Michael Fry Senior Lecturer in Mathematics Email mpfry@maths.tcd.ie Office Room 20, House 20 Westland Row

Research Interests

The papers listed below lead up to the 2020 paper which asks the question: Can any process in the electroweak model that includes the nonperturbative insertion of dynamical fermions--fermion loops--be calculated without resort to perturbation theory?

Nonperturbative information about any electroweak process resides in its representation as a product of functional integrals over the fields contributing to the process. Obviously, such a calculation requires that the functional integrals converge. The 2020 paper centres on the convergence of the functional integral over the Maxwell field. It is found that there are significant cancellations, pointing to convergence. However, there are potentially destabilizing remainder terms. Surprisingly, the convergence of the Maxwell integration hinges on the degeneracy of the bound states of a charged fermion in a random four-dimensional magnetic field. Information about this is sparse.

The question of convergence raised here is about the stability of the electroweak model. Does the nonperturbative inclusion of fermion loops in the model destabilize it? If so, then the answer to the opening question is no.

Related Publications

• M. P. Fry, Massive Schwinger model and four-dimensional QED: The connection, Physical Review D 45 (1992) 682-686.
• M. P. Fry, Fermionic Determinant of the Massive Schwinger Model, Physical Review D 47 (1993) 2629-2632 hep-th/9301013
• M. P. Fry, Fermion determinants in static, inhomogeneous magnetic fields, Physical Review D 51 (1995) 810. hep-th/9410126
• M. P. Fry, QED in strong, finite-flux magnetic fields, Physical Review D 53 (1996) 980. hep-th/9510203
• M. P. Fry, QED in inhomogeneous magnetic fields, Physical Review D 54 (1996) 6444. hep-th/9606037
• M. P. Fry, Paramagnetism, zero modes and mass singularities in QED in 1+1, 2+1 and 3+1 dimensions, Physical Review D 55 (1997) 968. hep-th/9611055
• M. P. Fry, Effective actions in QED in 1+1, 2+1 and 3+1 dimensions, Int. J. Mod. Phys. A 12 (1997) 1153.
• M. P. Fry, Chiral limit of the two-dimensional fermionic determinant in a general magnetic field, J. Math. Phys. 41 (2000) 1691-1710. hep-th/9911131
• M. P. Fry, Mass zeros in the one-loop effective actions of QED in 1 + 1 and 1 + 3 dimensions, Physical Review D 62 (2000) 125007. hep-th/0010008
• M. P. Fry, Fermion determinants, Int. J. Mod. Phys. A 17 (2002) 936. hep-th/0111244
• M. P. Fry, Fermion determinant for general background gauge fields, Physical Review D 67 (2003) 065017. hep-th/0301097
• M. P. Fry, Fermion Determinants 2003, Proceedings of the Sixth Workshop on Quantum Field Theory under the Influence of External Conditions, U. Oklahoma, Sept. 15-19, 2003, edited by Kimball A. Milton (Rinton Press, Princeton, NJ, 2004) p. 271 hep-th/0311145
• M. P. Fry, Fermion Determinants: Some Recent Analytic Results. Int. J. Mod. Phys. A20 (2005) 4492. hep-th/0411011
• M. P. Fry, Evidence for mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics, hep-th/0612218
• M. P. Fry, Mass zeros of the fermionic determinant in four-dimensional quantum electrodynamics, Physical Review D 75 (2007) 065002. [This is a reduced version of hep-th/0612218]
• M. P. Fry, Nonperturbative results for the mass dependence of the QED fermion determinant, Physical Review D 81 (2010) 107701. An extended version of this paper appears in hep-th/1005.4849
• M. P. Fry, Stability of QED, Physical Review D 84 (2011) 065021, arXiv: 1108.4345.
• M. P. Fry, Nonperturbative quantization of the electroweak model's electrodynamic sector, Physical Review D 91 (2015) 085026
• M. P. Fry, Strong, random field behavior of the Euclidean Dirac propagator, Physical Review D 98 (2018) 033002. arXiv:1807.11741 085026. arXiv:1504.03117
• M. P. Fry, Nonperturbative path integral quantization of the electroweak model:The Maxwell Integration, Physical Review D 101 (2020) 033010. arxiv:2002.05385

Postal address:

School of Mathematics
Trinity College
Dublin 2
Ireland

Departmental fax number: +353-1-896 2282.