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Register a new userEntropy and the Link Action in the Causal Set Path-Sum
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In causal set theory the gravitational path integral is replaced by a path-sum over a sample space $Omega_n$ of $n$-element causal sets. The contribution from non-manifold-like orders dominates $Omega_n$ for large $n$ and therefore must be tamed by a suitable action in the low energy limit of the theory. We extend the work of Loomis and Carlip on the contribution of sub-dominant bilayer orders to the causal set path-sum and show that the link action suppresses the dominant Kleitman-Rothschild orders for the same range of parameters.
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de Sitter cosmological horizons are known to exhibit thermodynamic properties similar to black hole horizons. In this work we study causal set de Sitter horizons, using Sorkins spacetime entanglement entropy (SSEE) formula, for a conformally coupled quantum scalar field. We calculate the causal set SSEE for the Rindler-like wedge of a symmetric slab of de Sitter spacetime in $d=2,4$ spacetime dimensions using the Sorkin-Johnston vacuum state. We find that the SSEE obeys an area law when the spectrum of the Pauli-Jordan operator is appropriately truncated in both the de Sitter slab as well as its restriction to the Rindler-like wedge. Without this truncation, the SSEE satisfies a volume law. This is in agreement with Sorkin and Yazdis calculations for the causal set SSEE for nested causal diamonds in $mathbb{M}^2$, where they showed that an area law is obtained only after truncating the Pauli-Jordan spectrum. In this work we explore different truncation schemes with the criterion that the SSEE so obtained obeys an area law.
The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first using quantities that have a direct correspondent in the case of a causal set, namely volumes, causal relations, and timelike lengths, as variables to describe the geometry. In this step, the local Lagrangian density $L(f;x)$ for a set of fields $f$ is recast into a quasilocal expression $L_0(f;p,q)$ that depends on pairs of causally related points $p prec q$ and is a function of the values of $f$ in the Alexandrov set defined by those points, and whose limit as $p$ and $q$ approach a common point $x$ is $L(f;x)$. We then describe how to discretize $L_0(f;p,q)$, and use it to define a discrete action.
The causal set theory (CST) approach to quantum gravity postulates that at the most fundamental level, spacetime is discrete, with the spacetime continuum replaced by locally finite posets or causal sets. The partial order on a causal set represents a proto-causality relation while local finiteness encodes an intrinsic discreteness. In the continuum approximation the former corresponds to the spacetime causality relation and the latter to a fundamental spacetime atomicity, so that finite volume regions in the continuum contain only a finite number of causal set elements. CST is deeply rooted in the Lorentzian character of spacetime, where a primary role is played by the causal structure poset. Importantly, the assumption of a fundamental discreteness in CST does not violate local Lorentz invariance in the continuum approximation. On the other hand, the combination of discreteness and Lorentz invariance gives rise to a characteristic non-locality which distinguishes CST from most other approaches to quantum gravity. In this review we give a broad, semi-pedagogical introduction to CST, highlighting key results as well as some of the key open questions. This review is intended both for the beginner student in quantum gravity as well as more seasoned researchers in the field.
This is the second paper in a series on the dynamics of matter fields in the causal set approach to quantum gravity. We start with the usual expression for the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field, in which the gauge field is represented by a connection form, and show how to write it in terms of holonomies between pairs of points, causal relations, and volumes or timelike distances, all of which have a natural correspondence in the causal set context. In the second part of the paper we present an alternative model, in which the gauge field appears as the result of a procedure inspired by the Kaluza-Klein reduction in continuum field theory, and the dynamics can be derived simply using the gravitational Lagrangian of the theory.
The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus additional scalar fields. Grassmann nature is being enforced by allowing measure to take both positive and negative values, and also by introducing a vector space to have both commutting dot product and anticommutting wedge product.
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