Quantum field theory of bound states IV. Relativistic theory of the excited states of hydrogen

1953 ◽  
Vol 219 (1139) ◽  
pp. 516-526 ◽  
Keyword(s):  
Excited States ◽  
Lamb Shift ◽  
Bound States ◽  
Bound State ◽  
Crossing Over ◽  
Quantum Field ◽  
Coupled Equations ◽  
First Approximation ◽  
Single Integral ◽  
The Difference

When allowance is made for the instability of the excited states of hydrogen it is necessary to replace the equation of Salpeter & Bethe (1951) by a set of coupled integral equations for representatives of the state vector. These representatives correspond to an electron-proton bound state and also to the electron and proton with any number of photons present. The coupled equations can be reduced to a single integral equation, which gives the electronproton bound state as an eigenstate of a modified propagator. The modified propagator is related to the two-body propagator of Salpeter & Bethe. The difference between the first approximation to the modified propagator and the first approximation to the two-body compound propagator (Eden 1952, 1953) can be represented by a displacement of its singularity in total energy-momentum space. This displacement gives in a relativistic form all the relevant contributions to the Lamb shift to this order; these include the contribution from low-energy transverse photons crossing over an arbitrary number of longitudinal photons; previously this term has always been deduced by physical arguments and obtained by non-relativistic methods (Bethe 1947; Salpeter 1952). The displacement of the singularity also gives decay coefficients to this order in the charge. The method can readily be extended to higher approximations.

THE NEXT STEP IN LEPTONIC DECAYS OF ETA AND KL BOUND STATES

1992 ◽  
Vol 07 (09) ◽  
pp. 1935-1951 ◽  
Author(s):  
G.A. KOZLOV
Keyword(s):  
Field Theory ◽  
Transition Form Factor ◽  
Bound States ◽  
Three Dimensional ◽  
Bound State ◽  
Quantum Field ◽  
Relative Momentum ◽  
Transition Form ◽  
Structure Transition ◽  
Leptonic Decays

A systematic discussion of the probability of eta and KL bound-state decays—[Formula: see text] and [Formula: see text](l=e, μ)—within a three-dimensional reduction to the two-body quantum field theory is presented. The bound-state vertex function depends on the relative momentum of constituent-like particles. A structure-transition form factor is defined by a confinement-type quark-antiquark wave function. The phenomenology of this kind of decays is analyzed.

ENERGY SPECTRA OF GLUINONIUM

2011 ◽  
Vol 20 (supp02) ◽  
pp. 200-209
Author(s):  
CÉSAR A. Z. VASCONCELLOS ◽  
DIMITER HADJIMICHEF ◽  
MÁRIO L. L. DA SILVA ◽  
MOISÉS RAZEIRA ◽  
ALEXANDRE MESQUITA ◽  
...  
Keyword(s):  
Energy Spectrum ◽  
Excited States ◽  
Bound States ◽  
Bound State ◽  
State Equation ◽  
Relativistic Case ◽  
Light Scalar ◽  
Pseudo Scalar ◽  
Relativistic Bound States

We investigate relativistic bound states for a hypothetical light scalar gluino pair (gluinonium), in the framework of the covariant Bethe-Salpeter equation (BSE). In this paper, we derive, from the covariant BSE for a fermion-anti-fermion system, using charge conjugation, the corresponding bound-state equation for a gluino pair and we then formulate, for a static harmonic kernel, the coupled differential equations for the corresponding static Bethe-Salpeter amplitude. The steps of our approach then include a numerical solution of the Bethe-Salpeter amplitude for a two-body interaction consisting of scalar, pseudo-scalar, and four-vector components and the determination of the energy spectrum for the ground and the radially excited states of massive gluinonium. We found the energy spectrum and radial distributions of fundamental and excited states of gluinonium. The comparison of the values obtained in the extreme relativistic case with the corresponding values predicted by a harmonic oscillator potential model shows that there is good agreement between the two formulations. The predictions of the binding energy of glunionium in the non-relativistic model are however systematically higher.

scholarly journals REVIEW OF THE N-QUANTUM APPROACH TO BOUND STATES

2011 ◽  
Vol 26 (06) ◽  
pp. 935-945 ◽  
Author(s):  
O. W. GREENBERG
Keyword(s):  
Hydrogen Atom ◽  
Bound States ◽  
Bound State ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Asymptotic Field ◽  
Quantum Approach ◽  
Future Work ◽  
Asymptotic Fields

We describe a method of solving quantum field theories using operator techniques based on the expansion of interacting fields in terms of asymptotic fields. For bound states, we introduce an asymptotic field for each (stable) bound state. We choose the nonrelativistic hydrogen atom as an example to illustrate the method. Future work will apply this N-quantum approach to relativistic theories that include bound states in motion.

BOUND STATE ENERGIES IN THE 1/N EXPANSION

1993 ◽  
Vol 08 (09) ◽  
pp. 1613-1628
Author(s):  
T. JAROSZEWICZ ◽  
P.S. KURZEPA
Keyword(s):  
Bound States ◽  
Symmetric Tensor ◽  
Bound State ◽  
Binding Energies ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Leading Order ◽  
3 Dimensional ◽  
Weakly Coupled

We derive and solve — in an arbitrary number of dimensions — Omnès-type equations for bound-state energies in weakly coupled quantum field theories. We show that, for theories defined in the 1/N expansion, these equations are exact to leading order in 1/N. We derive and discuss the weak coupling and nonrelativistic limits of the Omnès equations. We then calculate the binding energies and effective bound-state couplings in (1+1), (1+2) and (1+3)-dimensional O(N)-invariant ϕ4 theory. We consider both the scalar and symmetric tensor bound states.

scholarly journals EXACT-PROPAGATOR INSTANTANEOUS BETHE–SALPETER EQUATION FOR QUARK–ANTIQUARK BOUND STATES

2006 ◽  
Vol 21 (21) ◽  
pp. 1657-1673 ◽  
Author(s):  
ZHI-FENG LI ◽  
WOLFGANG LUCHA ◽  
FRANZ F. SCHÖBERL
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Bound States ◽  
Lattice Gauge Theory ◽  
Bound State ◽  
State Equation ◽  
Wave Functions ◽  
Quantum Field ◽  
Lattice Gauge ◽  
Instantaneous Approximation

Recently an instantaneous approximation to the Bethe–Salpeter formalism for the analysis of bound states in quantum field theory has been proposed which retains, in contrast to the Salpeter equation, as far as possible the exact propagators of the bound-state constituents, extracted nonperturbatively from Dyson–Schwinger equations or lattice gauge theory. The implications of this improvement for the solutions of this bound-state equation, i.e. the spectrum of the mass eigenvalues of its bound states and the corresponding wave functions, when considering the quark propagators arising in quantum chromodynamics are explored.

scholarly journals A conjecture on the minimal size of bound states

2020 ◽  
Vol 8 (4) ◽  
Author(s):  
Ben Freivogel ◽  
Thomas Gasenzer ◽  
Arthur Hebecker ◽  
Sascha Leonhardt
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Black Holes ◽  
Quantum Gravity ◽  
Bound States ◽  
Bound State ◽  
Quantum Field ◽  
Minimal Size ◽  
Sharp Form ◽  
Weak Gravity

We conjecture that, in a renormalizable effective quantum field theory where the heaviest stable particle has mass mm, there are no bound states with radius below 1/m1/m (Bound State Conjecture). We are motivated by the (scalar) Weak Gravity Conjecture, which can be read as a statement forbidding certain bound states. As we discuss, versions for uncharged particles and their generalizations have shortcomings. This leads us to the suggestion that one should only constrain rather than exclude bound objects. In the gravitational case, the resulting conjecture takes the sharp form of forbidding the adiabatic construction of black holes smaller than 1/m1/m. But this minimal bound-state radius remains non-trivial as M_\mathrm{P}\to \inftyMP→∞, leading us to suspect a feature of QFT rather than a quantum gravity constraint. We find support in a number of examples which we analyze at a parametric level.

scholarly journals Tetraquark state X(6900) and the interaction between diquark and antidiquark

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Hong-Wei Ke ◽  
Xin Han ◽  
Xiao-Hai Liu ◽  
Yan-Liang Shi
Keyword(s):  
Excited States ◽  
Bound States ◽  
Effective Interaction ◽  
Axial Vector ◽  
Bound State ◽  
Tetraquark State ◽  
Effective Coupling ◽  
Final State ◽  
Interaction Kernel ◽  
Quantum Numbers

AbstractRecently LHCb declared a new structure X(6900) in the final state di-$$J/\psi $$ J / ψ which is popularly regarded as a cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ tetraquark state. Within the Bethe–Salpeter (B–S) framework we study the possible cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound states and the interaction between diquark (cc) and antidiquark ($$\bar{c}\bar{c}$$ c ¯ c ¯ ). In this work cc ($$\bar{c}\bar{c}$$ c ¯ c ¯ ) is treated as a color anti-triplet (triplet) axial-vector so the quantum numbers of cc-$$\bar{c}\bar{c}$$ c ¯ c ¯ bound state are $$0^+$$ 0 + , $$1^+$$ 1 + and $$2^+$$ 2 + . Learning from the interaction in meson case and using the effective coupling we suggest the interaction kernel for the diquark and antidiquark system. Then we deduce the B–S equations for different quantum numbers. Solving these equations numerically we find the spectra of some excited states can be close to the mass of X(6900) when we assign appropriate values for parameter $$\kappa $$ κ introduced in the interaction (kernel). We also briefly calculate the spectra of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ bound states. Future measurement of bb-$$\bar{b}\bar{b}$$ b ¯ b ¯ state will help us to determine the exact form of effective interaction.

scholarly journals Diphoton decay of the Higgs boson and new bound states of top and antitop quarks

2015 ◽  
Vol 30 (21) ◽  
pp. 1550132 ◽  
Author(s):  
C. D. Froggatt ◽  
C. R. Das ◽  
L. V. Laperashvili ◽  
H. B. Nielsen
Keyword(s):  
Higgs Boson ◽  
Excited States ◽  
Atomic Physics ◽  
Bound States ◽  
Gluon Fusion ◽  
Top Quarks ◽  
Bound State ◽  
Sigma Level ◽  
Gluon Production ◽  
State Formula

We consider the constraints, provided by the LHC results on Higgs boson decay into 2 photons and its production via gluon fusion, on the previously proposed Standard Model (SM) strongly bound state S of six top quarks and six antitop quarks. A correlation is predicted between the ratios [Formula: see text] and [Formula: see text] of the Higgs diphoton decay and gluon production amplitudes, respectively to their SM values. We estimate the contribution to these amplitudes from one-loop diagrams involving the 12 quark bound state S and related excited states using an atomic physics based model. We find two regions of parameter space consistent with the ATLAS and CMS data on [Formula: see text] at the three sigma level: a region close to the SM values [Formula: see text] with the mass of the bound state [Formula: see text][Formula: see text]GeV and a region with [Formula: see text] corresponding to a bound state mass of [Formula: see text][Formula: see text]GeV.

scholarly journals ON THE BOUND STATES IN A NONLINEAR QUANTUM FIELD THEORY OF A SPINOR FIELD WITH HIGHER DERIVATIVES

1999 ◽  
Vol 14 (11) ◽  
pp. 1651-1662
Author(s):  
A. D. MITOV ◽  
M. N. STOILOV ◽  
D. Ts. STOYANOV
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Spinor Field ◽  
Bound States ◽  
Bound State ◽  
Quantum Field ◽  
Coupling Constant ◽  
Nonlinear Quantum ◽  
Higher Derivatives ◽  
Fermi Type

We consider a model with higher derivatives for a spinor field with Fermi-type self-interaction. The problem of two-particle bound states is investigated with the help of the Bethe–Salpeter equation. It is shown that a scalar bound state exists when the coupling constant has a very finely tuned magnitude.

scholarly journals Bound states of a Klein–Gordon particle in the presence of a smooth potential well

2020 ◽  
Vol 35 (23) ◽  
pp. 2050140
Author(s):  
Eduardo López ◽  
Clara Rojas
Keyword(s):  
Bound States ◽  
Gordon Equation ◽  
Bound State ◽  
Potential Well ◽  
One Dimensional ◽  
Smooth Potential ◽  
Klein Gordon ◽  
The One ◽  
Potential Parameters ◽  
Klein Gordon Equation

We solve the one-dimensional time-independent Klein–Gordon equation in the presence of a smooth potential well. The bound state solutions are given in terms of the Whittaker [Formula: see text] function, and the antiparticle bound state is discussed in terms of potential parameters.

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