THESIS
2017
ix, 103 pages : illustrations (some color) ; 30 cm
Abstract
In the standard electroweak theory that describes nature, the unstable sphaleron solutions
play a crucial role in the baryon number violating processes. For the periodic sphaleron potential,
we find the one-dimensional time-independent Schrödinger equation with the Chern-Simons number as the coordinate. We recall why the Chern-Simons number should be generalized
from a set of discrete values to a dynamical (quantum) variable. Via the construction
of an appropriate Hopf invariant and the winding number, we discuss how the geometric
information in the gauge fields is also captured in the Higgs field. We then discuss the choice
of the Hopf variable in relation to the Chern-Simons variable. For the effective Schrödinger equation, we construct the Bloch wave function and determine t...[
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In the standard electroweak theory that describes nature, the unstable sphaleron solutions
play a crucial role in the baryon number violating processes. For the periodic sphaleron potential,
we find the one-dimensional time-independent Schrödinger equation with the Chern-Simons number as the coordinate. We recall why the Chern-Simons number should be generalized
from a set of discrete values to a dynamical (quantum) variable. Via the construction
of an appropriate Hopf invariant and the winding number, we discuss how the geometric
information in the gauge fields is also captured in the Higgs field. We then discuss the choice
of the Hopf variable in relation to the Chern-Simons variable. For the effective Schrödinger equation, we construct the Bloch wave function and determine the corresponding conducting
(pass) band structure. We discuss the impact of such periodic potential and band structure
on the understanding of anomalous baryon/lepton number violation. It is suggested that
such processes at zero temperature may not be very suppressed at energies higher than the
sphaleron barrier height at 9 TeV.
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