Logarithmic Intertwining Operators and Vertex Operators

This is the first in a series of papers where we study logarithmic intertwining operators for various vertex subalgebras of Heisenberg and lattice vertex algebras. In this paper we examine logarithmic intertwining operators associated with rank one Heisenberg vertex operator algebra M(1) _a , of central charge 1 − 12a ². We classify these operators in terms of depth and provide explicit constructions in all cases. Our intertwining operators resemble puncture operators appearing in quantum Liouville field theory. Furthermore, for a = 0 we focus on the vertex operator subalgebra L(1, 0) of M(1)₀ and obtain logarithmic intertwining operators among indecomposable Virasoro algebra modules. In particular, we construct explicitly a family of hidden logarithmic intertwining operators, i.e., those that operate among two ordinary and one genuine logarithmic L(1, 0)-module.     

Asymptotics of Determinants of Bessel Operators

 For aL ^∞ (ℝ₊)∩L ¹ (ℝ₊) the truncated Bessel operator B _τ (a) is the integral operator acting on L ² [0,τ] with the kernel

Bounds on charged lepton mixing with exotic charged leptons

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ _L ^a ) where θ _L ^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ _L ^a ) form _E < 0.69 TeV. However, sin² (2θ _L ^a ) ≤ 1.52×10⁻⁵ form _E = 5 TeV, sin² (2θ _L ^a ) ≤ 2.41 ×10⁻⁷ form _E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ _L ^a ) for m_E < 1.97 TeV and sin² (2θ _L ^a ) ≤ 0.15 form _E = 5 TeV and sin² (2θ _L ^a ) ≤ 3.88×10^-2 form _E = 10 TeV.     

Effective Action and Phase Transitions in Yang-Mills Theory on Spheres

We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial curvature acts as an effective gluon mass we consider the compact Euclidean spacetime S ¹ × S ¹ × S ², with the radius of the first circle determined by the temperature a ₁ = (2π T)⁻¹. We show that covariantly constant Yang-Mills fields on S ² cannot be arbitrary but are rather a collection of monopole-antimonopole pairs. We compute the heat kernels of all relevant operators exactly and show that the gluon operator on such a background has negative modes for any compact semi-simple gauge group. We compute the infrared regularized effective action and apply the result for the computation of the entropy and the heat capacity of the quark-gluon gas. We compute the heat capacity for the gauge group SU(2N) for a field configuration of N monopole-antimonopole pairs. We show that in the high-temperature limit the heat capacity per unit volume is well defined in the infrared limit and exhibits a typical behavior of second-order phase transition ~ (T-T_c)^-3/2{\sim(T-T_c)^{-3/2}} with the critical temperature T _c  = (2π a)⁻¹, where a is the radius of the 2-sphere S ².     

A Maximum Entropy Method Based on Piecewise Linear Functions for the Recovery of a Stationary Density of Interval Mappings

Let S:[0,1]→[0,1] be a nonsingular transformation such that the corresponding Frobenius-Perron operator P _S :L ¹(0,1)→L ¹(0,1) has a stationary density f ^∗. We propose a maximum entropy method based on piecewise linear functions for the numerical recovery of f ^∗. An advantage of this new approximation approach over the maximum entropy method based on polynomial basis functions is that the system of nonlinear equations can be solved efficiently because when we apply Newton’s method, the Jacobian matrices are positive-definite and tri-diagonal. The numerical experiments show that the new maximum entropy method is more accurate than the Markov finite approximation method, which also uses piecewise linear functions, provided that the involved moments are known. This is supported by the convergence rate analysis of the method.     

Magnetic properties of LiNi<Subscript>0.5</Subscript>Mn<Subscript>0.47</Subscript>Al<Subscript>0.03</Subscript>O<Subscript>2</Subscript> as positive electrode for Li-ion batteries

The layered LiNi_0.5Mn_0.47Al_0.03O₂ was synthesized by wet chemical method and characterized by X-ray diffraction and analysis of magnetic measurements. The powders adopted the α-NaFeO₂ structure. This substitution of Al for Mn promotes the formation of Li(Ni_0.47²⁺Ni_0.03³⁺Mn_0.47⁴⁺Al_0.03³⁺)O₂ structures and induces an increase in the average oxidation state of Ni, thereby leading to the shrinkage of the lattice unit cell. The concentration of antisite defects in which Ni²⁺ occupies the (3a) Li lattice sites in the Wyckoff notation has been estimated from the ferromagnetic Ni²⁺(3a)–Mn⁴⁺(3b) pairing observed below 140 K. The substitution of 3% Al for Mn reduces the amount of antisite defects from 7% to 6.4–6.5%. The analysis of the magnetic properties in the paramagnetic phase in the framework of the Curie–Weiss law agrees well with the combination of Ni²⁺ (S = 1), Ni³⁺ (S = 1/2) and Mn⁴⁺ (S = 3/2) spin-only values. Delithiation has been made by the use of K₂S₂O₈. According to this process, known to be softer than the electrochemical one, the nickel ions in the (3b) sites are converted into Ni⁴⁺ in the high spin configuration, while Ni²⁺(3a)–Mn⁴⁺(3b) ferromagnetic pairs remain, as the Li⁺(3b) ions linked to the Ni²⁺(3a) ions in the antisite defects are not removed. The results show that the antisite defect is surrounded by Mn⁴⁺ ions, implying the nonuniform distribution of the cations in agreement with previous NMR and neutron experiments.     

Universality Limits of a Reproducing Kernel for a Half-Line Schrödinger Operator and Clock Behavior of Eigenvalues

We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schrödinger operators on the half-line. In particular, we define a reproducing kernel S _L for Schrödinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schrödinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by ${e^{\epsilon x}}We extend some recent results of Lubinsky, Levin, Simon, and Totik from measures with compact support to spectral measures of Schr?dinger operators on the half-line. In particular, we define a reproducing kernel S _L for Schr?dinger operators and we use it to study the fine spacing of eigenvalues in a box of the half-line Schr?dinger operator with perturbed periodic potential. We show that if solutions u(ξ, x) are bounded in x by e^ex{e^{\epsilon x}} uniformly for ξ near the spectrum in an average sense and the spectral measure is positive and absolutely continuous in a bounded interval I in the interior of the spectrum with x₀ ? I{\xi_0\in I}, then uniformly in I,

\fracSL(x0 + a/L, x0 + b/L)SL(x0, x0)? \fracsin(pr(x0)(a - b))pr(x0)(a - b),\frac{S_L(\xi_0 + a/L, \xi_0 + b/L)}{S_L(\xi_0, \xi_0)}\rightarrow \frac{\sin(\pi\rho(\xi_0)(a - b))}{\pi\rho(\xi_0)(a - b)},      8. On Local Borg–Marchenko Uniqueness Results      Fritz Gesztesy  Barry Simon 《Communications in Mathematical Physics》2000,211(2):273-287 We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl–Titchmarsh m-functions, m j (z), of two Schr?dinger operators , j≡ 1,2 in L 2((0,R)), 0<R≤∞, are exponentially close, that is, , 0<a<R, then q 1≡q 2 a.e. on [0,a]. The result applies to any boundary conditions at x≡ 0 and x≡R and should be considered a local version of the celebrated Borg–Marchenko uniqueness result (which is quickly recovered as a corollary to our proof). Moreover, we extend the local uniqueness result to matrix-valued Schr?dinger operators. Received: 22 October 1999 / Accepted: 2 November 1999      9. Quark-lepton compositeness: A three-body scenario      A N Mitra 《Pramana》1989,32(4):573-581 The Harari-Shupe model of quarks and leptons is viewed, not as a gauge theory, but as a quantum-mechanical three-body problem of the extreme relativistic type involving massless preons. Considerations based onS 3-symmetry in the available degrees of freedom (spin, isospin, space and hypercolour) are employed in conjunction with a spin-dependence ansatz on the three-preon forces (Σ a =σ μv (1) σ λμ (3) ) for an understanding of the three basic issues of (i) spin-1/2, (ii) generation structure and (iii) steeply rising mass patterns of quark-lepton families. The Σ a -dynamics is compatible with the interpretation of colour as a manifestation ofS 3-symmetry, as envisaged in the original Harari-Shupe proposal, while the interpretation of the generation structure devolves on the role of a certain quantum numberN which takes on three different classes of values (3n, 3n ± 1;n = 0, 1, 2, ...) according to theS 3-symmetry of thespatial wavefunction.      10. Saturation of Coulomb sum rules in the <Superscript>6</Superscript>Li case      A. Yu. Buki  I. S. Timchenko  N. G. Shevchenko 《The European Physical Journal A - Hadrons and Nuclei》2012,48(2):17 The Coulomb sums S L(q) of the 6Li nucleus have been obtained from electron scattering measurements at 3-momentum transfers q = 1.125–1.625 fm−1. It is found that at q > 1.35 fm−1 the Coulomb sum of the nucleus becomes saturated: S L(q) = 1 .      11. Ab initio cluster calculations of Co3+ spin states in RBaCo2O5.5 (R=Ho, Gd)      L. Siurakshina  B. Paulus  V. Yushankhai 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,63(4):445-450 Two types of oxygen-deficient perovskites RBaCo2O5.5(R=Ho,Gd) related to the “122” type structure (a p × 2a p × 2a p ) have been studied on the basis of ab initio cluster calculations. We consider the peculiar behavior of the trivalent ions Co3+(3d 6) in either octahedral or pyramidal oxygen coordinations, which is related to a structural first-order phase transition in both compounds. Relative energy positions of low spin (LS, S = 0), intermediate spin (IS, S = 1) and high spin (HS, S = 2) electron configurations are calculated for the low-and high-temperature lattice structures of RBaCo2O5.5. A combined analysis of the calculated results and experimental structural data leads to a simple model that captures the most prominent features of the phase transition common to both compounds.      12. The Squeezing Effect of Three-Mode Operator as an Extension from Two-Mode Squeezing Operator      Xue-xiang Xu 《International Journal of Theoretical Physics》2012,51(7):2056-2065 We theoretically study the squeezing effect in a 3-wave mixing process, generated by the operator S3 o exp[m(a1a2-a1fa2f)+n(a1a3-a1fa3f)]S_{3}\equiv \exp[\mu(a_{1}a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}a_{3}^{\dagger})]. The corresponding 3-mode squeezed vacuum state in Fock space and its uncertainty relation are presented. It turns out that S 3 may exhibit enhanced squeezing. By virtue of integration within an ordered product (IWOP) of operators, we also give the S 3’s normally ordered expansion. Finally, we calculate the Wigner function of 3-mode squeezed vacuum state by using the Weyl ordering invariance under similar transformations.      13. Quantum deformation of lorentz group      P. Podleś  S. L. Woronowicz 《Communications in Mathematical Physics》1990,130(2):381-431 A one parameter quantum deformationS μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS μ U(2). It shows thatS μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS μ U(2). The same construction applied to any compact quantum groupG c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG d ofG c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG c . The theory of smooth representations ofS μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS μ U(2) are classified. An application to 4D + differential calculus is presented. The nonsmooth case is also discussed.      14. Influence of chirality on the electron spin resonance in molecular magnets [MnII(H L )(H2O)][MnIII(CN)6] · 2H2O with chiral ligands L      R. B. Morgunov  F. B. Mushenok  M. V. Kirman 《Physics of the Solid State》2008,50(7):1303-1307 Chiral and racemic molecular ferrimagnets [MnII(HL)(H2O)][MnIII(CN)6] · 2H2O, where L = S-or R-1,2-diaminopropane for chiral samples (S-pn, R-pn) and L = rac-pn for racemic samples, are investigated by the electron spin resonance technique. It is revealed that the electron spin resonance spectra of the chiral and racemic samples differ from each other at temperatures below the Curie temperature T C = 21 K. The maximum in the temperature dependence of the integrated magnetic susceptibility χ(T) calculated by the double integration of the line centered at a negative field of −250 Oe for the racemic samples is broadened as compared to the maxima in the corresponding dependences for the enantiomers of the chiral samples with “right” (R) and “left” (S) symmetry. The new compounds under investigation differ from the previously synthesized crystals by the strong spin-orbit interaction between Mn3+ ions, which leads to a dependence of their magnetic properties on the chirality of the structure. Original Russian Text ? R.B. Morgunov, F.B. Mushenok, M.V. Kirman, 2008, published in Fizika Tverdogo Tela, 2008, Vol. 50, No. 7, pp. 1252–1256.      15. Radiative decays of basic scalar, vector and tensor mesons and the determination of the P-wave q multiplet      A.V. Anisovich  V.V. Anisovich  V.A. Nikonov 《The European Physical Journal A - Hadrons and Nuclei》2001,12(1):103-115       16. Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN      Antonio?BassettoEmail author  Shiyamala?Thambyahpillai 《Letters in Mathematical Physics》2011,98(1):97-110 A relation between circular 1/2 BPS ’t Hooft operators in 4d N=4{{\mathcal N}=4} SYM and instantonic solutions in 2D Yang-Mills theory (YM2) has recently been conjectured. Localization indeed predicts that those ’t Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM2, belonging to representations of the dual group L G. This conjecture has been tested in the case G = U(N) =  L G and for fundamental representations. In this paper, we examine this conjecture for the case of the groups G = SU(N) and L G = SU(N)/Z N and loops in different representations. Peculiarities when groups are not self-dual and representations not “minimal” are pointed out.      17. The K0 SK0 S final state in two-photon collisions and SU(3) tensor nonets      V. A. Schegelsky  A. V. Sarantsev  V. A. Nikonov  A. V. Anisovich 《The European Physical Journal A - Hadrons and Nuclei》2006,27(2):207-212 The K0 SK0 S final state in two-photon collisions is studied with the L3 experiment at LEP, using orbital angular momentum operators. The mass spectrum is dominated by the formation of tensor mesons, their two-photon partial width are determined. A signal at 1700-1800MeV is found to be a new tensor state f 2(1750) with mass M = (1755±10)MeV and width Γ = (67±12)MeV. All observed tensor resonances obey SU(3) relations. The f 2(1750) state forms a second tensor nonet together with f 2(1560) and a 2(1700). The SU(3) analysis allows us to determine with good accuracy mixing angles between nonstrange and strange components of the isoscalar members of tensor nonets.      18. Complex Harmonic-Oscillator Basis for the Relativistic Three-Body Problem      A.N. Mitra  A. Sharma  B. Mitra-Sodermark 《Few-Body Systems》1995,19(3):145-156 A complex harmonic-oscillator basis is employed for the three-body problem obeying S 3-symmetry. Unlike a real basis it generates an additional quantum number (N a ), in addition to the standard principal quantum number (N), and thus facilitates a more quantitative S 3-classification of the various states than is usually possible. It is shown that certain bilinear forms with definite S 3-symmetry properties, which can be constructed out of the linear harmonic-oscillator operators (a, a †) satisfy several uncoupled sets of SO(2, 1) algebras with spectra bounded from below. It is also briefly indicated how this S 3-formalism can be adapted to the core structure of a more general relativistic three-particle system with unequal-mass kinematics through an appropriate choice of internal variables. Received May 11, 1994; revised November 3, 1994; accepted for publication November 23, 1994      19. Fock-Space Projector Studied in Weyl Ordering Approach      Zhi-song Yu  Gui-hua Ren  Hong-yi Fan  Gen-Chang Cai  Nian-Quan Jiang 《International Journal of Theoretical Physics》2012,51(7):2256-2261 We find that the Fock space projector |n〉〈n| is a Weyl ordered Laguerre polynomial 2 ::(-)nLn ( 4afa ) e-2afa ::2{\,}^{:}_{:}(-)^{n}L_{n} ( 4a^{\dagger}a ) e^{-2a^{\dagger}a}{\,}^{:}_{:}, where a † a is the number operator,:: ::,{}^{:}_{:}\ {}^{:}_{:} denotes the Weyl ordering symbol. This brings convenience to derive the Wigner functions of many other quantum states.      20. Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3      Nirmala Chandrasekharan  Sukumaran Vasudevan 《Pramana》1994,43(1):21-31 FePS3 is a layered antiferromagnet (T N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate5 T 2g ground state of the Fe2+ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σi [δ(L iz 2 −2)+|λ|L i .S i ]−Σ ij J ij S i .S j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J nn k=27.7 K; andJ nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT N=122 K for FePS3, which is remarkably close to the observed value of theT N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS3, for which the high temperature series expansion susceptibility is available.

On Local Borg–Marchenko Uniqueness Results

We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl–Titchmarsh m-functions, m _j (z), of two Schr?dinger operators , j≡ 1,2 in L ²((0,R)), 0<R≤∞, are exponentially close, that is, , 0<a<R, then q ₁≡q ₂ a.e. on [0,a]. The result applies to any boundary conditions at x≡ 0 and x≡R and should be considered a local version of the celebrated Borg–Marchenko uniqueness result (which is quickly recovered as a corollary to our proof). Moreover, we extend the local uniqueness result to matrix-valued Schr?dinger operators. Received: 22 October 1999 / Accepted: 2 November 1999     

Quark-lepton compositeness: A three-body scenario

The Harari-Shupe model of quarks and leptons is viewed, not as a gauge theory, but as a quantum-mechanical three-body problem of the extreme relativistic type involving massless preons. Considerations based onS ₃-symmetry in the available degrees of freedom (spin, isospin, space and hypercolour) are employed in conjunction with a spin-dependence ansatz on the three-preon forces (Σ ^a =σ _μv ⁽¹⁾ σ _λμ ⁽³⁾ ) for an understanding of the three basic issues of (i) spin-1/2, (ii) generation structure and (iii) steeply rising mass patterns of quark-lepton families. The Σ ^a -dynamics is compatible with the interpretation of colour as a manifestation ofS ₃-symmetry, as envisaged in the original Harari-Shupe proposal, while the interpretation of the generation structure devolves on the role of a certain quantum numberN which takes on three different classes of values (3n, 3n ± 1;n = 0, 1, 2, ...) according to theS ₃-symmetry of thespatial wavefunction.     

Saturation of Coulomb sum rules in the <Superscript>6</Superscript>Li case

The Coulomb sums S _L(q) of the ⁶Li nucleus have been obtained from electron scattering measurements at 3-momentum transfers q = 1.125–1.625 fm⁻¹. It is found that at q > 1.35 fm⁻¹ the Coulomb sum of the nucleus becomes saturated: S _L(q) = 1 .     

Ab initio cluster calculations of Co3+ spin states in RBaCo2O5.5 (R=Ho, Gd)

Two types of oxygen-deficient perovskites RBaCo₂O_5.5(R=Ho,Gd) related to the “122” type structure (a _p × 2a _p × 2a _p ) have been studied on the basis of ab initio cluster calculations. We consider the peculiar behavior of the trivalent ions Co³⁺(3d ⁶) in either octahedral or pyramidal oxygen coordinations, which is related to a structural first-order phase transition in both compounds. Relative energy positions of low spin (LS, S = 0), intermediate spin (IS, S = 1) and high spin (HS, S = 2) electron configurations are calculated for the low-and high-temperature lattice structures of RBaCo₂O_5.5. A combined analysis of the calculated results and experimental structural data leads to a simple model that captures the most prominent features of the phase transition common to both compounds.     

The Squeezing Effect of Three-Mode Operator as an Extension from Two-Mode Squeezing Operator

We theoretically study the squeezing effect in a 3-wave mixing process, generated by the operator S₃ o exp[m(a₁a₂-a₁^fa₂^f)+n(a₁a₃-a₁^fa₃^f)]S_{3}\equiv \exp[\mu(a_{1}a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}a_{3}^{\dagger})]. The corresponding 3-mode squeezed vacuum state in Fock space and its uncertainty relation are presented. It turns out that S ₃ may exhibit enhanced squeezing. By virtue of integration within an ordered product (IWOP) of operators, we also give the S ₃’s normally ordered expansion. Finally, we calculate the Wigner function of 3-mode squeezed vacuum state by using the Weyl ordering invariance under similar transformations.     

Quantum deformation of lorentz group

A one parameter quantum deformationS _μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS _μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS _μ U(2). It shows thatS _μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS _μ U(2). The same construction applied to any compact quantum groupG _c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG _d ofG _c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG _c . The theory of smooth representations ofS _μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS _μ U(2) are classified. An application to 4D ₊ differential calculus is presented. The nonsmooth case is also discussed.     

Influence of chirality on the electron spin resonance in molecular magnets [MnII(H L )(H2O)][MnIII(CN)6] · 2H2O with chiral ligands L

Chiral and racemic molecular ferrimagnets [Mn^II(HL)(H₂O)][Mn^III(CN)₆] · 2H₂O, where L = S-or R-1,2-diaminopropane for chiral samples (S-pn, R-pn) and L = rac-pn for racemic samples, are investigated by the electron spin resonance technique. It is revealed that the electron spin resonance spectra of the chiral and racemic samples differ from each other at temperatures below the Curie temperature T _C = 21 K. The maximum in the temperature dependence of the integrated magnetic susceptibility χ(T) calculated by the double integration of the line centered at a negative field of −250 Oe for the racemic samples is broadened as compared to the maxima in the corresponding dependences for the enantiomers of the chiral samples with “right” (R) and “left” (S) symmetry. The new compounds under investigation differ from the previously synthesized crystals by the strong spin-orbit interaction between Mn³⁺ ions, which leads to a dependence of their magnetic properties on the chirality of the structure. Original Russian Text ? R.B. Morgunov, F.B. Mushenok, M.V. Kirman, 2008, published in Fizika Tverdogo Tela, 2008, Vol. 50, No. 7, pp. 1252–1256.     

Quantum ’t Hooft Loops of SYM $${{\mathcal N}=4}$$ as Instantons of YM2 in Dual Groups SU(N) and SU(N)/ZN

A relation between circular 1/2 BPS ’t Hooft operators in 4d N=4{{\mathcal N}=4} SYM and instantonic solutions in 2D Yang-Mills theory (YM₂) has recently been conjectured. Localization indeed predicts that those ’t Hooft operators in a theory with gauge group G are captured by instanton contributions to the partition function of YM₂, belonging to representations of the dual group ^L G. This conjecture has been tested in the case G = U(N) =  ^L G and for fundamental representations. In this paper, we examine this conjecture for the case of the groups G = SU(N) and ^L G = SU(N)/Z _N and loops in different representations. Peculiarities when groups are not self-dual and representations not “minimal” are pointed out.     

The K0 SK0 S final state in two-photon collisions and SU(3) tensor nonets

The K⁰ _SK⁰ _S final state in two-photon collisions is studied with the L3 experiment at LEP, using orbital angular momentum operators. The mass spectrum is dominated by the formation of tensor mesons, their two-photon partial width are determined. A signal at 1700-1800MeV is found to be a new tensor state f ₂(1750) with mass M = (1755±10)MeV and width Γ = (67±12)MeV. All observed tensor resonances obey SU(3) relations. The f ₂(1750) state forms a second tensor nonet together with f ₂(1560) and a ₂(1700). The SU(3) analysis allows us to determine with good accuracy mixing angles between nonstrange and strange components of the isoscalar members of tensor nonets.     

Complex Harmonic-Oscillator Basis for the Relativistic Three-Body Problem

A complex harmonic-oscillator basis is employed for the three-body problem obeying S ₃-symmetry. Unlike a real basis it generates an additional quantum number (N _a ), in addition to the standard principal quantum number (N), and thus facilitates a more quantitative S ₃-classification of the various states than is usually possible. It is shown that certain bilinear forms with definite S ₃-symmetry properties, which can be constructed out of the linear harmonic-oscillator operators (a, a ^†) satisfy several uncoupled sets of SO(2, 1) algebras with spectra bounded from below. It is also briefly indicated how this S ₃-formalism can be adapted to the core structure of a more general relativistic three-particle system with unequal-mass kinematics through an appropriate choice of internal variables. Received May 11, 1994; revised November 3, 1994; accepted for publication November 23, 1994     

Fock-Space Projector Studied in Weyl Ordering Approach

We find that the Fock space projector |n〉〈n| is a Weyl ordered Laguerre polynomial 2 ^:_:(-)ⁿL_n ( 4a^fa ) e^-2afa :_:2{\,}^{:}_{:}(-)^{n}L_{n} ( 4a^{\dagger}a ) e^{-2a^{\dagger}a}{\,}^{:}_{:}, where a ^† a is the number operator,^:_: ^:_:,{}^{:}_{:}\ {}^{:}_{:} denotes the Weyl ordering symbol. This brings convenience to derive the Wigner functions of many other quantum states.     

Magnetism,exchange and crystal field parameters in the orbitally unquenched Ising antiferromagnet FePS3

FePS₃ is a layered antiferromagnet (T _N=123 K) with a marked Ising anisotropy in magnetic properties. The anisotropy arises from the combined effect of the trigonal distortion from octahedral symmetry and spin-orbit coupling on the orbitally degenerate⁵ T _2g ground state of the Fe²⁺ ion. The anisotropic paramagnetic susceptibilities are interpreted in terms of the zero field Hamiltonian, ℋ=Σ_i [δ(L _iz ² −2)+|λ|L _i .S _i ]−Σ _ij J _ij S _i .S _j . The crystal field trigonal distortion parameter Δ, the spin-orbit coupling λ and the isotropic Heisenberg exchange,J _ij, were evaluated from an analysis of the high temperature paramagnetic susceptibility data using the Correlated Effective Field (CEF) theory for many-body magnetism developed by Lines. Good agreement with experiment were obtained for Δ/k=215.5 K; λ/k=166.5 K;J _nn k=27.7 K; andJ _nnn k=−2.3 K. Using these values of the crystal field and exchange parameters the CEF predicts aT _N=122 K for FePS₃, which is remarkably close to the observed value of theT _N. The accuracy of the CEF approximation was also ascertained by comparing the calculated susceptibilities in the CEF with the experimental susceptibility for the isotropic Heisenberg layered antiferromagnet MnPS₃, for which the high temperature series expansion susceptibility is available.