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Register a new userRestoring locality of scalar fields on a causal set by avoiding the use of dAlembertians
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Roman Sverdlov
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In this paper we address the non-locality issue of quantum field theory on a causal set by rewriting it in such a way that avoids the use of dAlembertian. We do that by replacing scalar field over points with scalar field over edges, where the edges are taken to be very long rather than very short. In particular, they are much longer than the size of the laboratory. Due to their large length, we can single out the edges that are almost parallel to each other, and then use directional derivatives in the direction of those edges (as opposed to dAlembertian) along with a constraint that the derivatives are small in the direction perpendicular to those edges, in order to come up with a plane wave. The scalar field is thought to reside at the future end of those edges, which renders the seemingly nonlocal effects of their large length as physically irrelevant. After that we add by hand the interaction of those plane waves that would amount to 4-vertex coupling of plane waves.
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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.
A procedure for evolving hyperbolic systems of equations on compact computational domains with no boundary conditions was recently described in [arXiv:1905.08657]. In that proposal, the computational grid is expanded in spacelike directions with respect to the outermost characteristic and initial data is imposed on the expanded grid boundary. We discuss a related method that removes the need for imposing boundary conditions: the computational domain is excised along a direction spacelike with respect to the innermost going characteristic. We compare the two methods, and provide example evolutions from a code that implements the excision method: evolution of a massless self-gravitating scalar field in spherical symmetry.
The purpose of this paper is two-fold. First, we would like to get rid of common assumption that causal set is bounded and attempt to model its scalar field action under the assumption that it isnt. Secondly, we would like to propose continuous measurement model in this context.
The goal of this paper is to introduce one of t
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