# Structure of the Ground State of the Electroweak Gauge Theory in a Strong Magnetic Field

Abstract: This thesis deals with the construction of perturbative methods for analyzing the phase transition of the electroweak gauge theory in a strong magnetic field at zero temperature. The first part is a self-contained description of the methods and results. The second part contains the articles on which the first part is based.

It should be emphasized that this thesis is organized in a non-traditional manner in the sense that the first part contains all essential material from the articles as well as original results, for instance Theorem 4.2, Section 6.2 and both Appendices, which have not been published previously in journals.

After the brief Introduction, Chapter 2 reviews the Weinberg--Salam model of electroweak interactions and proceeds to explain the instability in a strong magnetic field with respect to the production of W bosons. Chapter 3 describes how the instability, above a critical value of the magnetic field, leads to the formation of a new phase with a W-boson condensate. For the special case when the Higgs mass and the Z-boson mass are set equal, previous results by Ambjo{}rn and Olesen are used to illustrate the properties of this new phase.

In Chapter 4 a classical perturbative method is developed by means of which the W-boson phase can be analyzed near the critical value of the magnetic field for general values of the Higgs to Z-boson mass ratio. Great care is taken to label all possible perturbative solutions for the W condensate, so that the energy can be expressed in terms of simple geometric quantities. The classical solutions do correspond to coherent quantum states of W-boson pairs which are constructed in Chapter 5.

Finally in Chapter 6 values of the energy for classical and quantum solutions are analyzed and compared, and it is found that, above the critical magnetic field and for a Higgs mass larger than the Z mass, the ground state corresponds to a condensate of W-boson pairs whose density forms an hexagonal pattern in the directions perpendicular to the magnetic field. It is also shown that quantum effects will shift the critical magnetic field to a slightly higher value if periodic boundary conditions are imposed in the direction of the magnetic field. Analogies with Type-II superconductivity are explored.

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