Related papers: About Boundary Terms in Higher Order Theories
We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of gravity, such as F(R) gravity, and argue…
We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…
A general $f(\mathcal{R})$ gravitational theory is considered within the Palatini formalism. By applying the variational principle and the usual conditions on the boundary, we show explicitly that a surface term remains such that as in…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
In this paper we consider second-order field theories in a variational setting. From the variational principle the Euler-Lagrange equations follow in an unambiguous way, but it is well known that this is not true for the Cartan form. This…
In many relevant cases -- e.g., in hamiltonian dynamics -- a given vector field can be characterized by means of a variational principle based on a one-form. We discuss how a vector field on a manifold can also be characterized in a similar…
A variational principle is constructed for gravity coupled to an asymptotically linear dilaton and a p-form field strength. This requires the introduction of appropriate surface terms -- also known as `boundary counterterms' -- in the…
Inspired by problems arising in the geometrical treatment of Yang-Mills theories and Palatini's gravity, the covariant formulation of Hamiltonian dynamical systems as a Hamiltonian field theory of dimension $1+0$ on a manifold with boundary…
When generalizing the principle of least action for fields containing higher order derivatives, in general, it is not possible not to take into account the surface integrated term since it gives direct contribution to the forms of the…
We discuss the construction of boundary contributions to free string field theory actions in the context of the bosonic string. We show that it is generally possible to obtain a well-defined variational principle by adding a simple boundary…
In this paper, we analyze the variation of the gravitational action on a bounded region of spacetime whose boundary contains segments with various characters, including null. We develop a systematic approach to decompose the derivative of…
It is well-known that the presence of a spacetime boundary requires the conventional Einstein-Hilbert (EH) action to be supplemented by the Gibbons-Hawking (GH) boundary term in order to retain the standard variational procedure. When the…
We supplement the string field theory action with boundary terms to make its variational principle well-posed. Central to our considerations is the violation of the stress-energy tensor conservation in non-compact CFTs due to the boundary…
It is shown that under certain boundary conditions the virial theorem has to be modified. We analyze the origin of the extra term and compute it in particular examples. The Coulomb and harmonic oscillator with point interaction have been…
A well-defined variational principle for gravitational actions typically requires to cancel boundary terms produced by the variation of the bulk action with a suitable set of boundary counterterms. This can be achieved by carefully…
We consider free higher derivative theories of scalars and Dirac fermions in the presence of a boundary in general dimension. We establish a method for finding consistent conformal boundary conditions in these theories by removing certain…
Recently it has been proposed that the consistency with T-duality requires the effective action of string theory at order $\alpha'^n$ satisfies the least action principle provided that the values of the massless fields and their derivatives…
Augmented variational principles are introduced in order to provide a definition of relative conservation laws. As it is physically reasonable, relative conservation laws define in turn relative conserved quantities which measure, for…
A variational principle is introduced to provide a new formulation and resolution for several boundary value problems with a variational structure. This principle allows one to deal with problems well beyond the weakly compact structure. As…
We consider Witten's open string field theory in the presence of a non-trivial boundary of spacetime. For the kinetic term, we derive a Gibbons-Hawking-type contribution that has to be added to the action to guarantee a well-defined…