168 research outputs found
Spectral theory of a mathematical model in Quantum Field Theory for any spin
In this paper we use the formalism of S.Weinberg in order to construct a
mathematical model based on the weak decay of hadrons and nuclei. In particular
we consider a model which generalizes the weak decay of the nucleus of the
cobalt. We associate with this model a Hamiltonian with cutoffs in a Fock
space. The Hamiltonian is self-adjoint and has an unique ground state. By using
the commutator theory we get a limiting absorption principle from which we
deduce that the spectrum of the Hamiltonian is absolutely continuous above the
energy of the ground state and below the first threshold.Comment: A subsection revise
Weak interactions in a background of a uniform magnetic field. A mathematical model for the inverse beta decay.I
In this paper we consider a mathematical model for the inverse beta decay in
a uniform magnetic field. With this model we associate a Hamiltonian with
cutoffs in an appropriate Fock space. No infrared regularization is assumed.
The Hamiltonian is selfadjoint and has a ground state. We study its essential
spectrum and determine its spectrum. Conditions for uniqueness of ground state
are given. The coupling constant is supposed suffciently small.Comment: The proof of theorem 4.4 is not corrected in this preprin
A mathematical model for the Fermi weak interactions
We consider a mathematical model of the Fermi theory of weak interactions as
patterned according to the well-known current-current coupling of quantum
electrodynamics. We focuss on the example of the decay of the muons into
electrons, positrons and neutrinos but other examples are considered in the
same way. We prove that the Hamiltonian describing this model has a ground
state in the fermionic Fock space for a sufficiently small coupling constant.
Furthermore we determine the absolutely continuous spectrum of the Hamiltonian
and by commutator estimates we prove that the spectrum is absolutely continuous
away from a small neighborhood of the thresholds of the free Hamiltonian. For
all these results we do not use any infrared cutoff or infrared regularization
even if fermions with zero mass are involved
On the Infrared Problem for the Dressed Non-Relativistic Electron in a Magnetic Field
We consider a non-relativistic electron interacting with a classical magnetic
field pointing along the -axis and with a quantized electromagnetic field.
The system is translation invariant in the -direction and we consider the
reduced Hamiltonian associated with the total momentum along the
-axis. For a fixed momentum sufficiently small, we prove that
has a ground state in the Fock representation if and only if
, where is the derivative of the map . If , we obtain the
existence of a ground state in a non-Fock representation. This result holds for
sufficiently small values of the coupling constant
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