Related papers: Substituting fields within the action: consistency…
A didactic and systematic derivation of Noether point symmetries and conserved currents is put forward in special relativistic field theories, without a priori assumptions about the transformation laws. Given the Lagrangian density, the…
Usually we consider the symmetry of action as the symmetry of the theory, however, in the Keplar problem the scaling symmetry existing in equa tion of motion is not the ones for action. It changes the multiplicative c onstant of action and…
There exists a paradox in quantum field theory: substituting a field configuration which solves a subset of the field equations into the action and varying it is not necessarily equivalent to substituting that configuration into the…
We analyze how gauge fixing, which is required by any practical continuum approach to gauge systems, can interfere with the physical symmetries of such systems. In principle, the gauge fixing procedure, which deals with the (unphysical)…
It is proved that in order to keep both the Lagrangian and the motion equation of non-Abelian gauge fields unchanged under the gauge transformation simultaneously, a certain restriction conditions should be established between the gauge…
We introduce an generalized action functional describing the equations of motion and the variational equations for any Lagrangian system. Using this novel scheme we are able to generalize Noether's theorem in such a way that to any…
Study of gauge symmetry is carried over the different interacting and noninteracting field theoretical models through a prescription based on lagrangian formulation. It is found that the prescription is capable of testing whether a given…
On the basis of gauge principle in the field theory, a new variational formulation is presented for flows of an ideal fluid. The fluid is defined thermodynamically by mass density and entropy density, and its flow fields are characterized…
Anti-Hermitian mass terms are considered, in addition to Hermitian ones, for PT-symmetric complex-scalar and fermionic field theories. In both cases, the Lagrangian can be written in a manifestly symmetric form in terms of the PT-conjugate…
Several aspects of the connection between conserved integrals (invariants) and symmetries are illustrated within a hybrid Lagrangian-Hamiltonian framework for dynamical systems. Three examples are considered: a nonlinear oscillator with…
A statistical mechanism is proposed for symmetrization of an extra space. The conditions and rate of attainment of a symmetric configuration and, as a consequence, the appearance of gauge invariance in low-energy physics is discussed. It is…
Using a generalised Noether prescription we are able to extract all the currents and their conservation laws in space dependent shift symmetric theories. Various identities among the currents in the matter sector are found that form the…
Action-dependent field theories are systems where the Lagrangian or Hamiltonian depends on new variables that encode the action. They model a larger class of field theories, including non-conservative behavior, while maintaining a…
Equations of motion for a general relativistic post-Newtonian Lagrangian approach mainly refer to acceleration equations, i.e. differential equations of velocities. They are directly from the Euler-Lagrangian equations, and usually have…
Symmetries and, in particular, Cartan (Noether) symmetries and conserved quantities (conservation laws) are studied for the multisymplectic formulation of first and second order Lagrangian classical field theories. Noether-type theorems are…
We consider a classical field theory whose equations of motion follow from the least action principle, but the class of admissible trajectories is restricted by differential equations. The key element of the proposed construction is the…
Modified theories of gravity usually present new degrees of freedom, as well as higher order derivatives, wrong signs in certain terms and complicated couplings already present in the Lagrangian from the beginning or originated by the field…
A symmetry analysis is presented for the three-dimensional nonrelativistic motion of charged particles in arbitrary stationary electromagnetic fields. The general form of the Lie point symmetries is found along with the fields that respect…
Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition,…
Based on the most general principles of reality, gauge and reparametrization invariance, a problem of constructing the action describing dynamics of a classical color-charged particle interacting with background non-Abelian gauge and…