aurélien Deya ◽  
Massimiliano Gubinelli ◽  
Martina Hofmanová ◽  
Samy Tindel
Keyword(s):  
Conservation Laws ◽  
A Priori Estimates ◽  
A Priori ◽  
Priori Estimates

scholarly journals Discrete canonical analysis of three-dimensional gravity with cosmological constant

2015 ◽  
Vol 30 (15) ◽  
pp. 1550080
Author(s):  
J. Berra-Montiel ◽  
J. E. Rosales-Quintero
Keyword(s):  
Cosmological Constant ◽  
Constant Curvature ◽  
Three Dimensional ◽  
Canonical Analysis ◽  
Gauge Freedom ◽  
Dimensional Gravity ◽  
Local Symmetries ◽  
Lattice Approach ◽  
Hamiltonian Analysis ◽  
The Continuum

We discuss the interplay between standard canonical analysis and canonical discretization in three-dimensional gravity with cosmological constant. By using the Hamiltonian analysis, we find that the continuum local symmetries of the theory are given by the on-shell space–time diffeomorphisms, which at the action level, correspond to the Kalb–Ramond transformations. At the time of discretization, although this symmetry is explicitly broken, we prove that the theory still preserves certain gauge freedom generated by a constant curvature relation in terms of holonomies and the Gauss's law in the lattice approach.

Symmetries and conservation laws in gauge theories

1980 ◽  
Vol 127 (2) ◽  
pp. 257-273 ◽  
Author(s):  
R Jackiw ◽  
N.S Manton
Keyword(s):  
Conservation Laws ◽  
Gauge Theories
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