Summary
An Abelian gauge theory is investigated in the limit of vanishing Higgs fields. Exact, nonperturbative solutions are found which signal the presence of structureless gauge strings. These solutions may be static or time-dependent, but the time-dependent solution varies exponentially with field energy and momentum flowing radially inward toward the gauge string.
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References
See, for example,E. W. Kolb andM. S. Turner:The Early Universe (Addison-Wesley, 1990) and references therein;A. Vilenkin:Phys. Rep.,121, 263 (1985).
A Minkowski metric is used with signature (+,−,−,−).
The overdot represents differentiation with respect tot.
TheU(1) gauge group need not be identified with the electromagnetic gauge groupU(1)EM.
If the phase cndition φ=Nϕ (N=integer) is chosen for eq. (10), then eqs (27) and (28) have right-hand sides multiplied byN, suggesting the presence of a gauge string containingN units of quantized flux.
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M. Carmeli, Kh. Huleihil andE. Leibowitz:Gauge Fields: Classification and Equations of Motion (World Scientific, Singapore, 1989).
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Morris, J.R. Sourceless Abelian gauge strings. Nuov Cim A 104, 1051–1056 (1991). https://doi.org/10.1007/BF02813359
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DOI: https://doi.org/10.1007/BF02813359