scholarly journals Self-adjointness of the semi-relativistic Pauli–Fierz Hamiltonian

2015 ◽  
Vol 27 (07) ◽  
pp. 1550015 ◽  
Author(s):  
Takeru Hidaka ◽  
Fumio Hiroshima
Keyword(s):  
Radiation Field ◽  
Quantum Electrodynamics ◽  
Fock Space ◽  
Total Momentum ◽  
Momentum Operator ◽  
The Self ◽  
External Potential ◽  
Boson Fock Space ◽  
Quantized Radiation Field

The spinless semi-relativistic Pauli–Fierz Hamiltonian [Formula: see text] in quantum electrodynamics is considered. Here p denotes a momentum operator, A a quantized radiation field, M ≥ 0, Hf the free Hamiltonian of a Boson Fock space and V an external potential. The self-adjointness and essential self-adjointness of H are shown. It is emphasized that it includes the case of M = 0. Furthermore, the self-adjointness and the essential self-adjointness of the semi-relativistic Pauli–Fierz model with a fixed total momentum P ∈ ℝd: [Formula: see text] is also proven for arbitrary P.

scholarly journals LOCALIZATION OF THE NUMBER OF PHOTONS OF GROUND STATES IN NONRELATIVISTIC QED

2003 ◽  
Vol 15 (03) ◽  
pp. 271-312 ◽  
Author(s):  
FUMIO HIROSHIMA
Keyword(s):  
Radiation Field ◽  
Ground State ◽  
Fock Space ◽  
Adjoint Operator ◽  
Ground States ◽  
Electron System ◽  
Number Operator ◽  
Position Variable ◽  
Boson Fock Space ◽  
Quantized Radiation Field

One electron system minimally coupled to a quantized radiation field is considered. It is assumed that the quantized radiation field is massless, and no infrared cutoff is imposed. The Hamiltonian, H, of this system is defined as a self-adjoint operator acting on L2 (ℝ3) ⊗ ℱ ≅ L2 (ℝ3; ℱ), where ℱ is the Boson Fock space over L2 (ℝ3 × {1, 2}). It is shown that the ground state, ψg, of H belongs to [Formula: see text], where N denotes the number operator of ℱ. Moreover, it is shown that for almost every electron position variable x ∈ ℝ3 and for arbitrary k ≥ 0, ‖(1 ⊗ Nk/2) ψg (x)‖ℱ ≤ Dk e-δ|x|m+1 with some constants m ≥ 0, Dk > 0, and δ > 0 independent of k. In particular [Formula: see text] for 0 < β < δ/2 is obtained.

scholarly journals Analyticity of the self-energy in total momentum of an atom coupled to the quantized radiation field

2014 ◽  
Vol 267 (11) ◽  
pp. 4139-4196 ◽  
Author(s):  
Jérémy Faupin ◽  
Jürg Fröhlich ◽  
Baptiste Schubnel
Keyword(s):  
Radiation Field ◽  
Total Momentum ◽  
The Self ◽  
Self Energy ◽  
Quantized Radiation Field

scholarly journals LOCAL EXPONENTS AND INFINITESIMAL GENERATORS OF CANONICAL TRANSFORMATIONS ON BOSON FOCK SPACES

2004 ◽  
Vol 07 (04) ◽  
pp. 547-571 ◽  
Author(s):  
F. HIROSHIMA ◽  
K. R. ITO
Keyword(s):  
Canonical Transformation ◽  
Symplectic Group ◽  
Unitary Operator ◽  
Fock Space ◽  
Adjoint Operator ◽  
The Self ◽  
Canonical Transformations ◽  
Fock Spaces ◽  
Infinitesimal Generators ◽  
Boson Fock Space

A one-parameter symplectic group {etÂ}t∈ℝ derives proper canonical transformations indexed by t on a Boson–Fock space. It has been known that the unitary operator Ut implementing such a proper canonical transformation gives a projective unitary representation of {etÂ}t∈ℝ on the Boson–Fock space and that Ut can be expressed as a normal-ordered form. We rigorously derive the self-adjoint operator Δ(Â) and a local exponent [Formula: see text] with a real-valued function τÂ(·) such that [Formula: see text].

scholarly journals Singular Bogoliubov transformations and inequivalent representations of canonical commutation relations

2019 ◽  
Vol 31 (08) ◽  
pp. 1950026 ◽  
Author(s):  
Asao Arai
Keyword(s):  
Fock Space ◽  
Sufficient Conditions ◽  
Bogoliubov Transformation ◽  
Fock Representation ◽  
Canonical Commutation Relations ◽  
Commutation Relations ◽  
Direct Sum ◽  
Boson Fock Space ◽  
Inequivalent Representations ◽  
Bogoliubov Transformations

We introduce a concept of singular Bogoliubov transformation on the abstract boson Fock space and construct a representation of canonical commutation relations (CCRs) which is inequivalent to any direct sum of the Fock representation. Sufficient conditions for the representation to be irreducible are formulated. Moreover, an example of such representations of CCRs is given.

INTERMEDIATE NUMBER-SQUEEZED STATE OF THE QUANTIZED RADIATION FIELD

1995 ◽  
Vol 09 (25) ◽  
pp. 1673-1683 ◽  
Author(s):  
B. BASEIA ◽  
A.F. DE LIMA ◽  
A.J. DA SILVA
Keyword(s):  
Radiation Field ◽  
Intermediate State ◽  
Phase State ◽  
Squeezed State ◽  
Number State ◽  
Binomial State ◽  
Quantized Radiation Field

Following previous strategies by Stoler et al. which introduced the binomial state and Baseia et al. which introduced the intermediate number phase state, we introduce a new intermediate state of the quantized radiation field, which reduces to the number state and squeezed state in two different limits. This interpolating state exhibits nonclassical effects as sub-Poissonian, antibunching and squeezing, obtained from the corresponding expressions as function of the interpolating parameters.

scholarly journals MATRIX THEORY, HILBERT SCHEME AND INTEGRABLE SYSTEM

1998 ◽  
Vol 13 (34) ◽  
pp. 2731-2742 ◽  
Author(s):  
YUTAKA MATSUO
Keyword(s):  
Hilbert Scheme ◽  
Matrix Theory ◽  
Fock Space ◽  
Homology Class ◽  
Orthogonal Basis ◽  
Inner Product ◽  
Virasoro Symmetry ◽  
Hilbert Scheme Of Points ◽  
The Matrix ◽  
Boson Fock Space

We give a reinterpretation of the matrix theory discussed by Moore, Nekrasov and Shatashivili (MNS) in terms of the second quantized operators which describes the homology class of the Hilbert scheme of points on surfaces. It naturally relates the contribution from each pole to the inner product of orthogonal basis of free boson Fock space. These bases can be related to the eigenfunctions of Calogero–Sutherland (CS) equation and the deformation parameter of MNS is identified with coupling of CS system. We discuss the structure of Virasoro symmetry in this model.

scholarly journals su(2) AND su(1,1) DISPLACED NUMBER STATES AND THEIR NONCLASSICAL PROPERTIES

2000 ◽  
Vol 14 (30) ◽  
pp. 1099-1108 ◽  
Author(s):  
HONGCHEN FU ◽  
XIAOGUANG WANG ◽  
CHONG LI ◽  
JIANGONG WANG
Keyword(s):  
Radiation Field ◽  
Photon Number ◽  
Density Dependent ◽  
Nonclassical Properties ◽  
Number Distribution ◽  
Intermediate States ◽  
Quantized Radiation Field ◽  
Photon Number Distribution ◽  
Dependent Interaction

We study su(2) and su(1,1) displaced number states. These states are eigenstates of density-dependent interaction systems of quantized radiation field with classical current. These states are intermediate states interpolating between number and displaced number states. Their photon number distribution, statistical and squeezing properties are studied in detail. It shows that these states exhibit strong nonclassical properties.

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