Related papers: Linear Time-Dependent Invariants for Scalar Fields…
Space-like and time-like invariant space-time intervals are used to analyse measurements of spatial and temporal distances. The former are found to be Lorentz invariant --there is no `relativistic length contraction', whereas the latter…
Real-time classical SU($N$) gauge theories at non-zero temperature contain linear divergences. We introduce counterterms for these divergences in the equations of motion in the continuum and on the lattice. These counterterms can be given…
We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is…
The invariant is one of central topics in science, technology and engineering. The differential invariant is essential in understanding or describing some important phenomena or procedures in mathematics, physics, chemistry, biology or…
This letter investigates the Lie point symmetries and conserved quantities of the Lagrangian systems on time scales, which unify the Lie symmetries of the two cases for the continuous and the discrete Lagrangian systems. By defining the…
A simple local proof of Noether's Second Theorem is given. This proof immediately leads to a generalization of the theorem, yielding conservation laws and/or explicit relationships between the Euler--Lagrange equations of any variational…
By using the Lie's invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schr\"{o}dinger equations with variable coefficients. Starting from the equivalence generators we construct…
We propose the method for obtaining invariants of arbitrary representations of Lie groups that reduces this problem to known problems of linear algebra. The basis of this method is the idea of a special extension of the representation…
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
We construct infinite dimensional symmetries of a complex, free scalar field on curved space-times generated by isometries of the space-time. We use the Anti de-Sitter backgrounds as an example and check that the boundary terms appearing in…
We present an intersection-theoretical approach to the invariants of plane curve singularities $\mu$, $\delta$, $r$ related by the Milnor formula $2\delta=\mu+r-1$. Using Newton transformations we give formulae for $\mu$, $\delta$, $r$…
For k-symplectic Hamiltonian field theories, we study infinitesimal transformations generated by certain kinds of vector fields which are not Noether symmetries, but which allow us to obtain conservation laws by means of a suitable…
We develop a non-linear framework for describing long-wavelength perturbations in multiple-field inflation. The basic variables describing inhomogeneities are defined in a non-perturbative manner, are invariant under changes of time slicing…
Based on the recent result that, if the masses of timelike fields are point-dependent fields themselves, the action of matter fields is conformal form-invariant in its standard form, and on the active and passive approaches to conformal…
The linear approximation of scalar-tensor theories of gravity is obtained in the physical (Jordan) frame under the 4+0 (covariant) and 3+1 formalisms. Then the weak-field limit is analyzed and the conditions leading to significant…
The method of Lagrangians with covariant derivative (MLCD) is applied to a special type of Lagrangian density depending on scalar and vector fields as well as on their first covariant derivatives. The corresponding Euler-Lagrange's…
Ermakov systems possessing Noether point symmetry are identified among the Ermakov systems that derive from a Lagrangian formalism and, the Ermakov invariant is shown to result from an associated symmetry of dynamical character. The Ermakov…
In this Letter, we find suitable potentials in the multiple scalar fields scenario by using the Noether symmetry approach. We discussed three models with multiple scalar fields: N-quintessence with positive kinetic terms, N-phantom with…
We present a general algorithm constructing a discretization of a classical field theory from a Lagrangian. We prove a new discrete Noether theorem relating symmetries to conservation laws and an energy conservation theorem not based on any…