Eliminating unphysical photon components from Dirac-Maxwell Hamiltonian quantized in the Lorenz gauge

@article{Futakuchi2015EliminatingUP,
  title={Eliminating unphysical photon components from Dirac-Maxwell Hamiltonian quantized in the Lorenz gauge},
  author={Shinichiro Futakuchi and Kouta Usui},
  journal={arXiv: Mathematical Physics},
  year={2015}
}
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2 Citations
Background Citations
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2 Citations

Causality in quantum field theory with classical sources

In an exact quantum-mechanical framework we show that space-time expectation values of the second-quantized electromagnetic fields in the Coulomb gauge in the presence of a classical conserved source…

non-symmetric Hamiltonians, and Gupta-Bleuler

The Gupta-Bleuler formalism for the Dirac-Maxwell model in the Lorenz gauge is investigated. A full description in detail will appear in [7].

References

SHOWING 1-10 OF 27 REFERENCES

Construction of two‐dimensional quantum electrodynamics

We investigate quantum electrodynamics in two dimensions, (QED)2, in the constructive method. We construct a cutoff Hamiltonian defined on the Fock space with an indefinite metric, and discuss its…

A particle-field Hamiltonian in relativistic quantum electrodynamics

We mathematically analyze a Hamiltonian Hτ(V,g) of a Dirac particle—a relativistic charged particle with spin 1/2—minimally coupled to the quantized radiation field, acting in the Hilbert space…

Non-relativistic limit of a Dirac-Maxwell operator in relativistic quantum electrodynamics

The non-relativistic (scaling) limit of a particle-field Hamiltonian H, called a Dirac–Maxwell operator, in relativistic quantum electrodynamics is considered. It is proven that the non-relativistic…

New Criteria for Self-Adjointness and its Application to Dirac–Maxwell Hamiltonian

We present a new theorem concerning a sufficient condition for a symmetric operator acting in a complex Hilbert space to be essentially self-adjoint. By applying the theorem, we prove that the…

The Lehmann-Symanzik-Zimmermann Formalism for Manifestly Covariant Quantum Electrodynamics

/~Zimmermann formalism is presented for manifestly covariant quantum electrodynamics involving, a gauge parameter a. Contrary to Kiilll5n's assertion, it is shown that one can consistently formulate…

Physical subspace in a model of the quantized electromagnetic field coupled to an external field with an indefinite metric.

We study a model of the quantized electromagnetic field interacting with an external static source ρ in the Feynman (Lorentz) gauge and construct the quantized radiation field Aμ (μ = 0, 1, 2, 3) as…

Canonical linear transformation on fock space with an indefinite metric

We first construct a Fock space with an indefinite metric 〈,〉=( , Θ), where Θ is a unitary and Hermitian operator. We define a Θ-selfadjoint (Segal's) field Φϕ(f) which obeys the canonical…

Dirac Operators Coupled to the Quantized Radiation Field: Essential Self-adjointness à la Chernoff

We study the Dirac operator D0 in an external potential V, coupled to a quantized radiation field with energy Hf and vector potential A. Our result is a Chernoff-type theorem, i.e., we prove, for the…

A NEW METHOD FOR THE TREATMENT OF LONGITUDINAL AND SCALAR PHOTONS

Gupta has introduced an alternative method of quantization for the Maxwell field which differs from the usual one in that the scalar part of the field is quantized by means of the indefinite metric…

Construction of dynamics and time-ordered exponential for unbounded non-symmetric Hamiltonians

We prove under certain assumptions that there exists a solution of the Schrodinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which…