Related papers: Higher derivative scalar-tensor monomials and thei…
In these notes we study hyperplane arrangements having at least one logarithmic derivation of degree two that is not a combination of degree one logarithmic derivations. It is well-known that if a hyperplane arrangement has a linear…
We develop some aspects of the theory of derivators, pointed derivators, and stable derivators. As a main result, we show that the values of a stable derivator can be canonically endowed with the structure of a triangulated category.…
Higher-derivative theories of free higher-spin fields are investigated focusing on their symmetries. Generalizing familiar two-derivative constrained formulations, we first construct less-constrained Einstein-like and Maxwell-like…
In this paper I shall show how notions of Finsler geometry can be used to construct a new type of geometry using a scalar field, f, on the cotangent bundle of a differentiable manifold, M. This new geometry will be called Lorentzian…
We consider a new form of theories of gravity in which the action is written in terms of the Ricci scalar and its first and second derivatives. Despite the higher derivative nature of the action, the theory is free from ghost under an…
We study the covariant derivatives of an eigenfunction for the Laplace-Beltrami operator on a complete, connected Riemannian manifold with nonzero constant sectional curvature. We show that along every parallel tensor, the covariant…
In this article, we give all the Weitzenb\"ock-type formulas among the geometric first order differential operators on the spinor fields with spin $j+1/2$ over Riemannian spin manifolds of constant curvature. Then we find an explicit…
This is a book on higher-categorical diagrams, including pasting diagrams. It aims to provide a thorough and modern reference on the subject, collecting, revisiting and expanding results scattered across the literature, informed by recent…
A discussion of an extended class of higher-derivative classical theories of gravity is presented. A procedure is given for exhibiting the new propagating degrees of freedom, at the full non-linear level, by transforming the…
We describe how to approximate the Riemann curvature tensor as well as sectional curvatures on possibly infinite-dimensional shape spaces that can be thought of as Riemannian manifolds. To this end, we extend the variational time…
In this work we study various aspects of supersymmetric three-dimensional higher-derivative field theories. We classify all possible models without derivative terms in the auxiliary field of the fermionic sector and find that scalar field…
A brief discussion of the recent interest in light scalar mesons motivates the study of a generalized linear sigma model. In an SU(3) flavor invariant version of the model there is a prediction that the the lighter scalars have sizeable…
We discuss a class of teleparallel scalar-torsion theories of gravity, which is parametrized by five free functions of the scalar field. The theories are formulated covariantly using a flat, but non-vanishing spin connection. We show how…
After dimensional reduction to three dimensions, the lowest order effective actions for pure gravity, M-theory and the Bosonic string admit an enhanced symmetry group. In this paper we initiate study of how this enhancement is affected by…
The fourth derivative models for two dimensional gravity are shown to be equivalent to the special version of the nonlinear sigma models coupled to 2d quantum gravity. The reduction consists in the introduction of the auxiliary scalar…
In the context of the Higher-Order Maxwell-Einstein-Scalar (HOMES) theories, which are invariant under spacetime diffeomorphisms and $U(1)$ gauge symmetry, we study two broad subclasses: the first is up to linear in $R_{\mu\nu\alpha\beta}$,…
Higher derivative corrections are ubiquitous in effective field theories, which seemingly introduces new degrees of freedom at successive order. This is actually an artefact of the implicit local derivative expansion defining effective…
We trace derivations through Demazure's correspondence between a finitely generated positively graded normal $k$-algebras $A$ and normal projective $k$-varieties $X$ equipped with an ample $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $D$. We…
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann…
The higher order symmetries are investigated in a covariant Hamiltonian formulation. The covariant phase-space approach is extended to include the presence of external gauge fields and scalar potentials. The special role of the Killing-Yano…