Abstract
The tachyonic regime of the quantum fluctuations of a self-interacting scalar field around its vacuum mean value is studied within a kinetic approach. We derive a quantum kinetic equation which determines the time evolution of the momentum distribution function of produced tachyonic modes and includes memory effects. The back-reaction of the quantum fluctuations on the vacuum mean field is taken into account, while their interaction is neglected. We show that the tachyonic modes do not correspond to real particles and contribute to the decay rate of the metastable vacuum state.
Highlights
We aim to derive a quantum kinetic equation describing the production of the tachyonic modes for a self-interacting neutral massive scalar field
For the model of a self-interacting scalar field, we have derived a non-Markovian quantum kinetic equation determining the momentum distribution of the tachyonic modes. These modes are produced in quantum fluctuations of the scalar field around its vacuum mean value when the system is in a metastable phase
Despite the fact that the fluctuations Hamiltonian is not bounded from below in the tachyonic regime, the conservation of energy prevents any catastrophic production of tachyons
Summary
Quantum fluctuations of a scalar field can enter a tachyonic regime where their frequency becomes imaginary. Its effective action develops an imaginary part [8], the fluctuations Hamiltonian becomes unbounded from below, while the Hilbert space of states acquires an indefinite metric [3] All these changes are indicative of a new, metastable phase. We aim to derive a quantum kinetic equation describing the production of the tachyonic modes for a self-interacting neutral massive scalar field. The critical momentum changes in tune with the time dependence of the vacuum mean field φ. The vacuum mean field modifies the equation for fluctuations via a time dependent frequency, while the fluctuations react back on the vacuum mean field via the source term J in Eq(7) and on the fluctuations themselves via the “external force” term Fχ(k, t) in Eq(10)
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