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Mass renormalization in nonrelativistic quantum electrodynamics
 J. Math. Phys
, 2005
"... The effective mass meff of the the PauliFierz Hamiltonain with ultraviolet cutoff Λ and the bare mass m in nonrelativistic QED with spin 1/2 is investigated. Analytic properties of meff in coupling constant e are shown and explicit forms of constants a1(Λ/m) and a2(Λ/m) depending on Λ/m such that m ..."
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Cited by 17 (4 self)
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The effective mass meff of the the PauliFierz Hamiltonain with ultraviolet cutoff Λ and the bare mass m in nonrelativistic QED with spin 1/2 is investigated. Analytic properties of meff in coupling constant e are shown and explicit forms of constants a1(Λ/m) and a2(Λ/m) depending on Λ/m such that meff/m = 1 + a1(Λ/m)e 2 + a2(Λ/m)e 4 + O(e 6) are given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants b1,b2,c1 and c2 such that b1 ≤ lim Λ→∞ a1(Λ/m) ≤ b2, −c1 log(Λ/m) ≤ lim Λ→∞ a2(Λ/m)
Nonrelativistic limit of a Dirac polaron in relativistic quantum electrodynamics
"... A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral R3 H(p)dp of a family of selfa ..."
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Cited by 5 (1 self)
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A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral R3 H(p)dp of a family of selfadjoint operators H(p) acting in the Hilbert space ⊕4Frad, where Frad is the Hilbert space of the quantum radiation field. The fibre operator H(p) is called the Hamiltonian of the Dirac polaron with total momentum p ∈ R3. The main result of this paper is concerned with the nonrelativistic (scaling) limit of H(p). It is proven that the nonrelativistic limit of H(p) yields a selfadjoint extension of a Hamiltonian of a polaron with spin 1/2 in nonrelativistic quantum electrodynamics.
ON THE NONRELATIVISTIC LIMIT OF A MODEL IN QUANTUM ELECTRODYNAMICS
, 905
"... Abstract. We consider a (semi)relativistic spin1/2 particle interacting with quantized radiation. The Hamiltonian has the form ˆ HV c: = {c2[(p + A) 2 +σ ·B] + (mc2) 2} 1/2 −mc2 + V + Hf. Assuming that the potential V  is bounded with respect to the momentum p, we show that ˆ HV c converges in ..."
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Cited by 3 (2 self)
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Abstract. We consider a (semi)relativistic spin1/2 particle interacting with quantized radiation. The Hamiltonian has the form ˆ HV c: = {c2[(p + A) 2 +σ ·B] + (mc2) 2} 1/2 −mc2 + V + Hf. Assuming that the potential V  is bounded with respect to the momentum p, we show that ˆ HV c converges in normresolvent sense to the usual PauliFierz operator when c, the speed of light, tends to ∞. 1.
Heisenberg Operators of a Dirac Particle Interacting with the Quantum Radiation
"... We consider a quantum system of a Dirac particle interacting with the quantum radiation field, where the Dirac particle is in a 4 × 4Hermitian matrixvalued potential V. Under the assumption that the total Hamiltonian HV is essentially selfadjoint (we denote its closure by ¯ HV), we investigate pr ..."
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Cited by 2 (0 self)
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We consider a quantum system of a Dirac particle interacting with the quantum radiation field, where the Dirac particle is in a 4 × 4Hermitian matrixvalued potential V. Under the assumption that the total Hamiltonian HV is essentially selfadjoint (we denote its closure by ¯ HV), we investigate properties of the Heisenberg operator xj(t): = eit ¯ HV xje−it ¯ HV (j = 1, 2, 3) of the jth position operator of the Dirac particle at time t ∈ R and its strong derivative dxj(t)/dt (the jth velocity operator), where xj is the multiplication operator by the jth coordinate variable xj (the jth position operator at time t = 0). We prove that D(xj), the domain of the position operator xj, is invariant under the action of the unitary operator e−it ¯ HV for all t ∈ R and establish a mathematically rigorous formula for xj(t). Moreover, we derive asymptotic expansions of Heisenberg operators in the coupling constant q ∈ R (the electric charge of the Dirac particle).
Dynamics for nonsymmetric Hamiltonians, and GuptaBleuler formalism for DiracMaxwell operator
"... The GuptaBleuler formalism for the DiracMaxwell model in the Lorenz gauge is investigated. A full description in detail will appear in [7]. 1 ..."
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The GuptaBleuler formalism for the DiracMaxwell model in the Lorenz gauge is investigated. A full description in detail will appear in [7]. 1
Ground State of a Model in Relativistic Quantum Electrodynamics with a Fixed Total Momentum
, 2008
"... A system of a single relativistic electron interacting with the quantized electromagnetic field is considered. We mainly study this system with a fixed total momentum p — This system is called the Dirac polaron. We analyze the lowest energy E(p) of the Dirac polaron, and derive some properties: conc ..."
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A system of a single relativistic electron interacting with the quantized electromagnetic field is considered. We mainly study this system with a fixed total momentum p — This system is called the Dirac polaron. We analyze the lowest energy E(p) of the Dirac polaron, and derive some properties: concavity, symmetricity, and the inverse energy inequality E(p) ≤ E(0), p ∈ R 3. Furthermore, we consider the existence of the ground state of the Dirac polaron. We show that the Dirac polaron has a ground state under a condition which includes an infrared regularization condition and an ultraviolet cutoff. This ensures that the relativistic dressed one electron state exists.