On kaonic hydrogen. Quantum field theoretic and relativistic covariant approach

We study kaonic hydrogen, the bound K ^- p state A _{K p} . Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K ^- p scattering for arbitrary relative momenta. The amplitude of low-energy K ^- p scattering near threshold is defined by the contributions of three resonances , and and a smooth elastic background. The amplitudes of inelastic channels of low-energy K ^- p scattering fit experimental data on the near-threshold behaviour of the cross-sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculation of the partial width of the radiative decay of pionic hydrogen and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to the calculation of the partial widths of radiative decays of kaonic hydrogen and . We show that the contribution of these decays to the width of the energy level of the ground state of kaonic hydrogen is less than 1 .Received: 7 October 2003, Revised: 29 November 2003, Published online: 22 June 2004PACS: 11.10.Ef Lagrangian and Hamiltonian approach - 13.75.Gx Pion-baryon interactions - 21.10.-k Properties of nuclei; nuclear energy levels - 36.10.-k Exotic atoms and molecules (containing mesons, muons, and other unusual particles)A.N. Ivanov: Permanent address: State Polytechnical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian FederationN.I. Troitskaya: Permanent address: State Polytechnical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation.     

On kaonic deuterium. Quantum field-theoretic and relativistic covariant approach

We study kaonic deuterium, the bound K^-d state A_{K d}. Within a quantum field-theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic deuterium in terms of the amplitude of K^-d scattering for arbitrary relative momenta. Near threshold our formula reduces to the well-known DGBT formula. The S-wave amplitude of K^-d scattering near threshold is defined by the resonances (1405), (1750) and a smooth elastic background, and the inelastic channels K^-d NY and K^-d NY, where Y = ^±,^{0} and ^{0}, where the final-state interactions play an important role. The Ericson-Weise formula for the S-wave scattering length of K^-d scattering is derived. The total width of the energy level of the ground state of kaonic deuterium is estimated using the theoretical predictions of the partial widths of the two-body decays A_Kd NY and experimental data on the rates of the NY pair production in the reactions K^-d NY. We obtain _{1s} = (630±100)eV. For the shift of the energy level of the ground state of kaonic deuterium we predict _{1s} = (325±60)eV.     

Variational field theoretic approach to relativistic meson-nucleon scattering

Non-perturbative polaron variational methods are applied, within the so-called particle or world-line representation of relativistic field theory, to study scattering in the context of the scalar Wick-Cutkosky model. Important features of the variational calculation are that it is a controlled approximation scheme valid for arbitrary coupling strengths, the Green functions have all the cuts and poles expected for the exact result at any order in perturbation theory and that the variational parameters are simultaneously sensitive to the infrared as well as the ultraviolet behaviour of the theory. We generalize the previously used quadratic trial action by allowing more freedom for off-shell propagation without a change in the on-shell variational equations and evaluate the scattering amplitude at first order in the variational scheme. Particular attention is paid to the s-channel scattering near threshold because here non-perturbative effects can be large. We check the unitarity of a our numerical calculation and find it greatly improved compared to perturbation theory and to the zeroth order variational results.     

On kaonic hydrogen. Phenomenological quantum field theoretic model revisited

We argue that due to isospin and U-spin invariance of strong low-energy interactions the S-wave scattering lengths a ⁰ ₀ and a ¹ ₀ of ˉN scattering with isospin I = 0 and I = 1 satisfy the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0 valid to leading order in chiral expansion. In the model of strong low-energy ˉN interactions at threshold (Eur. Phys. J. A 21, 11 (2004)) we revisit the contribution of the Σ(1750) resonance, which does not saturate the low-energy theorem a ⁰ ₀ +3a ¹ ₀ = 0, and replace it by the baryon background with properties of an SU(3) octet. We calculate the S-wave scattering amplitudes of K^-N and K^-d scattering at threshold. We calculate the energy level displacements of the ground states of kaonic hydrogen and deuterium. The result obtained for kaonic hydrogen agrees well with recent experimental data by the DEAR Collaboration. We analyse the cross-sections for elastic and inelastic K^-p scattering for laboratory momenta 70MeV/c < p _K < 150MeV/c of the incident K^--meson. The theoretical results agree with the available experimental data within two standard deviations.     

On conformally covariant spinor field equations

A spinor field equation, covariant with respect to the general conformal group (including reflections), should consist in general of not less than eight linear equations and then, in Minkowski space, could be represented by not less than two massless Dirac equations. Their reduction through projectors to only one equation, while not spoiling conformal covariance implies unphysical consequences. It is shown instead that two Dirac equations may be brought unambiguously through a stereographic projection to a manifestly conformal covariant form inE _4,2 space. The physical implications are discussed and it is shown that if the fundamental elementary interactions are expressed in terms of conformal semispinors (which can never appear as free particles), then the corresponding physical Dirac spinors appear in the elementary interactions in terms of their chiral projections. This could indicate both the conformally invariant origin of weak interactions and their fundamental character. The possibility of constructing unified models from conformally invariant Lagrangians is envisaged.Invited talk at the Symposium on Mathematical Methods in the Theory of Elementary Particles, Liblice castle, Czechoslovakia, June 18–23, 1978.A preliminary version was issued as Internal Report IC/78/43, ICTP Trieste May 1978, see also Lett. Nuovo Cim.21 (1978), 473.I am indebted to Prof. I. T.Todorov for interesting discussions.     

The proton-proton reaction,solar neutrinos,and a relativistic field theoretic model of the deuteron

In a series of recent papers, Ivanov et al. and Oberhummer et al. have calculated the rate for the p + p → d + e⁺ + ν_e reaction with a zero-range four-fermion effective interaction and find a result 2.9 times higher than the standard value calculated from non-relativistic potential theory. Their procedure is shown to give a wrong answer because their assumed interaction disagrees with low-energy pp scattering data.     

Pion-pion phase shifts from covariant perturbation theory for a chiral invariant field theoretic model

The Lehmann model for pion -pion scattering consists of a low-energy expansion of the scattering amplitude to fourth order in the momenta on the basis of the chiral-invariant pion-nucleon Lagrangian. Because of the non-renormalizability of the pion Lagrangian two parameters remain undetermined in the pion-loop contribution. Using covariant perturbation theory and superpropagator methods, we calculate these two parameters independently of the choice of the pion field coordinates. The resulting phase shifts are shown to be in very good agreement with the data.     

Explicitly covariant light-front dynamics and relativistic few-body systems

The wave function of a composite system is defined in relativity on a space–time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane ω·x=0, where ω is an arbitrary four-vector with ω²=0. The standard non-covariant approach is recovered as a particular case for ω=(1, 0, 0,−1). Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review.The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented.The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, and 1 systems.The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron and scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straightforward applications to the pion and nucleon form factors and the ρ−π transition are also made.     

On the structure of unitary conformal field theory II: Representation theoretic approach

Two-dimensional, unitary rational conformal field theory is studied from the point of view of the representation theory of chiral algebras. Chiral algebras are equipped with a family of co-multiplications which serve to define tensor product representations. Chiral vertices arise as Clebsch-Gordan operators from tensor product representations to irreducible subrepresentations of a chiral algebra. The algebra of chiral vertices is studied and shown to give rise to representations of the braid groups determined by Yang-Baxter (braid) matrices. Chiral fusion is analyzed. It is shown that the braid- and fusion matrices determine invariants of knots and links. Connections between the representation theories of chiral algebras and of quantum groups are sketched. Finally, it is shown how the local fields of a conformal field theory can be reconstructed from the chiral vertices of two chiral algebras.     

General relativistic Boltzmann equation, II: Manifestly covariant treatment

In a preceding article we presented a general relativistic treatment of the derivation of the Boltzmann equation. The four-momenta occurring in this formalism were all on-shell four-momenta, verifying the mass-shell restriction p²=m²c². Due to this restriction, the resulting Boltzmann equation, although covariant, turned out to be not manifestly covariant. In the present article we switch from mass-shell momenta to off-shell momenta, and thereby arrive at a Boltzmann equation that is manifestly covariant.     

A field theoretic approach to the atomic collision problems

It is an endeavour to make field theoretic approach available to the domain of electronic and atomic collision physics. The capacity of QED is demonstrated in explaining atomic collision phenomena in Coulomb gauge and depending on energy, in relativistic Lorentz gauge. Feynman diagrams are used to calculate bound state collision problems in atomic physics.     

Quantum transitions of relativistic electrons in a superstrong magnetic field

The probability of emission of a hard γ-quantum in relativistic electron transitions to the ground (or near it) level in a magnetic field H ～ H₀ = m²c³/e₀? = 4.41 × 10¹³G is obtained. For the inverse transitions from these levels the cross-section of electron photoexitation is calculated.     

Mass,matter, and energy. A relativistic approach

The debate concerning the relations between matter and motion has the same age as philosophy itself. In modern times this problem was transformed into the one concerning the relations between mass and energy. Newton identified mass with matter. Classical thermodynamics brought this conception to its logical conclusion, establishing an ontic dichotomy between mass-matter and energy. On the basis of this pre-relativistic conception, Einstein's famous equation has been interpreted as a relation of equivalence between mass-matter and energy. Nevertheless, if we reject this epistemologically illegitimate identification, it is possible to elaborate a unitary conception of matter, which at the same time is an argument for the unity between matter and motion. In particular, the classical antithesis between matter and field becomes obsolete in the frame of the proposed interpretation.     

On generally covariant quantum field theory and generalized causal and dynamical structures

We give an example of a generally covariant quasilocal algebra associated with the massive free field. Maximal, two-sided ideals of this algebra are algebraic representatives of external metric fields. In some sense, this algebra may be regarded as a concrete realization of Ekstein's ideas of presymmetry in quantum field theory. Using ideas from our example and from usual algebraic quantum field theory, we discuss a generalized scheme, in which maximal ideals are viewed as algebraic representatives of dynamical equations or Lagrangians. The considered frame is no quantum gravity, but may lead to further insight into the relation between quantum theory and space-time geometry.