A field theoretic approach to the formation of positronium negative ions in positronium-hydrogen collisions at low energy

The total cross-section, for positronium negative ions formation in positronium-hydrogen collision is calculated in a field-theoretic way for low energy positronium. In this non-relativistic region, cross-section shows a distinct structure unlike Born cross-section, as calculated byStancanelli andFerrante (Nuovo Cimento68B (1970), 137). At higher energies beyond 80 eV the field-theoretic cross-section decreases at a faster rate compared to the cross-section by the latter authors.     

A field theoretic cluster model of multiperipheral production

A field theoretic cluster model of multiproduction process in hadron-hadron collisions at high energy is considered. The multiproduction here is a two-step process. In the first step clusters are produced. We use a field theoretic formalism to describe cluster creation. A validity of the standard approximations, that are usually made in multiperipheral models is discussed. A modified strong ordering hypothesis is proposed. This leads to the Feynman scaling violation. Then cluster decay is considered. Expressions for semi-inclusive pion distributions in rapidity are given and a comparison with experimental data is made.     

Dirac equation in low dimensions: The factorization method

We present a general approach to solve the (1+1)$(1+1)$ and (2+1)$(2+1)$-dimensional Dirac equations in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the factorization method can be applied. We show that the presence of electric potentials in the Dirac equation leads to two Klein–Gordon equations including an energy-dependent potential. We then generalize the factorization method for the case of energy-dependent Hamiltonians. Additionally, the shape invariance is generalized for a specific class of energy-dependent Hamiltonians. We also present a condition for the absence of the Klein paradox (stability of the Dirac sea), showing how Dirac particles in low dimensions can be confined for a wide family of potentials.     

低对称畸变晶场下YIG和YGG:Fe~(3+)吸收光谱的理论解释

本文利用络合物中Fe~(3+)的SCF-d轨道理论,分别在实际的低对称场D_(3d)和S_4下对YIG和YGG:Fe~(3+)中的d-d跃迁谱进行了理论计算。仅用两个参数和μ就解释了YIG中10800cm~(-1),21150cm~(-1),25700cm~(-1),27600cm~(-1)处的谱分裂,并且指出YGG:Fe~(3+)中的26320cm~(-1),26970cm~(-1)为Fe~(3+)对的双中心跃迁谱。基本澄清了YIG和YGG:Fe~(3+)吸收谱理论的某些混淆。     

Quantum field theories in all dimensions

In this paper we exhibit a large class of hermitian scalar field theories satisfying the Wightman axioms. For eachd>0, and each polynomialP, we exhibit a collection of theories which are loosely but legitimately based on aP() interaction ind space dimensions. One of the features of the construction is that the Wightmann-point function of each theory is a sum of finitely many integrals associated with Feynman-like graphs. Thus, it is in closed form.     

A study of correlation expansions of field theoretic amplitudes

The subject of this paper is a study of interference terms in transition amplitudes of the multiperipheral type. The production amplitude is expressed in the language of continuous-mass-spectrum field theory. The strong-ordering approach is compared with the first term of the correlation expansion. The condition for neglecting correlation terms is found.     

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.     

Application of nonperturbative quantum field theoretic methods to hadron-nucleus collisions: Background theory

An exposition of the background theory necessary for understanding the application of nonperturbative QFT methods (LSZ reduction formalism) to hadron-nucleus collisions, for example the derivation of pi-nucleus (πn) Low and Chew Low equations, is given. The many channels and complex targets on the one hand, and the quantized field interactions on the other, introduce subtleties not well covered in particle theory or potential scattering literature. By specializing the πn Low Equation we derive a “pi-nucleon Low equation in the nuclear medium.” The second main goal of the paper is to compare this equation with Dover and Lemmer's analogous equation arrived at by graphical arguments. This requires especially making explicit the analyticity properties left tacit in their work. In is concluded that the two are essentially different.     

Boson-fermion Demixing and collapse in low dimensions

We evaluate in a mean-field model the equilibrium stability conditions of a gaseous mixture of bosonic and spin-polarized fermionic atoms inside a pancake-shaped or a cigar-shaped harmonic trap, under conditions such that the trap thickness approaches the magnitude of the s-wave scattering lengths but the atoms still experience collisions in three dimensions. With decreasing dimensionality, the Fermi pressure plays an increasingly dominant role. Full demixing in the case of repulsive boson-fermion interactions can be induced by squeezing the thickness of the clouds in a pancake-shaped trap or by lowering the number of trapped fermions in a cigar-shaped trap. Collapse under attractive interspecies interaction in quasi-one-dimensional confinement is inhibited within the range of validity of a mean-field model.     

Some non-abelian phase spaces in low dimensions

A non-abelian phase space, or a phase space of a Lie algebra, is a generalization of the usual (abelian) phase space of a vector space. It corresponds to a para-Kähler structure in geometry. Its structure can be interpreted in terms of left-symmetric algebras. In particular, a solution of an algebraic equation in a left-symmetric algebra which is an analogue of classical Yang–Baxter equation in a Lie algebra can induce a phase space. In this paper, we find that such phase spaces have a symplectically isomorphic property. We also give all such phase spaces in dimension 4 and some examples in dimension 6. These examples can be a guide for a further development.     

Lattice topological field theory in two dimensions

The lattice definition of a two-dimensional topological field theory (TFT) is given generically, and the exact solution is obtained explicitly. In particular, the set of all lattice topological field theories is shown to be in one-to-one correspondence with the set of all associative algebrasR, and the physical Hilbert space is identified with the centerZ(R) of the associative algebraR. Perturbations of TFT's are also considered in this approach, showing that the form of topological perturbations is automatically determined, and that all TFT's are obtained from one TFT by such perturbations. Several examples are presented, including twistedN=2 minimal topological matter and the case whereR is a group ring.     

Simple superconformal field theories in two dimensions

Superconformal field theories with first-order lagrangians, the super BC-systems, are considered on an arbitrary Riemann surface with an arbitrary gravitino field. The corresponding functional integrals are carefully defined, and the Weyl, supersymmetry, and holomorphic anomalies are computed. All the anomalies have a common coefficient. The holomorphic anomaly involves terms quadratic in the gravitino field.     

Resonant scattering of ultracold atoms in low dimensions

Low energy scattering amplitudes for two atoms in one- and two-dimensional atomic waveguides are derived for short range isotropic and resonant interactions in high partial wave channels. Taking into account the finite width of the resonance which was neglected in previous works is shown to have important implications in the properties of the confinement induced resonances. For spin polarized fermions in quasi-1D waveguides, it imposes a strong constraint on the atomic density for achieving the Fermi Tonks Girardeau gas. For a planar waveguide, the characteristics of the 2D induced scattering resonances in p- and d-waves are determined as a function of the 3D scattering parameters and of the waveguide frequency.