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We study the Dirac-Maxwell model quantized in the Lorenz gauge. In thisgauge, the space of quantum mechanical state vectors inevitably be anindefinite metric vector space so that the canonical commutation relation (CCR)is realized in a Lorentz covariant manner. In order to obtain a physicalsubspace in which no negative norm state exists, the method first proposed byGupta and Bleuler is applied with mathematical rigor. It is proved that asuitably defined physical subspace has a positive semi-definit metric, andnaturally induces a physical Hilbert space with a positive definite metric. Theoriginal Dirac-Maxwell Hamiltonian naturally defines an induced Hamiltonian onthe physical Hilbert space which is essentially self-adjoint.

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