Related papers: Gravity and Matter in Causal Set Theory
It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with…
We explore the idea of asymptotic silence in causal set theory and find that causal sets approximated by continuum spacetimes exhibit behaviour akin to asymptotic silence. We make use of an intrinsic definition of spatial distance between…
We figure out the explicit expression for the trace of the field equations associated to generic higher derivative theories of gravity endowed with Lagrangians depending upon the metric and its Riemann tensor, together with arbitrary order…
In this note, we establish a version of the local Cauchy-Crofton formula for definable sets in Henselian discretely valued fields of characteristic zero. It allows to compute the motivic local density of a set from the densities of its…
The Lagrangian dynamics of a single fluid element within a self-gravitational matter field is intrinsically non-local due to the presence of the tidal force. This complicates the theoretical investigation of the non-linear evolution of…
In this paper we introduce a new general framework for the study of phenomenological quantum gravity theories (PQG). The key idea is the introduction of two different types of spacetime, an observer-independent spacetime (modeled by a…
A first- and second-order relation between cosmic density and peculiar-velocity fields is presented. The calculation is purely Lagrangian and it is derived using the second-order solutions of the Lagrange-Newton system obtained by Buchert &…
In this paper we will define a Lagrangian for scalar and gauge fields on causal sets, based on the selection of an Alexandrov set in which the variations of appropriate expressions in terms of either the scalar field or the gauge field…
We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory…
The goal of this work, motivated by the desire to understand causality in classical and quantum gravity, is an in depth investigation of causality in classical field theories with quasilinear equations of motion, of which General Relativity…
We derive the equations of linear cosmological perturbations for the general Lagrangian density $f (R,\phi, X)/2+L_c$, where $R$ is a Ricci scalar, $\phi$ is a scalar field, and $X=-(\nabla \phi)^2/2$ is a field kinetic energy. We take into…
We show that in cosmology the gravitational action of the far away matter has quite relevant effects, if retardation of the forces and discreteness of matter (with its spatial correlation) are taken into account. The expansion rate is found…
We discuss the physical meaning and the geometric interpretation of causality implementation in classical field theories. Causality is normally implemented through kinematical constraints on fields but we show that in a zero-distance limit…
We extend a recent formulation of quantum continuum mechanics [J. Tao et. al, Phys. Rev. Lett. {\bf 103}, 086401 (2009)] to many-body systems subjected to a magnetic field. To accomplish this, we propose a modified Lagrangian approach, in…
The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived…
The coupling of gravity to matter is explored in the linearized gravity limit. The usual derivation of gravity-matter couplings within the quantum-field-theoretic framework is reviewed. A number of inconsistencies between this derivation of…
By summarizing and extending the Lagrangian densities of the general relativity and the Kibble's gauge theory of gravitation,a further generalized Lagrangian density for a gravitational system is obtained and analyzed in greater detail,…
A reflexive relation on a set can be a starting point in defining the causal structure of a spacetime in General Relativity and other relativistic theories of gravity. If we identify this relation as the relation between lightlike separated…
I present a model of discrete gravity, which is formulated in terms of a topological gauge theory with defects. The theory has no local degrees of freedom and the gravitational field is trivial everywhere except at a number of colliding…
This article describes the regularization of the generally relativistic gauge field representation of gravity on a piecewise linear lattice. It is a part of the program concerning the classical relativistic theory of fundamental…