arXiv subjects

James P. Edwards

Publications and source records attributed to James P. Edwards.

46 records · Page 3Linked to original sources

arXiv2017

Worldline colour fields and non-Abelian quantum field theory

In the worldline approach to non-Abelian field theory the colour degrees of freedom of the coupling to the gauge potential can be incorporated using worldline "colour" fields. The colour fields generate Wilson loop interactions whilst Chern-Simons terms project onto an irreducible representation of the gauge group. We analyse this augmented worldline theory in phase space focusing on its supersymmetry and constraint algebra, arriving at a locally supersymmetric theory in superspace. We demonstrate canonical quantisation and the path integral on $S^{1}$ for simple representations of $SU(N)$.

hep-th↗

arXiv2017

The Yukawa potential: ground state energy and critical screening

We study the ground state energy and the critical screening parameter of the Yukawa potential in non-relativistic quantum mechanics. After a short review of the existing literature on these quantities, we apply fifth-order perturbation theory to the calculation of the ground state energy, using the exact solutions of the Coulomb potential together with a cutoff on the principal number summations. We also perform a variational calculation of the ground state energy using a Coulomb-like radial wave function and the exact solution of the corresponding minimization condition. For not too large values of the screening parameter, close agreement is found between the perturbative and variational results. For the critical screening parameter, we devise a novel method that permits us to determine it to ten digits. This is the most precise calculation of this quantity to date, and allows us to resolve some discrepancies between previous results.

physics.atom-ph↗

arXiv2017

One-particle reducible contribution to the one-loop scalar propagator in a constant field

Recently, Gies and Karbstein showed that the two-loop Euler-Heisenberg Lagrangian receives a finite one-particle reducible contribution in addition to the well-known one-particle irreducible one. Here, we demonstrate that a similar contribution exists for the propagator in a constant field already at the one-loop level, and we calculate this contribution for the scalar QED case. We also present an independent derivation of the Gies-Karbstein result using the worldline formalism, treating the scalar and spinor QED cases in a unified manner.

hep-th↗

arXiv2016

Mixed symmetry Wilson-loop interactions in the worldline formalism

Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling. The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation. By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop interaction between the gauge field and the matter field taken to transform in a chosen representation. This work has direct application to physical observables such as scattering amplitudes in the presence of such a matter multiplet and lifts the restriction on the type of matter that has previously featured in worldline calculations.

hep-th↗

arXiv2016

Non-commutativity in polar coordinates

We reconsider the fundamental commutation relations for non-commutative $\mathbb{R}^{2}$ described in polar coordinates with non-commutativity parameter $θ$. Previous analysis found that the natural transition from Cartesian coordinates to polars led to a representation of $\left[\hat{r}, \hatφ\right]$ as an everywhere diverging series. We compute the Borel resummation of this series, showing that it can subsequently be extended throughout parameter space and hence provide an interpretation of this commutator. Our analysis provides a complete solution for arbitrary $r$ and $θ$ that reproduces the earlier calculations at lowest order. We compare our results to previous literature in the (pseudo-)commuting limit, finding a surprising spatial dependence for the coordinate commutator when $θ\gg r^{2}$. We raise some questions for future study in light of this progress.

hep-th↗

arXiv2016

Mixed symmetry tensors in the worldline formalism

We consider the first quantised approach to quantum field theory coupled to a non-Abelian gauge field. Representing the colour degrees of freedom with a single family of auxiliary variables the matter field transforms in a reducible representation of the gauge group which - by adding a suitable Chern-Simons term to the particle action - can be projected onto a chosen fully (anti-)symmetric representation. By considering F families of auxiliary variables, we describe how to extend the model to arbitrary tensor products of F reducible representations, which realises a U(F) "flavour" symmetry on the worldline particle model. Gauging this symmetry allows the introduction of constraints on the Hilbert space of the colour fields which can be used to project onto an arbitrary irreducible representation, specified by a certain Young Tableau. In particular the occupation numbers of the wavefunction - i.e. the lengths of the columns (rows) of the Young Tableau - are fixed through the introduction of Chern-Simons terms. We verify this projection by calculating the number of colour degrees of freedom associated to the matter field. We suggest that, using the worldline approach to quantum field theory, this mechanism will allow the calculation of one-loop scattering amplitudes with the virtual particle in an arbitrary representation of the gauge group.

hep-th↗

arXiv2015

Contact interactions between particle worldlines

We construct contact interactions for bosonic and fermionic point particles. We first relate the resulting theories to classical electrostatics by taking functional averages over worldlines whose endpoints are fixed to charged particles. Counting those paths which pass through a space-time point $x^μ$ gives the static electric field at that point, provided we take the limit where the length measured along the worldlines is large. We also investigate corrections to the classical field that arise beyond leading order in this limit before constructing a theory of point particles that interact when their worldlines intersect. We quantise this theory and show that the partition function contains propagator couplings between the endpoints of the particles before discussing how this is related to the worldline formalism of quantum field theory and general action at a distance theories.

hep-th↗

arXiv2015

Unified theory in the worldline approach

We explore unified field theories based on the gauge groups $SU(5)$ and $SO(10)$ using the worldline approach for chiral fermions with a Wilson loop coupling to a background gauge field. Representing path ordering and chiral projection operators with functional integrals has previously reproduced the sum over the chiralities and representations of standard model particles in a compact way. This paper shows that for $SU(5)$ the $\bar{\mathbf{5}}$ and $\mathbf{10}$ representations -- into which the Georgi-Glashow model places the left-handed fermionic content of the standard model -- appear naturally and with the familiar chirality. We carry out the same analysis for flipped $SU(5)$ and uncover a link to $SO(10)$ unified theory. We pursue this by exploring the $SO(10)$ theory in the same framework, the less established unified theory based on $SU(6)$ and briefly consider the Pati-Salam model using $SU(4) \!\times \!SU(2)\! \times\! SU(2)$.

hep-th↗

arXiv2014

Delta-function Interactions for the Bosonic and Spinning Strings and the Generation of Abelian Gauge Theory

We construct contact interactions for bosonic and spinning strings. In the tensionless limit of the spinning string this reproduces the super-Wilson loop that couples spinor matter to Abelian gauge theory. Adding boundary terms that quantise the motion of charges results in a string model equivalent to spinor QED. The strings represent lines of electric flux connected to the charges. The purely bosonic model is spoilt by divergences that are excluded from the spinning model by world-sheet supersymmetry, indicating a preference for spinor matter.

hep-th↗

arXiv2014

QED as the tensionless limit of the spinning string with contact interaction

We outline how QED with spinor matter can be described by the tensionless limit of spinning strings with contact interactions. The strings represent electric lines of force with charges at their ends. The contact interaction is constructed from a delta-function on the world-sheet which, although off-shell, decouples from the world-sheet metric. Integrating out the string degrees of freedom with fixed boundary generates the super-Wilson loop that couples spinor matter to electromagnetism in the world-line formalism. World-sheet and world-line, but not spacetime, supersymmetry underpin the model.

hep-th↗