A Condensed Matter Interpretation of SM Fermions and Gauge Fields

We present the bundle (Aff(3)⊗ℂ⊗Λ)(ℝ³), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each (ℂ⊗Λ)(ℝ³) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space (Aff(3)⊗ℂ)(ℤ³). This space allows a simple physical interpretation as a phase space of a lattice of cells. We find the SM SU(3) _c ×SU(2) _L ×U(1) _Y action on (Aff(3)⊗ℂ⊗Λ)(ℝ³) to be a maximal anomaly-free gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with ℤ₂-degenerated vacuum state. We construct anticommuting fermion operators for the resulting ℤ₂-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.     

Rigorous Analysis of Discontinuous Phase Transitions via Mean-Field Bounds

 We consider a variety of nearest-neighbor spin models defined on the d-dimensional hypercubic lattice ℤ ^d . Our essential assumption is that these models satisfy the condition of reflection positivity. We prove that whenever the associated mean-field theory predicts a discontinuous transition, the actual model also undergoes a discontinuous transition (which occurs near the mean-field transition temperature), provided the dimension is sufficiently large or the first-order transition in the mean- field model is sufficiently strong. As an application of our general theory, we show that for d sufficiently large, the 3-state Potts ferromagnet on ℤ ^d undergoes a first-order phase transition as the temperature varies. Similar results are established for all q-state Potts models with q≥3, the r-component cubic models with r≥4 and the O(N)-nematic liquid-crystal models with N≥3. Received: 22 July 2002 / Accepted: 12 January 2003 Published online: 5 May 2003 RID="⋆" ID="⋆" ? Copyright rests with the authors. Reproduction of the entire article for non-commercial purposes is permitted without charge. Communicated by J. Z.Imbrie     

A possible minimal gauge–Higgs unification

A possible minimal model of the gauge–Higgs unification based on the higher dimensional spacetime M ⁴⊗(S ¹/Z ₂) and the bulk gauge symmetry SU(3) _C ⊗SU(3) _W ⊗U(1) _X is constructed in some detail. We argue that the Weinberg angle and the electromagnetic current can be correctly identified if one introduces the extra U(1) _X above and a bulk scalar triplet. The VEV of this scalar as well as the orbifold boundary conditions will break the bulk gauge symmetry down to that of the standard model. A new neutral zero-mode gauge boson Z′ exists that gains mass via this VEV. We propose a simple fermion content that is free from all the anomalies when the extra brane-localized chiral fermions are taken into account as well. The issues on recovering a standard model chiral-fermion spectrum with the masses and flavor mixing are also discussed, where we need to introduce the two other brane scalars which also contribute to the Z′ mass in the similar way as the scalar triplet. The neutrinos can get small masses via a type I seesaw mechanism. In this model, the mass of the Z′ boson and the compactification scale are very constrained being, respectively, given in the ranges: 2.7 TeV<m _Z′<13.6 TeV and 40 TeV<1/R<200 TeV.     

Neutral currents in left-right symmetric gauge models

We analyse all the neutral-current phenomena following from the general class of gauge models based on the group SU(2) _L ⊗ SU(2) _R ⊗ U(1). It is found that the neutral-current couplings in these models bear a remarkable similarity to those in the standard Weinberg-Salam gauge model. The parameter which plays the role of sin²ϑ_w is found to lie between 0 and 1/2. Comparison with experimental data shows that even a model with the ratio of the masses of the twoZ bosons as small as 1.9 is not ruled out.     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ⁻ could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ⊗ (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)⊗(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ⊗ (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ⁻ radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ⁿ⁻ fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

Cation disordering in Ag2HgI4 and Cu2HgI4

The cation order-disorder transitions in Ag₂HgI₄ and Cu₂HgI₄ are first order. This is unusual, since in other superionic conductors the cation disordering is gradual with temperature if there is no structural phase transition. These two materials are also unique in that they have two disordering cations rather than one. A study of a two species lattice gas model shows that this extra degree of freedom is responsible for the first order nature of this transition on the fcc lattice.     

Rotational bands in the doubly odd 130Cs nucleus

The band structures built on the 5^- isomeric state ( T _1/2 = 3.46 m) in the doubly odd ¹³⁰Cs nucleus have been established up to I = 24? via the ¹²⁴Sn(¹¹B, 5n)¹³⁰Cs reaction. The previously observed bands based on the πh _11/2⊗νh _11/2, πg _7/2⊗νh _11/2 and πd _5/2⊗νh _11/2 configurations and a positive-parity side band with multiple connections to the α = 0 signature partner of the yrast πh _11/2⊗νh _11/2 band have been extended to higher spins. A new band based on the πh _11/2⊗νg _7/2 configuration is observed. The yrast πh _11/2⊗νh _11/2 band exhibits anomalous signature splitting whose magnitude decreases up to spin 15 and then increases without restoring the normal signature splitting. Received: 20 February 2001 / Accepted: 9 May 2001     

Observation of a πh9/2 ⊗ νi13/2 oblate band in 188Tl

Excited states in ¹⁸⁸Tl have been studied experimentally using the ¹⁵⁷Gd (³⁵Cl, 4n) reaction at a beam energy of 170MeV. A rotational band built on the πh _9/2 ⊗ νi _13/2 configuration with oblate deformation has been established for ¹⁸⁸Tl. Based on the structure systematics of the oblate πh _9/2 ⊗ νi _13/2 bands in the heavier odd-odd Tl nuclei, we have tentatively proposed spin values for the new band in ¹⁸⁸Tl. The πh _9/2 ⊗ νi _13/2 oblate band in ¹⁸⁸Tl shows low-spin signature inversion, and it can be interpreted qualitatively by the two-quasiparticle plus rotor model including a J-dependent p-n residual interaction.     

Is U(1) H a good family symmetry?

We analyze U(1) _H as a horizontal symmetry and its possibilities to explain the known elementary-fermion masses. We find that only two candidates, in the context of SU(3) _c ⊗SU(2) _L ⊗U(1) _Y ⊗U(1) _H nonsupersymmetric, are able to fit the experimental resultm _b≪m _t.     

Classification of Subsystems for Local Nets¶with Trivial Superselection Structure

Let ℱ be a local net of von Neumann algebras in four spacetime dimensions satisfying certain natural structural assumptions. We prove that if ℱ has trivial superselection structure then every covariant, Haag-dual subsystem ℬ is of the form ℱ₁ ^G ⊗I for a suitable decomposition ℱ=ℱ₁⊗ℱ₂ and a compact group action. Then we discuss some application of our result, including free field models and certain theories with at most countably many sectors. Received: 26 January 2000 / Accepted: 28 September 2000     

Gravity waves accompanying supernova explosions

Gravitational radiation arising during the formation of a protoneutron star is studied. Here it is mainly large-scale nonuniformities that develop inside the star. The entropy and density profiles of such nonuniformities resemble the “mushroom cloud” of a nuclear explosion. A bubble of hot neutron matter floats to the surface of the star, like the “mushroom cloud” of an explosion in the earth’s atmosphere. Depending on the symmetry of the problem, from two to six bubbles can float upward at the same time. The characteristic masses of such bubbles are 0.01M _⊗ and the radial velocities reach ∼0.1c. The energy radiated in the form of gravitational waves in one cycle of bubbles floating to the surface is ∼10⁻² M _⊗ c ²−10⁻¹⁰ M _⊗ c ². Such cycles occur repeatedly as the neutron star cools. This phase can last up to seconds. The total energy radiated in the form of gravitational radiation can reach 10⁻¹ M _⊗ c ². Pis’ma Zh. éksp. Teor. Fiz. 64, No. 12, 817–822 (25 December 1996)     

A frustrated quantum spin-s model on the Union Jack lattice with spins s > 1/2

The zero-temperature phase diagrams of a two-dimensional (2D) frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number s = 1 and s = \frac32\frac{3}{2}. The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that all nearest-neighbour (NN) exchange bonds are present with identical strength J ₁ > 0, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength J ₂ ≡ κ J ₁ > 0. The bonds are arranged such that on the 2×2 unit cell they form the pattern of the Union Jack flag. Clearly, the NN bonds by themselves (viz., with J ₂ = 0) produce an antiferromagnetic Néel-ordered phase, but as the relative strength κ of the frustrating NNN bonds is increased a phase transition occurs in the classical case (s→ ∞) at κ _c ^cl = 0.5 to a canted ferrimagnetic phase. In the quantum cases considered here we also find strong evidence for a corresponding phase transition between a Néel-ordered phase and a quantum canted ferrimagnetic phase at a critical coupling κ _c1 = 0.580 ± 0.015 for s = 1 and κ _c1 = 0.545 ± 0.015 for s = \frac32\frac{3}{2}. In both cases the ground-state energy E and its first derivative dE/dκ seem continuous, thus providing a typical scenario of a second-order phase transition at κ = κ _c1. However, the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. Thus, the phase transition at κ = κ _c1 between the Néel antiferromagnetic phase and the canted ferrimagnetic phase for both the s = 1 and s = \frac32\frac{3}{2} Union Jack models is similar in nature to that found previously for the s = \frac12\frac{1}{2} Union Jack model. It is thus also completely comparable to the transition in the s = \frac12\frac{1}{2} XXZ model on the 2D square lattice between two Néel antiferromagnetic phases, one aligned along the z-axis and the other along some perpendicular direction in the xy-plane.     

High-spin states of<Superscript>125</Superscript>Sb: Particle-core excitation coupling

Excited states of¹²⁵Sb have been studied using in-beam γ spectroscopy techniques via the¹²⁴Sn(⁷Li, α2n) reaction at a beam energy of 32 MeV. A high-spin level scheme including 21 new γ-transitions and 14 new excited states have been established. Three isomers have been identified at 1970, 2110 and 2471 keV and the ranges of their half-lives have been estimated from the delayed coincidence data. The level structure of¹²⁵Sb is discussed in terms of particle-core excitation coupling. With the help of empirical shell model calculations the three isomers are proposed to have three-quasiparticle πg_7/2⊗v(h _11/2 s _1/2)₅₋, πg_7/2⊗v(h _11/2 d _3/2)₇₋ and πg_7/2⊗v(h ₁₁^2/2)₁₀ ⁺ configurations, respectively.     

High-spin states in odd-odd 168Lu

High-spin states in the odd-odd ¹⁶⁸Lu nucleus, populated in the ¹⁵⁴Sm(¹⁹F,5n) reaction at a beam energy of 96 MeV, were investigated using in-beam γ-ray spectroscopy techniques. The BC neutron crossing in the yrast band, based on πg _7/2[404]7/2⁺⊗νi _13/2[642]5/2⁺ configuration, occurs at ħω= 0.31 MeV. The two side bands, based on πh _11/2[514]9/2⁻⊗νi _13/2[642]5/2⁺ and πh _9/2[541]1/2⁻⊗νi _13/2[642]5/2⁺ configurations, show anomalous signature-splitting and signature-inversion in the first one, to occur at ħω= 0.24 MeV. A moderately delayed BC-crossing is anticipated in the second one. Received: 15 June 1998 / Revised version: 11 January 1999     

Group theoretical aspects ofU B(6) ⊗U F(20) symmetry limits of IBFM related to theU B(5) andO B(6) limits of IBM

TheU ^B(6)⊗U ^F(20) Bose-Fermi dynamical symmetry of interacting boson-fermion model arises when the odd nucleon occupies single particle orbits withj=1/2, 3/2, 5/2, and 7/2. The subgroup structures ofU ^B(6)⊗U ^F(20) related to theU ^B(5) andO ^B(6) limits of sdIBM (U ^B(6)) are analysed. Broadly speaking,U ^B(6)⊗U ^F(20) admitsU ^BF(5)⊗U _s ^F (4), Spin^BF(5)⊗U _k ^F (5) andU ^BF(5)⊗U _s ^F (2) limits withU ^B(5) core and Spin^BF(6),O ^BF(5)⊗U _s ^F (4), Spin^BF(6)⊗U _k ^F (5) andO ^BF(6)⊗U _s ^F (2) limits withO ^B(6) core respectively. For each of these seven symmetry limits, group chains, quantum numbers labelling the basis states, generators and Casimir operators for the various subgroups and energy formulas are given. Recoupling coefficients (reduced Wigner coefficients) for constructing wavefunctions of low-lying states are tabulated and these will allow (together with sdIBMU ^B(5) andO ^B(6) limit results) one to calculateB(E2)’s,B(M1)’s, one and two nucleon transfer strengths etc. in the seven symmetry limits. Experimental examples for theU ^B(6)⊗U ^F(20) symmetry limits are briefly discussed.     

Surface States and Spectra

Let ℤ₊ ^{d +1}= ℤ⁺×ℤ₊, let H ₀ be the discrete Laplacian on the Hilbert space l ²(ℤ₊ ^{d +1}) with a Dirichlet boundary condition, and let V be a potential supported on the boundary ∂ℤ₊ ^{d +1}. We introduce the notions of surface states and surface spectrum of the operator H=H ₀+V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on σ(H ₀) with probability one. To prove this result we combine Aizenman–Molchanov theory with techniques of scattering theory. Received: 18 September 2000 / Accepted: 21 November 2000     

High-spin states of rotational bands built upon νi13/2 in 166Lu

High-Spin states of odd-odd ¹⁶⁶Lu were populated using the ¹³⁹La(³⁰Si,3nγ)¹⁶⁶Lu at a beam energy of 120 MeV. Twelve new γ-rays were placed on top of the previously known two rotational bands built upon πg _7/2⊗νi _13/2 and πh _11/2⊗νi _13/2. Extending high-spin states up to 21⁺ and 25⁻ for each band, we have observed the onset of band crossing near ħω _c ≈ 0.35 MeV. The band crossing frequency of the yrast πh _11/2⊗νi _13/2 band is consistent with the neutron BC band crossing observed in lighter odd-odd Lu isotopes.     

Rotational structures in the 125Cs nucleus

The collective band structures of the ¹²⁵Cs nucleus have been investigated by in-beam γ-ray spectroscopic techniques following the ¹¹⁰Pd ( ¹⁹F, 4n) reaction at 75MeV. The previously known level scheme, with rotational bands built on πg_7/2, πg_9/2 and πh_11/2 orbitals, has been extended and evolves into bands involving rotationally aligned ν(h_11/2)² and π(h_11/2)² quasiparticles. A strongly coupled band has been reassigned a high-K πh_11/2 ⊗ νg_7/2 ⊗ νh_11/2 three-quasiparticle configuration and a new side band likely to be its chiral partner has been identified. Configurations assigned to various bands are discussed in the framework of Principal/Tilted Axis Cranking (PAC/TAC) model calculations.