Symmetry breaking in dynamical spacetimes

The behaviour of scalar electrodynamics under symmetry breaking by the Higgs mechanism is studied in a class of dynamical spacetimes—those having a Bianchi type I symmetry—which includes the spatially flat Robertson-Walker spacetimes. The Einstein equations are used to obtain the effective Lagrangian, from which it is shown thateither the gauge field does not become massive during symmetry breaking (in marked contrast with the case in which the background spacetime is static),or the symmetry breaking chooses not only a direction in the phase space of the Higgs field, but also a spatial direction in the spacetime sections.     

Constants of motion for linear evolution systems

A complete enumeration of all conserved densities, polynomial in x, t and the field derivatives, is given for a general class of skew-symmetric simple linear evolution systems which include the Klein—Gordon and Dirac equations.     

Particles without quarks

Based on a theory of primitive particles presented in two earlier papers, further applications to macro- and microphenomena are considered—for example, weather phenomena, earthquakes, photoemission, collision of particles, violation of parity, and decay modes. A broad class of leptons withSU(3) symmetry is proposed, together with a quarkless model of particles.     

A Remark on the Notion of Robust Phase Transitions

We point out that the high-qPotts model on a regular lattice at its transition temperature provides an example of a nonrobust—in the sense recently proposed by Pemantle and Steif—phase transition.     

Higgs Field—Fermion Coupling in the Tensor Dirac Theory

In previous work, the Dirac and Einstein equations were unified in a tetradformulation of a Kaluza—Klein model which gives precisely the usualDirac—Einstein Lagrangian. In this model, the self-adjoint modes of the tetraddescribe gravity, whereas the isometric modes of the tetrad together with a scalarfield describe fermions. The tetrad Kaluza—Klein model is based on a constrainedYang—Mills formulation of the Dirac Lagrangian in which the bispinor field is mapped to a set of SL(2, R) × U(1) gauge potentialsA ^K _a and a complex scalarfield . In this paper we generalize the map (A ^K _a , ) to multiplets of nbispinor fields representing a fermion multiplet as in standard electroweak theory.We show that the Lagrangian for bispinor multiplets used in the Standard Modelbecomes a constrained Yang—Mills Lagrangian, for which the Higgs fielddetermines a noninvariant gauge metric, thereby breaking the full gauge symmetry.     

Theoretical investigation of some hexagonal ferrite ac data

An almost new method has been confirmed for experimentalists to have a first insight into the solid under study, by investigating the Cole–Cole diagrams of both the electric modulus M^* and the permittivity ε^* at different temperatures. All points of M^* function at different temperatures of the investigated hexagonal ferrite data have been collected in one semicircular master curve for each composition. This indicates that the studied compositions belong to a category of solids having what we have referred to as an “electric stiffness” as the dominating property, which is the reciprocal to an “electric compliance”—this would be the dominating property if the permittivity ε^* points could be collected in a master curve. In the present work, it has been found that the Cole–Cole diagrams of M^* have given some detailed information that are not obviously displayed in the conductivity representation.Moreover, a fitting of the investigated experimental data of the hexagonal ferrites—BaZn_2-xMg_xFe₁₆O₂₇, where (x=0.0,0.4,0.8,1.2,1.6 and 2)—with Dyre's macroscopic model of ac conductivity has been performed.An indirect method of fitting of the investigated data with the percolation path approximation (PPA) final equation of Dyre's macroscopic model has shown quite satisfactory results especially at relatively low frequencies . Whereas for the effective medium approximation (EMA) final equation of Dyre's macroscopic model the fitting has failed in hexagonal ferrites on contrary with a limited success found in a previous work with spinel ferrites. This is attributed to the more complex structure of hexagonal ferrites than that of spinel ferrites which makes the EMA no more suitable.     

Nucleation of crystals from their liquid phase

Liquids can be supercooled below their melting temperature T_m or pressurized above their melting pressure P_m. Many authors relate the maximum degree of supercooling—or overpressurization—to a value of the liquid–solid interfacial tension by using the standard theory of nucleation. The main goal of this review is to examine whether this relation is justified or not. We consider general arguments and two main examples: liquid helium which is simple and pure, consequently a model system, and liquid water which is complex but ubiquitous. To cite this article: S. Balibar, F. Caupin, C. R. Physique 7 (2006).     

ABCD law for partially coherent Gaussian light,propagating through first-order optical systems

This paper shows under what condition the well-knownABCD law — which can be applied to describe the propagation of one-dimensional Gaussian light through first-order optical systems (orABCD systems) — can be extended to more than one dimension. It is shown that in the two-dimensional (or higher-dimensional) case anABCD law only holds for partially coherent Gaussian light for which the matrix of second-order moments of the Wigner distribution function is proportional to a symplectic matrix. Moreover, it is shown that this is the case if we are dealing with a special kind of Gaussian Schell model light, for which the real parts of the quadratic forms that arise in the exponents of the Gaussians are described by the same real, positive-definite symmetric matrix.     

Oxide growth and tunneling characteristics of Sn-SnO x -Sn junctions

Sn—SnO _x —Sn tunneling junctions were prepared by thermal oxidation of vacuum deposited Sn-films. The thickness growth of the oxide was followed by ellipsometric measurements. From logarithmic conductivity measurements the barrier heights were determined. The tunneling characteristic could be well described by the two-band-tunneling model using a value of 0.14 for the ratio of the effective masses in the oxide and the metal.     

Advances in optoelectronics in europe—the RACE and ESPRIT programmes

EditorialSpecial issue

Advances in optoelectronics in europe—the RACE and ESPRIT programmes     

Topological charges in monopole theories

Let us consider a monopole theory with a compact, simply connected gauge group and the Higgs field in the adjoint representation. Using root theory we show that.(i) The homotopy class of the Higgs field is ap-tuple of integers wherep is the dimension of the centre of the residual symmetry group. These Higgs charges can be expressed as surface integrals of differential forms.(ii) To any invariant polynomial on the Lie algebra is associated a topological invariant which turns out to be a combination of the Higgs charges.(iii) Electric charge is quantized. The monopole's magnetic charge is a combination — with the Higgs charges as coefficients — ofp basic magnetic charges which satisfy generalized Dirac conditions.The example ofG=SU(N) is worked out in detail.     

Observation of the surface photoelectric effect of metals: Surface photoyield spectra of aluminum

Surface photoemission spectra of metals have been discussed theoretically since Sommerfeld developed his model of a metal in 1928, the so-called jellium model. The subject is still highly controversial among theorists. A spectroscopic technique — surface photoemission spectroscopy on jellium (SPJ) — which fully exploits the properties of synchrotron radiation, made it possible to separate unambiguously the photoyield caused by the surface photoelectric effect of metals optically excited byp-polarized light from other contributions to the yield. The technique was applied to aluminum and surface photoyield spectra were obtained for the first time. The extreme surface sensitivity, which is implicit in the transition matrix element of the surface photoexcitation process of metals, was experimentally confirmed. The new technique, therefore, provides one of the most powerfull tools for the investigation of the charge distribution and the dielectric response at metal surfaces.     

The quantum theory of second class constraints: Kinematics

The problem of second class quantum constraints is here set up in the context ofC*-algebras, utilizing the connection with state conditions as given by the heuristic quantization rules. That is, a constraint set is said to be first class if all its members can satisfy the same state condition, and second class otherwise. Several heuristic models are examined, and they all agree with this definition. Given then a second class constraint set, we separate out its first class part as all those constraints which are compatible with the others, and we propose an algebraic construction for imposition of the constraints. This construction reduces to the normal one when the constraints are first class. Moreover, the physical automorphisms (assumed as conserving the constraints) will also respect this construction. The final physical algebra obtained is free of constraints, gauge invariant, unital, and with the right choice, simple. ThisC*-algebra also contains a factor algebra of the usual observables, i.e. the commutator algebra of the constraints. The general theory is applied to two examples—the elimination of a canonical pair from a boson field theory, as in the two dimensional anomalous chiral Schwinger model of Rajaraman [14], and the imposition of quadratic second class constraints on a linear boson field theory.     

Statistical geometry and space-time

In this paper I try to construct a mathematical tool by which the full structure of Lorentz geometry to space time can be given, but beyond that the background — to speak pictorially — the subsoil for electromagnetic and matter waves, too. The tool could be useful to describe the connections between various particles, electromagnetism and gravity and to compute observables which were not theoretically related, up to now. Moreover, the tool is simpler than the Riemann tensor: it consists just of a setS of line segments in space time, briefly speaking.To prevent misunderstanding: I am far from asserting to have really solved any physical problem. This short paper gives some mathematical ideas, only, which might — I hope — prove to be helpful in future     

Conformal field algebras with quantum symmetry from the theory of superselection sectors

According to the theory of superselection sectors of Doplicher, Haag, and Roberts, field operators which make transitions between different superselection sectors—i.e. different irreducible representations of the observable algebra—are to be constructed by adjoining localized endomorphisms to the algebra of local observables. We find the relevant endomorphisms of the chiral algebra of observables in the minimal conformal model with central chargec=1/2 (Ising model). We show by explicit and elementary construction how they determine a representation of the braid groupB which is associated with a Temperley-Lieb-Jones algebra. We recover fusion rules, and compute the quantum dimensions of the superselection sectors. We exhibit a field algebra which is quantum group covariant and acts in the Hilbert space of physical states. It obeys local braid relations in an appropriate weak sense.     

On intrinsic randomness of dynamical systems

We discuss the problem of nonunitary equivalence, via positivity-preserving similarity transformations, between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes. Dynamical systems admitting such nonunitary equivalence with stochastic Markov processes are said to beintrinsically random. In a previous work, it was found that the so-called Bernoulli systems (discrete time) are intrinsically random in this sense. This result is extended here by showing that a more general class of dynamical systems—the so-calledK systems andK flows—are intrinsically random. The connection of intrinsic randomness with local instability of motion is briefly discussed. We also show that Markov processes associated through nonunitary equivalence tononisomorphic K flows are necessarily non-isomorphic.Dr. Goldstein's research was supported in part by NSF Grant No. PHY78-03816.     

Identity Rule for Classical and Quantum Theories

It is shown that the identity rule — arule of inference which has the form of modus ponens butwith the operation of identity substituted for theoperation of implication — turns any ortholatticeinto either an orthomodular lattice (a model of a quantumtheory) or a distributive lattice (a model of aclassical theory). It is also shown that — asopposed to the implication algebras — one cannotconstruct an identity algebra although the identity rule contains theoperation of identity as the only operation.     

Time-Reverse ODESSA. A 1D Exchange Experiment for Rotating Solids with Several Groups of Equivalent Nuclei

A one-dimensional exchange experiment is proposed for magic-angle-spinning samples with several groups of equivalent nuclei undergoing internal exchange, such as pure reorientation, as opposed to mutual exchange. The method, which we term time-reverse ODESSA, is an extension of the recently proposed 1D ODESSA experiment for a single group of exchanging nuclei. When several different groups of spins are present, as is usually the case for carbon-13 in polymers and molecular crystals, the normal ODESSA spectrum yields phase-twisted spectra which are difficult to analyze quantitatively. This problem is solved in the time-reverse ODESSA experiment which yields pure absorption spectra for all families of side bands, as long as only internal exchange need be considered. The experiment consists of the usual three pulse sequence of 2D exchange,P1—t₁—P2—τ_m—P3—t₂(acquisition), except that the evolution time is fixed at half a rotation period,t₁= T_R/2, the mixing time is set to an odd number of half rotation periods, τ_m= (2G− 1)T_R/2, and the acquisition starts att₂= T_R/2 after the detection pulse,P3. The method is demonstrated using the carbon-13 spectra of dimethyl sulfone and an enriched sample of tropolone, and is applied to the study of the π flip of the inner benzene ring of 1,4-diphenoxybenzene. The scope and limitations of the method are discussed.     

A class of metric theories of gravitation on Minkowski spacetime

A class of metric theories of gravitation on Minkowski spacetime is considered, which is—provided that certain assumptions (staying close to the original ideas of Einstein) are made—the almost most general one that can be considered. In addition to the Minkowskian metric G a dynamical metric H (called the Einstein metric)is defined by means of a second-rank tensor field S (referred to as gravitational potential).The theory is defined by a Lagrangian , from which the field equations as well as, e.g., the energy-momentum tensor field for the gravitational field follow. The case of weak fields is considered explicitly. The static, spherically and time-inversal symmetric field is calculated, and as a first step to investigate the theory's viability the parameters are fitted to the experimental data of the perihelion advance and the deflection of light at the Sun. Finally the question of gauge freedoms in the gravitational potential is briefly discussed.