Abstract
The spontaneous baryogenesis scenario explains how a baryon asymmetry can develop while baryon violating interactions are still in thermal equilibrium. However, generation of the chemical potential from the derivative coupling is dubious since the chemical potential may not appear after the Legendre transformation. The geometric phase (Pancharatnam-Berry phase) results from the geometrical properties of the parameter space of the Hamiltonian, which is calculated from the Berry connection. In this paper, using the formalism of the Berry phase, we show that the chemical potential defined by the Berry connection is consistent with the Legendre transformation. The framework of the Berry phase is useful in explaining the mathematical background of the spontaneous baryogenesis, and also is useful for calculating the asymmetry of the non-thermal particle production in time-dependent backgrounds. Using the formalism, we show that the mechanism can be extended to more complex situations.
Highlights
Quantum mechanics is distinguishable from the classical counterpart by the phase factor, which explains many characteristic phenomena of the quantum theory
We examined the spontaneous baryogenesis scenario using the framework of the Berry phase
The chemical potential is not the derivative coupling of the Nambu-Goldstone boson but the Berry connection defined for the “Berry transformation”
Summary
Quantum mechanics is distinguishable from the classical counterpart by the phase factor, which explains many characteristic phenomena of the quantum theory. The Aharonov-Bohm(AB) effect [1] illuminates the importance of the geometric phase in quantum mechanics It explains why an interference pattern can appear even though a magnetic field is confined in a solenoid and put away from the orbit. The phase coming from the first term is the conventional Berry phase, which may appear both in the adiabatic and the nonadiabatic evolutions. If the phase appears from the state mixing, it is called the nonadiabatic Berry phase. The first term (the Berry connection) gives the chemical potential when the spontaneous baryogenesis scenario is considered in the formalism of the Berry phase. Since the Berry connection vanishes in the adiabatic limit ( its integral may not vanish in a topological background), the evolution has to be nonadiabatic in order to generate a sensible chemical potential. To show our idea in a simple model, we start with the Schrödinger written as equation for the state ψ t 0
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