Related papers: General invertible transformation and physical deg…
We formulate explicitly the necessary and sufficient conditions for the local invertibility of a field transformation involving derivative terms. Our approach is to apply the method of characteristics of differential equations, by treating…
We discuss a field transformation from fields $\psi_a$ to other fields $\phi_i$ that involves derivatives, $\phi_i = \bar \phi_i(\psi_a, \partial_\alpha \psi_a, \ldots ;x^\mu)$, and derive conditions for this transformation to be…
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of…
The Universal Field Equations, recently constructed as examples of higher dimensional dynamical systems which admit an infinity of inequivalent Lagrangians are shown to be linearised by a Legendre transformation. This establishes the…
Relativistic field theory for a vector field on a curved space-time is considered assuming that the Lagrangian field density is quadratic and contains field derivatives of first order at most. By applying standard variational calculus, the…
Invertible disformal transformations serve as a useful tool to explore ghost-free scalar-tensor theories. In this paper, we construct a generalization of invertible disformal transformations that involves arbitrary higher-order covariant…
In this paper I shall consider field theories in a space of four-dimensions which have field variables consisting of the components of a metric tensor and scalar field. The field equations of these scalar-tensor field theories will be…
Multiple scalar fields appear in vast modern particle physics and gravity models. When they couple to gravity non-minimally, conformal transformation is utilized to bring the theory into Einstein frame. However, the kinetic terms of scalar…
Because scaling symmetries of the Euler-Lagrange equations are generally not variational symmetries of the action, they do not lead to conservation laws. Instead, an extension of Noether's theorem reduces the equations of motion to…
Any local field theory can be equivalently reformulated in the so-called unfolded form. General unfolded equations are non-Lagrangian even though the original theory is Lagrangian. Using the theory of a scalar field as a basic example, the…
In this paper, we discuss a gravitational theory based on the generalized gauge field. Our Lagrangian is invariant not only under local Lorentz transformation and the ordinary gauge transformation but also under a new gauge transformation.…
The change of variable theorem is proved under the sole hypothesis of differentiability of the transformation. Specifically, it is shown under this hypothesis that the transformed integral equals the given one over every measurable subset…
As an example of what happens with physically relevant theories like effective gravity, we consider the covariant relativistic theory of a scalar field of arbitrarily higher differential order. A procedure based on the Legendre…
New reparametrisation invariant field equations are constructed which describe $d$-brane models in a space of $d+1$ dimensions. These equations, like the recently discovered scalar field equations in $d+1$ dimensions, are universal, in the…
A variant of the usual Lagrangian scheme is developed which describes both the equations of motion and the variational equations of a system. The required (prolonged) Lagrangian is defined in an extended configuration space comprising both…
Whether Jordan's and Einstein's frame descriptions of F(R) theory of gravity are physically equivalent, is a long standing debate. However, practically none questioned on true mathematical equivalence, since classical field equations may be…
This paper expands on previous work to derive and motivate the Lagrangian formulation of field theories. In the process, we take three deliberate steps. First, we give the definition of the action and derive Euler-Lagrange equations for…
The application of a gauge covariant derivative to the Euler-Lagrange equation yields a shortcut to the equations of motion for a field subject to an external force. The gauge covariant derivative includes an external force as an intrinsic…
We reformulate the self-dual Einstein equation as a trio of differential form equations for simple two-forms. Using them, we can quickly show the equivalence of the theory and 2D sigma models valued in an infinite-dimensional group, which…
We generalize the fractional variational problem by allowing the possibility that the lower bound in the fractional derivative does not coincide with the lower bound of the integral that is minimized. Also, for the standard case when these…