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Calculating the infra-red limit of quantum field theory using analyticity of correlation functions. (2000)
Journal Article
Kjærgaard, L., & Mansfield, P. (2000). Calculating the infra-red limit of quantum field theory using analyticity of correlation functions. Journal of High Energy Physics, 2000(03), Article 008. https://doi.org/10.1088/1126-6708/2000/03/008

We describe a general method for calculating the infra-red limit of physical quantities in unitary quantum field theories. Using analyticity of Green functions in a complex scale parameter, the infra-red limit is expressed as a contour integral entir... Read More about Calculating the infra-red limit of quantum field theory using analyticity of correlation functions..

The O(N) σ-model Laplacian (1996)
Journal Article
Mansfield, P., & Pachos, J. (1996). The O(N) σ-model Laplacian. Physics Letters B, 365(1-4), 169-174. https://doi.org/10.1016/0370-2693%2895%2901333-4

For fields that vary slowly on the scale of the lightest mass the logarithm of the vacuum functional of a massive quantum field theory can be expanded in terms of local functionals satisfying a form of the Schrödinger equation, the principal ingredie... Read More about The O(N) σ-model Laplacian.

Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional (1999)
Journal Article
Mansfield, P., & Sampaio, M. (1999). Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional. Nuclear Physics B, 545(1-3), 623-655. https://doi.org/10.1016/s0550-3213%2898%2900871-2

For slowly varying fields the Yang-Mills Schrödinger functional can be expanded in terms of local functionals. We show how analyticity in a complex scale parameter enables the Schrödinger functional for arbitrarily varying fields to be reconstructed... Read More about Yang-Mills beta-function from a large-distance expansion of the Schrödinger functional.

Brane fusion in the bosonic string and the emergence of fermionic strings (2001)
Journal Article
Englert, F., Houart, L., & Taormina, A. (2001). Brane fusion in the bosonic string and the emergence of fermionic strings. Journal of High Energy Physics, 2001(08), https://doi.org/10.1088/1126-6708/2001/08/013

We review the emergence of the ten-dimensional fermionic closed string theories from subspaces of the Hilbert space of the 26-dimensional bosonic closed string theory compactified on an E8 × SO(16) lattice. They arise from a consistent truncation pro... Read More about Brane fusion in the bosonic string and the emergence of fermionic strings.

Solving the functional Schrödinger equation: Yang-Mills string tension and surface critical scaling (2004)
Journal Article
Mansfield, P. (2004). Solving the functional Schrödinger equation: Yang-Mills string tension and surface critical scaling. Journal of High Energy Physics, 2004(04), https://doi.org/10.1088/1126-6708/2004/04/059

Motivated by a heuristic model of the Yang-Mills vacuum that accurately describes the string-tension in three dimensions we develop a systematic method for solving the functional Schrödinger equation in a derivative expansion. This is applied to the... Read More about Solving the functional Schrödinger equation: Yang-Mills string tension and surface critical scaling.

The consistency of topological expansions in field theory: “BRST anomalies” in strings and Yang-Mills (1994)
Journal Article
Mansfield, P. (1994). The consistency of topological expansions in field theory: “BRST anomalies” in strings and Yang-Mills. Nuclear Physics B, 416(1), 205-226. https://doi.org/10.1016/0550-3213%2894%2990583-5

Many field theories of physical interest have configuration spaces consisting of disconnected components. Quantum mechanical amplitudes are then expressed as sums over these components. We use the Faddeev-Popov approach to write the terms in this top... Read More about The consistency of topological expansions in field theory: “BRST anomalies” in strings and Yang-Mills.

Short distance properties from large distance behaviour. (1998)
Journal Article
Mansfield, P., Pachos, J., & Sampaio, M. (1998). Short distance properties from large distance behaviour. International Journal of Modern Physics A, 13(23), 4101-4122. https://doi.org/10.1142/s0217751x9800192x

For slowly varying fields the vacuum functional of a quantum field theory may be expanded in terms of local functionals. This expansion satisfies its own form of the Schrödinger equation from which the expansion coefficients can be found. For scalar... Read More about Short distance properties from large distance behaviour..

Finite Vevs from a large distance vacuum wave functional. (2000)
Journal Article
Jaramillo, A., & Mansfield, P. (2000). Finite Vevs from a large distance vacuum wave functional. International Journal of Modern Physics A, 16(04), 581-600. https://doi.org/10.1142/s0217751x00000288

We show how to compute vacuum expectation values from derivative expansions of the vacuum wave functional. Such expansions appear to be valid only for slowly varying fields, but by exploiting analyticity in a complex scale parameter we can reconstruc... Read More about Finite Vevs from a large distance vacuum wave functional..

Planar Skyrmions: vibrational modes and dynamics (2005)
Journal Article
Piette, B., & Ward, R. (2005). Planar Skyrmions: vibrational modes and dynamics. Physica D: Nonlinear Phenomena, 201(1-2), 45-55. https://doi.org/10.1016/j.physd.2004.12.001

We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter α, with α=0 corresponding to the O(3) sigma-model. If two Skyrmions collide head-on, then they can either coalesce or scatter—this depends o... Read More about Planar Skyrmions: vibrational modes and dynamics.