Related papers: About Boundary Terms in Higher Order Theories
We study Einstein gravity in a finite spatial region. By requiring a well-defined variational principle, we identify all local boundary conditions, derive surface observables, and compute their algebra. The observables arise as induced…
In this paper, we investigate whether Variational Principles can be associated with the Helmholtz equation subject to impedance (absorbing) boundary conditions. This model has been extensively studied in the literature from both…
Infinite order differential equations have come to play an increasingly significant role in theoretical physics. Field theories with infinitely many derivatives are ubiquitous in string field theory and have attracted interest recently also…
Recent work has shown that the addition of an appropriate covariant boundary term to the gravitational action yields a well-defined variational principle for asymptotically flat spacetimes and thus leads to a natural definition of conserved…
Effective theories are non-local at the scale of the eliminated heavy particles modes. The gradient expansion which represents such non-locality must be truncated to have treatable models. This step leads to the proliferation of the degrees…
We utilize quantum superposition principle to establish the improvable upper and lower bounds on the stronger uncertainty relation, i.e., the "weighted-like" sum of the variances of observables. Our bounds include some free parameters which…
A Lorentz non-invariant higher derivative effective action in flat spacetime, characterised by a constant vector, can be made invariant under infinitesimal Lorentz transformations by restricting the allowed field configurations. These…
We develop furthur the correspondence between a d+1 dimensional theory and a d dimensional one with the "radial" (d+1)th corodinate \rho playing the role of an evolution parameter. We discuss the evolution of an effective action defined on…
We reexamine the problem of having nonconservative equations of motion arise from the use of a variational principle. In particular, a formalism is developed that allows the inclusion of fractional derivatives. This is done within the…
A methodology on making the variational principle well-posed in degenerate systems is constructed. In the systems including higher-order time derivative terms being compatible with Newtonian dynamics, we show that a set of position…
In the area of symbolic-numerical computation within computer algebra, an interesting question is how "close" a random input is to the "critical" ones, like the singular matrices in linear algebra or the polynomials with multiple roots for…
This dissertation investigates three main topics, all of which dealing with alternative, higher-order gravity theories in four dimensions. Firstly, we study the variational and conformal structure of those theories. Next, we analyse their…
Different routes towards the canonical formulation of a classical theory result in different canonically equivalent Hamiltonians, while their quantum counterparts are related through appropriate unitary transformation. However, for…
We consider the most general class of linear boundary-value problems for ordinary differential systems, of order $r\geq1$, whose solutions belong to the complex space $C^{(n+r)}$, with $0\leq n\in\mathbb{Z}$. The boundary conditions can…
If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
Based on the principle of relativity, we find that the sufficient and necessary condition for the general covariance of a field theory actually requires more than the invariance of its local Langrangian density. If the spacetime is not a…
The higher derivative field theories are notorious for the stability problems both at classical and quantum level. Classical instability is connected with unboundedness of the canonical energy, while the unbounded energy spectrum leads to…
Lately, to provide a solid ground for quantization of the open string theory with a constant B-field, it has been proposed to treat the boundary conditions as hamiltonian constraints. It seems that this proposal is quite general and should…
The boundary state formalism is used to confirm predictions from non-commutativity for the derivative corrections to the Dirac--Born--Infeld and Chern--Simons actions, at all orders in derivatives. As anticipated by S. Mukhi, the method…