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Roman Sverdlov

Publications and source records attributed to Roman Sverdlov.

31 records · Page 2Linked to original sources
arXiv2010

Pilot Wave model that includes creation and annihilation of particles

The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing determinism. This has been previously attempted in an article by the same author titled "Incorporating particle creation and annihilation in Pilot Wave model", in a much less satisfactory way. In this paper I would like to "clean up" some of the things. In particular, I would like to get rid of a very unnatural concept of "visibility" of particles, which makes the model much simpler. On the other hand, I would like to add a mechanism for decoherence, which was absent in the previous version.

physics.gen-ph↗
arXiv2010

Completely local interpretation of quantum field theory

The purpose of this paper is to come up with a framework that "converts" existing concepts from configuration space to ordinary one. This is done by modeling our universe as a big "computer" that simulates configuration space. If that "computer" exists in ordinary space and is ran by "classical" laws, our theory becomes "classical" by default. We have first applied this concept to a version of quantum field theory in which elementary particles have size (that is, a theory that does not yet exists). After that, we have also done the same with Pilot Wave model of discrete jumps, due to Dürr et el.

physics.gen-ph↗
arXiv2010

Incorporating particle creation and annihilation into Bohm's Pilot Wave model

The purpose of this paper is to come up with a Pilot Wave model of quantum field theory that incorporates particle creation and annihilation without sacrificing causality. In some sense, this work echoes the work of Nikolić (I call "visibility" what he calls "effectiveness"), but in my work I choose position and visibility as beables, as opposed to field beables that are used in his.

physics.gen-ph↗
arXiv2010

Causal set as a discretized phase spacetime

The first goal of this paper is to show that discreteness, locality, and relativistic covariance can peacefully coexist if the ordinary spacetime (OST) is replaced with phase spacetime (PST) as a geometric background of a Poisson process, where PST is a spacetime generalization of a notion of phase space (this is a 7-dimensional version of the 8-dimensional structure proposed by Caianiello). Furthermore, Caianiello's idea of finite acceleration is implemented. After this is done, the paper then goes on to generalize the geometric notions obtained from the intuition of PST to a general discrete causal set, without any geometric background. It then takes advantage of the absence of lightcone singularity to attempt to tackle the definition of PST-like causal set; that is, a discrete system that approximates the geometrical properties that we would expect from continuum PST. Finally, the paper proceeds to introduce quantum field theory on a causal set, and shows that the locality gained by switching from OST to PST brings us one step closer to be able to treat quantum field theory on a causal set analytically rather than numerically.

gr-qc↗
arXiv2009

Novel definition of Grassmann numbers and spinor fields

The goal of this paper is to define fermionic field in terms of non-orthonormal vierbeins, where fluctuations away from orthonormality are viewed as fermionic field. Furthermore, Grassmann numbers are defined in a way that makes literal sense.

gr-qc↗
arXiv2009

Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets

This is is a copy of dissertation that I have submitted in defense of my ph.d. thesis, with some minor changes that I have made since then. The goal of the project is to generalize matter fields and their Lagrangians from regular space time to causal sets.

gr-qc↗
arXiv2009

Dynamics for causal sets with matter fields: A Lagrangian-based approach

We present a framework for the dynamics of causal sets and coupled matter fields, which is a simplification and generalization of an approach we recently proposed. Given a set of fields including the gravitational one, the main step in implementing our proposal consists in writing their continuum-based action using as variables for the spacetime geometry the causal order and volume element. One then discretizes the resulting expression, with a procedure designed to maintain covariance. After a discussion of the general framework, we treat in detail the case of scalar fields, Yang-Mills gauge fields and the gravitational field.

gr-qc↗
arXiv2008

Spinor fields in Causal Set 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.

gr-qc↗
arXiv2008

A Geometrical Description of Spinor Fields

The goal of this paper is to present the way to define fermionic fields and their Lagrangians in terms of three orthogonal vector fields of norm 1 together with two real valued scalar fields. This paper is based on a toy model where there are no Grassmann variables.

gr-qc↗
arXiv2008

Gauge Fields in Causal Set Theory

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.

gr-qc↗
arXiv2008

Gravity and Matter in Causal Set Theory

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.

gr-qc↗