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A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…
We review higher-dimensional unified theories from the general relativity, rather than the particle physics side. Three distinct approaches to the subject are identified and contrasted: compactified, projective and noncompactified. We…
We investigate higher-dimensional $\Delta$-systems indexed by finite sets of ordinals, isolating a particular definition thereof and proving a higher-dimensional version of the classical $\Delta$-system lemma. We focus in particular on…
When higher-derivative terms are added to a gravitational action, black hole solutions and their thermodynamic properties are generally corrected. Recent progress has shown that, by treating higher-derivative operators as perturbations, the…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
We generalize the dual notions of "expansion" and "collapse" so they can be applied to arbitrary metric spaces. We also expand the theory to allow for infinitely many such moves. Those tools are then employed to prove a variety of…
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the…
Quantum cosmology implies corrections to the classical equations of motion which may lead to significant departures from the classical trajectory, especially at high curvature near the big-bang singularity. Corrections could in principle be…
We study conformal theories of gravity, i.e. those whose action is invariant under the local transformation g_{\mu\nu} -> \omega^2 (x) g_{\mu\nu}. As is well known, in order to obtain Einstein gravity in 4D it is necessary to introduce a…
We examine the phenomenological implications at colliders for the existence of higher-derivative gravity terms as extensions to the Randall-Sundrum model. Such terms are expected to arise on rather general grounds, e.g., from string theory.…
We consider higher derivative CP(N) model in 2+1 dimensions with the Wess-Zumino-Witten term and the topological current density squared term. We quantize the theory by using the auxiliary gauge field formulation in the path integral method…
In effective field theory, the positivity bounds of higher derivative operators are derived from analyticity, causality, and unitarity. We show that the positivity bounds on some operators of the effective field theory, e.g.,…
We consider a general Kaluza-Klein reduction of a truncated Lovelock theory. We find necessary geometric conditions for the reduction to be consistent. The resulting lower-dimensional theory is a higher derivative scalar-tensor theory,…
Higher-dimensional theories with time-like and space-like extra dimensions are compared both from the conceptual and from the phenomenological points of view. In this context causality and unitarity are discussed. It is shown that…
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 study higher-order theories of gravitation; in particular, we will focus our attention on the second-order theory, in which conformal symmetry can be implemented.
The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order theories of gravity. We can define effective pressure and energy density directly connected to the Ricci scalar of curvature of a generic…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
We present a high-order compact finite difference approach for a class of parabolic partial differential equations with time and space dependent coefficients as well as with mixed second-order derivative terms in $n$ spatial dimensions.…
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…