arXiv subjects

J. Dimock

Publications and source records attributed to J. Dimock.

25 records · Page 2Linked to original sources

arXiv2004

Quantum electrodynamics on the 3-torus. II-The RG flow

We continue the study of quantum electrodynamics on a three dimensional torus as a limit of a lattice gauge theory. In this paper we give a preliminary treatment of the renormalization group flow. We study the propagators which arise under multiple block spin averaging, both in global and local versions. We also study low order perturbation theory. However we do not control remainders. This is left to the more complete treatment of the following paper.

math-ph↗

arXiv2004

Multiparticle Schrodinger operators with point interactions in the plane

We study a system of N bosons in the plane interacting with delta function potentials. After a coupling constant renormalization we show that the Hamiltonian defines a self-adjoint operator and obtain a lower bound for the energy. The same results hold if one includes a regular inter-particle potential.

math-ph↗

arXiv2003

Local String Field Theory

We consider open bosonic strings. The non-interacting multi-string theory is described by certain free string field operators which we construct. These are shown to have local commutators with respect to a center of mass coordinate. The construction is carried out both in the light cone gauge and in a covariant formulation.

math-ph↗

arXiv2003

Markov quantum fields on a manifold

We study scalar quantum field theory on a compact manifold. The free theory is defined in terms of functional integrals. For positive mass it is shown to have the Markov property in the sense of Nelson. This property is used to establish a reflection positivity result when the manifold has a reflection symmetry. In dimension d=2 we use the Markov property to establish a sewing operation for manifolds with boundary circles. Also in d=2 the Markov property is proved for interacting fields.

math-ph↗

arXiv2002

Quantum electrodynamics on the 3-torus -I

We study the ultraviolet problem for quantum electrodynamics on a three dimensional torus. We start with the lattice gauge theory on a toroidal lattice and seek to control the singularities as the lattice spacing is taken to zero. This is done by following the flow of a sequence of renormalization group transformations. The analysis is facilitated by splitting the space of gauge fields into large and small fields at each step following Balaban. In this paper we explore the first step in detail.

math-ph↗

arXiv2001

Locality in Free String Field Theory-II

We study the covariant free bosonic string field theory and explore its locality (causality) properties. We find covariant string fields which are strictly local and covariant, but act on an unconstrained Hilbert space with an indefinite inner product. From these we also define observable fields which act on the physical Hilbert space with an definite inner product. These are shown to be approximately local.

math-ph↗

arXiv1999

Sine-Gordon Revisited

We study the sine-Gordon model in two dimensional space time in two different domains. For beta > 8 pi and weak coupling, we introduce an ultraviolet cutoff and study the infrared behavior. A renormalization group analysis shows that the model is asymptotically free in the infrared. For beta < 8 pi and weak coupling, we introduce an infrared cutoff and study the ultraviolet behavior. A renormalization group analysis shows that the model is asymptotically free in the ultraviolet.

math-ph↗