GROUND STATE OF THE YUKAWA MODEL WITH CUTOFFS

2011 ◽  
Vol 14 (02) ◽  
pp. 225-235 ◽  
Author(s):  
TOSHIMITSU TAKAESU
Keyword(s):  
Ground State ◽  
Spectral Gap ◽  
Fock Space ◽  
Adjoint Operator ◽  
Coupling Constants ◽  
Dirac Field ◽  
Yukawa Model ◽  
Klein Gordon

The ground state of the Yukawa model is considered. The Yukawa model describes the system of a Dirac field interacting with a Klein–Gordon field. By introducing ultraviolet cutoffs and spatial cutoffs, the total Hamiltonian is defined as a self-adjoint operator on a boson–fermion Fock space. It is shown that the total Hamiltonian has a positive spectral gap for all values of coupling constants. In particular, the existence of the ground state is proven.

scholarly journals Essential spectrum of a fermionic quantum field model

2014 ◽  
Vol 17 (04) ◽  
pp. 1450024 ◽  
Author(s):  
Toshimitsu Takaesu
Keyword(s):  
State Space ◽  
Essential Spectrum ◽  
Fock Space ◽  
Adjoint Operator ◽  
The State ◽  
Dirac Field ◽  
Quantum Field ◽  
Interaction System ◽  
Tensor Product Space ◽  
Klein Gordon

An interaction system of a fermionic quantum field is considered. The state space is defined by a tensor product space of a fermion Fock space and a Hilbert space. It is assumed that the total Hamiltonian is a self-adjoint operator on the state space and bounded from below. Then it is proven that a subset of real numbers is the essential spectrum of the total Hamiltonian. It is applied to a Yukawa interaction system, which is a system of a Dirac field coupled to a Klein–Gordon, and the HVZ theorem is obtained.

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 Spectral Theory for a Mathematical Model of the Weak Interaction—Part I: The Decay of the Intermediate Vector BosonsW±

2009 ◽  
Vol 2009 ◽  
pp. 1-52 ◽  
Author(s):  
J.-M. Barbaroux ◽  
J.-C. Guillot
Keyword(s):  
Ground State ◽  
State Energy ◽  
Fock Space ◽  
Adjoint Operator ◽  
Weak Decay ◽  
Spectral Interval ◽  
Coupling Constant ◽  
Small Coupling ◽  
Small Coupling Constant ◽  
Intermediate Vector

We consider a Hamiltonian with cutoffs describing the weak decay of spin 1 massive bosons into the full family of leptons. The Hamiltonian is a self-adjoint operator in an appropriate Fock space with a unique ground state. We prove a Mourre estimate and a limiting absorption principle above the ground state energy and below the first threshold for a sufficiently small coupling constant. As a corollary, we prove the absence of eigenvalues and absolute continuity of the energy spectrum in the same spectral interval.

Microwave Spectrum and Nuclear Quadrupole Coupling of 2-Chloropyridine

1987 ◽  
Vol 42 (2) ◽  
pp. 197-206 ◽  
Author(s):  
M. Meyer ◽  
U. Andresen ◽  
H. Dreizler
Keyword(s):  
Excited State ◽  
Ground State ◽  
Microwave Spectrum ◽  
Coupling Constants ◽  
Vibrationally Excited ◽  
Isotopic Species ◽  
Quadrupole Coupling ◽  
Nuclear Quadrupole ◽  
Mo Theory

The microwave spectrum of 2-chloropyridine, 2-Cl(C5H4N), has been studied to determine the 35Cl, 37Cl and 14N nuclear quadrupole coupling constants. The results are discussed within a simple MO theory. We propose an approximate r0-structure under certain assumptions. In addition to the ground state we observed one vibrationally excited state of both chlorine isotopic species of 2-chloropyridine.

A [3Fe–3S]3+ cluster with exclusively μ-sulfide donors

2016 ◽  
Vol 52 (6) ◽  
pp. 1174-1177 ◽  
Author(s):  
Yousoon Lee ◽  
Ie-Rang Jeon ◽  
Khalil A. Abboud ◽  
Ricardo García-Serres ◽  
Jason Shearer ◽  
...  
Keyword(s):  
Mössbauer Spectroscopy ◽  
Ground State ◽  
Hyperfine Coupling ◽  
Mossbauer Spectroscopy ◽  
Variable Temperature ◽  
Coupling Constants ◽  
Hyperfine Coupling Constants ◽  
Mößbauer Spectroscopy ◽  
Pyramidal Geometry ◽  
Anisotropic Hyperfine

A [3Fe–3(μ-S)]3+ cluster is reported in which each ferric center has a distorted trigonal pyramidal geometry, with an S = 1/2 ground state for the cluster and unusually anisotropic hyperfine coupling constants as determined by variable temperature magnetometry and Mössbauer spectroscopy.

scholarly journals Microwave Spectrum and Quadrupole Coupling Constants of 2-Bromothiophene

1975 ◽  
Vol 30 (4) ◽  
pp. 541-548 ◽  
Author(s):  
P. J. Mjöberg ◽  
W. M. Ralowski ◽  
S. O. Ljunggren
Keyword(s):  
Ground State ◽  
Second Order ◽  
Coupling Constants ◽  
Order Perturbation ◽  
Vibrationally Excited ◽  
Rotational Constants ◽  
Isotopic Species ◽  
Principal Axes ◽  
Quadrupole Coupling ◽  
Hyperfine Splittings

Abstract The microwave spectra of the two 79Br and 81Br isotopic species of 2-bromothiophene have been measured in the region 18000-40000 MHz.For both isotopic species, the rotational constants of the ground state and one vibrationally excited state were determined, as well as the centrifugal distortion coefficients of the ground state. The ground state rotational constants in MHz are as follows:C4H332S79Br C4H332S81BrA = 5403.432 ±0.111 5403.563 ±0.095,B = 1139.0689±0.0010 1126.5173±0.0011 C = 940.5142±0.0018 931.9315±0.0009.In order to perform a second-order perturbation treatment of the quadrupole interaction, the matrix elements of products of direction cosines in terms of the symmetric top wave functions have been derived. By the first-and second-order perturbation analysis of the hyperfine splittings of the rotational lines, the nuclear quadrupole coupling constants have been determined. The values in MHz areXaa = 592.7 ±1.5 493.7 ±1.5,Xbb = -295.3 ±0.6 -245.6 ±0.7, Xcc = -297.4 ±1.6 -248.1 ±1.6,Xab = 80 ±9 64±8 ,in the principal axes system of the molecule.

scholarly journals QUANTUM ELECTRODYNAMICS OF RELATIVISTIC BOUND STATES WITH CUTOFFS

2004 ◽  
Vol 01 (02) ◽  
pp. 271-314 ◽  
Author(s):  
JEAN-MARIE BARBAROUX ◽  
MOUEZ DIMASSI ◽  
JEAN-CLAUDE GUILLOT
Keyword(s):  
Current Density ◽  
Coulomb Potential ◽  
Ground State ◽  
Quantum Electrodynamics ◽  
Bound States ◽  
Coupling Constants ◽  
Relativistic Electrons ◽  
Small Coupling ◽  
Electrons And Positrons ◽  
Relativistic Bound States

We consider a Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the current density with transversal photons and the Coulomb interaction of charge density with itself. We prove that the Hamiltonian is self-adjoint and has a ground state for sufficiently small coupling constants.

Stable standing waves for the two-dimensional Klein–Gordon–Schrödinger system

2010 ◽  
Vol 140 (5) ◽  
pp. 1011-1039 ◽  
Author(s):  
Hiroaki Kikuchi
Keyword(s):  
General Theory ◽  
Perturbation Method ◽  
Ground State ◽  
Standing Waves ◽  
Orbital Stability ◽  
Two Dimensional ◽  
Spatial Dimensions ◽  
Klein Gordon ◽  
Linearized Operator ◽  
Schrödinger System

AbstractWe study the orbital stability of standing waves for the Klein–Gordon–Schrödinger system in two spatial dimensions. It is proved that the standing wave is stable if the frequency is sufficiently small. To prove this, we obtain the uniqueness of ground state and investigate the spectrum of the appropriate linearized operator by using the perturbation method developed by Genoud and Stuart and Lin and Wei. Then we apply to our system the general theory of Grillakis, Shatah and Strauss.

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