Concerning conservation laws resulting from geometric invariance groups for field theories

1974 ◽  
Vol 15 (6) ◽  
pp. 683-686 ◽  
Author(s):  
Benjamin F. Plybon
Keyword(s):  
Conservation Laws ◽  
Field Theories ◽  
Geometric Invariance ◽  
Invariance Groups

Perturbations of conservation laws in field theories

1986 ◽  
Vol 167 (2) ◽  
pp. 354-389 ◽  
Author(s):  
Judith M Arms ◽  
Ian M Anderson
Keyword(s):  
Conservation Laws ◽  
Field Theories

scholarly journals USING CONSERVATION LAWS TO SOLVE TODA FIELD THEORIES

1996 ◽  
Vol 11 (10) ◽  
pp. 1831-1853 ◽  
Author(s):  
ERLING G.B. HOHLER ◽  
KÅRE OLAUSSEN
Keyword(s):  
Field Theory ◽  
Differential Equations ◽  
Conservation Laws ◽  
Closed System ◽  
Transformation Group ◽  
Field Theories ◽  
Real Form ◽  
Local Conservation ◽  
Considerable Detail ◽  
Toda Field Theory

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be used to solve it. We show that for models where the conservation laws can be written in one-sided forms, [Formula: see text] like the problem can always be reduced to solving a closed system of ordinary differential equations. We investigate the A1, A2 and B2 Toda field theories in considerable detail from this viewpoint. One of our findings is that there is in each case a transformation group intrinsic to the model. This group is built on a specific real form of the Lie algebra used to label the Toda field theory. It is the group of field transformations which leaves the conserved densities invariant.

scholarly journals HIGHER-ORDER NOETHER SYMMETRIES IN k-SYMPLECTIC HAMILTONIAN FIELD THEORY

2013 ◽  
Vol 10 (08) ◽  
pp. 1360013
Author(s):  
NARCISO ROMÁN-ROY ◽  
MODESTO SALGADO ◽  
SILVIA VILARIÑO
Keyword(s):  
Field Theory ◽  
Conservation Laws ◽  
Vector Fields ◽  
Higher Order ◽  
Field Theories ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Noether's Theorem ◽  
Infinitesimal Transformations

For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by some kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of suitable generalizations of Noether's theorem.

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