Wade Cherrington's Theoretical Physics research homepage

About me

My theoretical research focuses on computational quantum field theory from a statistical geometry perspective. I also provide consulting services in software development, computational fluid dynamics (CFD) and related simulation disciplines.

Current Research

My research in theoretical physics currently focuses on spin foam approaches to lattice gauge theory and quantum gravity. I am collaborating with Dan Christensen and his group at UWO. Computational facilities for my research have been provided by SHARCNET.

Spin Foam Methods for Lattice Gauge Theory

Yang-Mills.  Spin foam models can be constructed that are exactly dual to conventional lattice field theory, and reveal the gauge-invariant geometric and topological features of Yang-Mills theory. Our spin foam algorithm and code[6] has been verified against conventional methods, and provides a new approach to field theory on the lattice.

Pure Yang-Mills Vacuum

Visualization of a spin foam configuration on a 83 lattice (with periodic boundary conditions) for the group SU(2).

Free Fermion Vacuum

Visualization of a polymer configuration on a 163 lattice (with periodic boundary conditions) for a two-component fermion field.

Yang-Mills with Dynamical Fermions.  By using the polymer decomposition of the fermion determinant, one is lead to an exactly dual model of dynamical fermions coupled to Yang-Mills on the lattice, consisting of spin foams bounded by polymers. Currently, spin network recoupling methods are being applied to develop efficient algorithms for vertex amplitudes modified from their vacuum structure by the presence of polymer lines. The algorithm[5] that results is exact, local and constructed entirely from gauge-invariant configurations.

Coupled Configuration

A coupled configuration with a single polymer present. Static loops of this form are used to study confinement.

Coupled Configuration

A two polymer configuration that can arise in the coupled system. Static loops of this form are used to define the two-point correlation function, which relates to the glueball spectrum.

Extensions.  In the pure Yang-Mills sector, we are optimizing the D=3, SU(2) vacuum algorithm and extending the code to D=4 [4] and G=SU(3). Concurrently, we are generalizing the code to Wilson loop observables and dynamical fermions.

Relation to spin foam quantum gravity.   Lattice spin foam algorithms can be naturally generalized to act as matter probes for spin foam quantum gravity, for example by following canonical methods for coupling matter to the pure gravity sector.   Alternatively, our research may help in the study of emergent matter-like structure from quantum geometry, as we expect it to be more natural to relate the emergent structures to a dual (spin-foam) formulation of the Standard Model than the conventional formulation.

Spin Foam Methods for Confinement

We have shown in[1,2] that spin foam methods can provide a new perspective on the behavior of a Yang-Mills theory at weak coupling, leading to a new means of understanding the behavior of Wilson loop-type observables.

Spin Foam Models of Quantum Gravity

Spin foams provide a general framework for performing path integral computations of quantum gravity. A model that has been studied for some time is the Barrett-Crane model, which has both Riemannian and Lorentzian versions.

The Lorentzian Barrett-Crane model is particularly challenging to compute. A duality transformation[7,8] which changes variables from representation labels at dual faces to normals of tetrahedra has been found and allows the computation of observables involving both representation and normal variables, such as Regge curvature.

Publications & Pre-prints

  1. J. Wade Cherrington. "Dual Non-abelian Yang-Mills Simulations in Four Dimensions" (2009). [arxiv]
  2. J. Wade Cherrington. "A Gauge-Invariant mechanism for Confinement and Mass Gap: Part II - SU(2) and D=3" (2009). To appear in Nuclear Physics B. [arXiv]
  3. J. Wade Cherrington. "A Gauge-Invariant mechanism for Confinement and Mass Gap: Part I - General Framework" (2009). To appear in Nuclear Physics B. [arXiv]
  4. J. Wade Cherrington. "Recent Development in Dual Lattice Algorithms" (2008), Proceedings of the XXVI International Symposium on Lattice Field Theory. [arXiv]
  5. J. Wade Cherrington, J. Daniel Christensen. "A Dual Non-abelian Yang-Mills Amplitude in Four Dimensions" (2008), Nuclear Physics B 813(3),370-382. [arXiv]
  6. J. Wade Cherrington. "A Dual Algorithm for Non-abelian Yang-Mills coupled to Dynamical Fermions" (2008). Nuclear Physics B 794, 195-215. [arXiv]
  7. J. Wade Cherrington, J. Daniel Christensen, Igor Khavkine. "Dual Computations of Non-abelian Yang-Mills on the Lattice" (2007), Phys. Rev. D 76, 094503. [arXiv]
  8. J. Wade Cherrington. "Finiteness and Dual Variables for Lorentzian Spin Foam Models" (2006), Class. Quant. Grav. 23, 701-720. [arXiv]
  9. J. Wade Cherrington, J. Daniel Christensen. "Positivity in Lorentzian Barrett-Crane Models of Quantum Gravity" (2006), Class. Quant. Grav. 23, 721-736. [arXiv]

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