States on the current algebra

We introduce the field algebra Σ$\text{D}$(M;ⁿ?ⁿ$\text{g}$) associated with the current algebra $\text{D}$_r(M;$\text{g}$) for the Lie algebra $\text{g}$ over physical space M. The Heisenberg magnet model is generalized to this continuum. It is shown that the Hamiltonian can be given meaning as implementing a derivation of the field algebra in certain representations.We introduce new representations of the current algebra. For example, if G = SU(2), a representation in L²(R³)?³ is [σ(?)F]^j = ε^jkl?_kψ_l for (?_k) = ? in $\text{D}$_r(M;$\text{g}$)(ψ_l = F. This has cyclic subrepresentations with prime parts.     

Anomalous mass dependence of glueball exclusive decay rates

Exclusive decays such as G → ππ are studied in the framework ofperturbative QCD. We discuss the possibility of the constituent gluons' virtualness scaling as the glueball mass M_G, which is a picture equivalent to a glueball containing a few slow-moving, heavy gluons. In this case, the decay rate exhibits a pinch singularity which enhances it by a factor of order (M_G²/m_q²)² over the dimensional scaling expectation. This singularity is partially suppressed by Sudakov effects which reduce the enhancement factor to $\text{(M}{}_{\mathrm{<mtext>G</mtext>}}{}^2\text{/m}{}_{\mathrm{<mtext>q</mtext>}}{}^2\text{)}{}^{\mathrm{2n}}\text{,}\text{where}\text{n ? 0.4}$.     

On generalized Clifford groups II

The earlier study of the irreducible representations of the generalized Clifford groups G^m_n in the case where m is a prime number, is now extended to the case where m is any integer. The analysis of class structure and hence the construction of the irreducible representations of G^m_n for a non-prime integer m is found to be more complicated. This investigation also requires the properties of the generalized Clifford algebras C^m_n(I) which are studied in Section 2 of the paper. The case of infinite generalized Clifford group, i.e. G^∞_n involving the infinite- order root of unity as well as the physical relevance of the generalized Clifford groups are briefly dealt with.     

On generalized Clifford groups. I

It is shown that using the basis elements of the generalized Clifford algebra C^m_n we can construct a group G?^m_n called the generalized Clifford group (G.C.G.) which is a generalization of the Dirac group of the 16 Dirac matrices and their negative counterparts. We have studied the irreducible representations of G.C.G. and we have found the connection with the group of linear transformations leaving invariant the expression $\text{∑}\text{i=1}\text{n}\text{(x}{}^{\mathrm{i}}\text{)}{}^{\mathrm{m}}$ for m>2.     

Relativity groups in the presence of matter

We show that the action of the boosts on an infinite system can be described continuously by bundle maps of Hilbert bundles based on the manifoldsG/G ₀, whereG is the full relativity group andG ₀ its closed subgroup which can be unitarily implemented on the fibre, which is a Hilbert space. We then develop a general theory of group representations on product bundlesM × ?, whereM is a manifold and ? a Hilbert space. We construct certain bundle representations of the Galilei and the Poincaré group and find that they correspond to various classes of elementary excitations. In particular, we define nonrelativistic zero-mass systems and obtain an analogue of the Faraday effect for the passage of hot electrons through matter. Our construction remains valid for the case whenG ₀ is the product of a lattice translation group and the time translations. We conclude that many qualitative features of the physics of condensed matter can be directly understood in terms of relativity group action on a bundle space as state space, which also suggests some avenues for further work.     

Correlation between band structure and hydride formation in dilute palladium alloys

Data on the free energy change ΔG, following solution of hydrogen in dilute Pd-alloys Pd_1?xM_x have been reviewed for different concentrations of M (M = Au, Ag, Pt, Ir, Rh, V, Cu, Ni, Pb, Sn and Ti) in both the α and β phases. The dependence of ΔG values upon the nature of the substituents (transition metals) is consistently explained within the framework of a metal-hydrogen bonding mechanism in the hydrides. For the β-hydride the ΔG values can be calculated on the basis of the equation ΔG = ΔG_pd + a(T)(〈?^M_LB〉 ? 〈?^Pd_LB〉)x, where $\text{ΔG}{}_{\mathrm{<mtext>Pd</mtext>}}\text{= ? 0.0489}\text{eV}\text{H}$ atom and is the free energy change of solution of hydrogen in pure Pd, a(T) = 0.194 at T = 298 K, 〈?^m_LB〉 and 〈?^pd_LB〉 are the average energies of the lowest band of the pure constituents ($\text{〈?}{}^{\mathrm{<mtext>Pd</mtext>}}{}_{\mathrm{<mtext>LB</mtext>}}\text{〉 = ?9.15}\text{eV}\text{atom}$). The stability of the palladium-hydrogen bond in dilute Pd-alloys depends on the value of 〈?^M_LB〉; for substituents having lower 〈?^M_LB〉 values than Pd the bond will strengthen, while for those having higher 〈?^M_LB〉 values it will weaken. This behaviour agrees well with the general trend of the stability of the stoichiometric hydrides predicted by Gelatt, Ehrenreich and Weiss using band structure results.     

Lifting classes of principal bundles

Given a principal G-bundle P over X, we define a particularly suitable equivalence relation between liftings of P with respect to a group morphism σ:M→G. Supposing that σ has a central kernel C, we obtain a free operation of H¹(X$\text{C}$) (with coefficients in the sheaf of C-valued functions) on the set of lifting classes of P, which is natural under change of groups and base spaces. It is simply transitive, if in addition σ is an epimorphism; otherwise we classify its orbits by sections in the associated bundle P × _G(G/σM).For $\text{C=}\text{Z}{}_{\mathrm{n}}$ we relate the lifting classes to similar classes of n-th roots of associated line bundles. In the differentiable case and for an epimorphism σ with discrete kernel, there is a natural lifting of partial principal connections in each of these lifting classes. Finally, we indicate some applications to geometric quantization.     

Verification of the laws of luminescence of solids for manganese complexes of benzyl-trimethylammonium and 2-chloropyridinium

A formula at low temperature for the function G($\text{1}\text{λ}$) = I_λλ⁶ has been derived in terms of configuration curve theory and checked on luminescence spectra near 77 K. The vibrational quantum in the excited state has been calculated from the decrease of G($\text{1}\text{λ}{}_{\mathrm{M}}$), where λ_M is the wavelength of the maxima of G at low temperature, as a function of temperature.     

A measurement of e+e− → pp for (1975 ⩽ s ⩽ 2250) MeV

The $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→}\text{p}\text{p}$ cross section has been measured in the energy interval (1975 ? 2E ? 2250) MeV for |cosθ| < 0.7. The measurement is based on ～ 100 events, thus improving by a factor 3 on the previous existing statistics in this energy interval. The form factor |G|² is given as a function of energy under the assumption |G_E| = |G_M|. We also give the first measurement of the differential cross section, averaged over the energy interval, and estimate the ratio G_M|/|G_E| from it.     

Continuum limit of QED2 on a lattice

A path integral is defined for the vacuum expectation values of Euclidean QED₂ on a periodic lattice. Wilson's expression is used for the coupling between fermion and gauge fields. The action for the gauge field by itself is assumed to be a quadratic in place of Wilson's periodic action. The integral over the fermion field is carried out explicitly to obtain a Matthews-Salam formula for vacuum expectation values. For a combination of gauge and fermion fields $\text{G}$ on a lattice with spacing proportional to N^?1, N?Z⁺, the Matthews-Salam formula for the vacuum expectation 〈G〉_N has the form ($\text{G}$)_N=∫d_nu;W_N($\text{G}$,f), where dμ is an N-independent measure on a random electromagnetic field ? and $\text{W}{}_{\mathrm{N}}\text{(G, ?)}$ is an N-dependent function of ? determined by $\text{G}$. For a class of $\text{G}$ we prove that as N → ∞, $\text{W}{}_{\mathrm{N}}\text{(C, ?)}$ has a limit $\text{W(G, ?)}$ except possibly for a set of ? of measure zero. In subsequent articles it will be shown that ∫d_nu;W_N($\text{G}$,f) exists and lim_N→∞∫d_nu;W_N($\text{G}$,f).     

A low right-handed scale in a supersymmetric context

We investigate the prospects for a low right-handed scale M_R in the context of locally supersymmetric O(10), limiting ourselves to the most interesting case of a single breaking scale between the grand unified scale M_X and the W-mass. It is found that supersymmetry seems to imply a unique solution as regards the Higgs content and the intermediate symmetry group if a low right-handed scale (less than 10⁴ GeV) exist at all. Apart from a minimal set of representations providing the symmetry battern, the Higgs sector consist of a pair of 16 and $\text{16}$ spinor representations ying at scale M_R and the residual symmetry is SU(3)_c × U(1)_B?L × SU(2)_L × U(1)_R.     

Brownian motion on a manifold as a limit of Brownian motions with drift

Let ?ⁿ be n-dimensional Euclidean space and let M ? ?ⁿ be a smooth compact m-dimensional Riemannian manifold (without boundary) embedded in ?ⁿ. By a Brownian motion on M we mean a Markovian process whose transition semigroup is defined by the generator ?½Δ_M, where Δ_M stands for the Laplace-Beltrami operator on M (see, e.g., [2]). This note extends a series of papers in which a measure generated by a Brownian motion on M on the space of trajectories (with values in M) can be represented as the weak limit of measures on the space of trajectories in the ambient space ?ⁿ (see [7–10]). Namely, we claim that a sequence of diffusion processes on ?n which are Brownian motions with drift (in the direction of the manifold) with infinitely increasing modulus converges in distribution to a Brownian motion on the manifold.     

Higgs bosons and matter-antimatter oscillations in GUTS

The presence of Higgs bosons of diquark and dilepton types at intermediate mass scales in GUTs is analysed in connection with the possible generation of neutron-antineutron and hydrogen-antihydrogen oscillations. Their renormalization effects on the calculation of the parameters sin²θ_w and m_b/m_τ are investigated in SU(5) and in an SO(10) version with a left-right symmetric breaking chain. In correspondence with suitable combination of higgses, we find solutions in SU(5) for n_G=3 and reasonable values of sin²θ_w, m_b/m_τ and proton lifetime τ_p, which allow detectable $\text{n}\text{-}\text{n}$, but undetectable $\text{H}\text{-}\text{H}$ transitions. Solutions of this type, but with higher τ_p, are also found in a particular scheme of SO(10), where the intermediate mass is at the scale M_R at which the left-right symmetry is broken and is of order 10²×m_w. This modifies then conclusions of analyses of SO(10) models, where either no diquarks and dileptons or only a specific set of them are taken into account.An extension of our analysis to supersymmetric versions of SU(5) and SO(10) does not produce acceptable solutions.     

Dynamical group quantization

The projective unitary irreducible representations U(G) of the space-time symmetry group G provides a unique quantization scheme for elementary particles. By extension a direct method of quantization for more general systems by the projective unitary representations U^$\text{G}$(G) induced from a dynamical group $\text{G}$ is outlined. Reducible relativistic composite systems are defined and the geometry of $\text{G}$ is discussed.     

1- Products in the method of orbits for nilpotent groups

On each orbit W of the coadjoint representation of any nilpotent (connected, simply connected) Lie group G, we construct 1-products and associated Von Neumann algebras $\text{G}$. G acts canonically on $\text{G}$ by automorphisms. In the unique faithful, irreducible representation of $\text{G}$, this action is implemented by the unitary irreducible representation of G corresponding to W by the Kirillov method. This construction is uniquely determined by W and gives the classification of all unitary irreducible representations of G.     

Calculation of the carrier concentration dependence of the Auger lifetime in degenerate n-type (Hg,Cd)Te

The Auger 1 lifetime expression for degenerate n-type (Hg_1?xCd_x)Te has been derived by replacing the Fermi-Dirac distribution functions for the pair of Auger collision electrons with step functions. The lifetime is calculated as a function of carrier concentration, _n0 for several values of energy gap and temperature using a non-parabolic band structure. We find that for strong degeneracy, the lifetime, τ_AlsuD varies as n₀^?γ where 0.7 ?γ? 1 and that γ is dependent upon the energy gap. The relatively slow dependence of τ_Al^D upon n₀, compared to the non-degenerate case () is due to the dependence of τ_Al on the threshold energy which for the degenerate case is a linear function of the Fermi energy, hence, a function of n₀.     

Unitary operators with discrete spectrum induced by measure preserving transformations

The purpose of this paper is to prove the following theorem.Theorem. Given a countable subset Λ on the circle K and an integer-valued function n(λ) on Λ, there exists a dynamical system with discrete spectrum (X,$\text{F}$,μ,T) such that Λ is the set of all eigenvalues of T and n(λ) is the multiplicity function of T if and only if there exist two systems of subgroups {G_i}_i∈N and $\text{{S}{}_{\mathrm{j}}\text{}}{}_{\mathrm{j\in M}}\text{(}\text{N}\text{??}{}_0\text{,}\text{M}\text{??}{}_0\text{)}$ of the circle such that Λ = G ∪ S and

$\text{n(λ)=}\text{∞}\text{for}\text{λ∈S,}\text{{i∈N; λ∈G}{}_{\mathrm{i}}\text{}}\text{for}\text{λ∈G?S,}$

where $\text{G =}\text{?}\text{i∈N}\text{G}{}_{\mathrm{i}}\text{, S =}\text{?}\text{j∈M}\text{S}{}_{\mathrm{j}}$.     

Bosonic construction of the Lie algebras of some non-compact groups appearing in supergravity theories and their oscillator-like unitary representations

We give a construction of the Lie algebras of the non-compact groups appearing in four dimensional supergravity theories in terms of boson operators. Our construction parallels very closely their emergence in supergravity and is an extension of the well-known construction of the Lie algebras of the non-compact groups $\text{SP}\text{(2n,}\text{R}$ and $\text{SO}\text{(2n)}{}^1$ from boson operators transforming like a fundamental representation of their maximal compact subgroup U(n). However this extension is non-trivial only for n?4 and stops at n = 8 leading to the Lei algebras of SU(4) × SU(1, 1), SU(1, 1), SU(5, 1), SO(12)¹ and E₇(7). We then give a general construction of an infinite class of unitary irreducible representations of the respective non-compact groups (except for E₇₍₇₎ and SO(12)¹ obtained from the extended construction). We illustrate our construction with the examples of SU(5, 1) and SO(12)¹.     

Limit cycle in a bound exciton recombination model in non-equilibrium semiconductors

A non-equilibrium semiconductor model involving the processes of photogeneration of electron-hole pairs (e-h) (rate G), stimulated creation of excitons from e-h (rate constant C) and decay of excitons on recombination centres (rate constant k) is analyzed in this paper for steady states and limit cycle behaviour. Considering the exciton decay to be similar to enzymatic processes in chemical reactions obeying a Michaelis-Menten law, and choosing units such that k = 1 = N, where N is the concentration of recombination centres, the model represents a 2-parameter (C and G) 2-dimensional (exciton and electron-hole concentrations x, n) dynamical system with a unique steady state (x₀,n₀) which is unstable in the region (l ? G)³?4C, the equality sign corresponding to the bifurcation curve in parameter space. In the region (l ? G)³ > 4C the system displays a unique stable limit cycle which is obtained in analytical form by employing a two-time-scales method for parameters in the neighbourhood of the bifurcation curve. The limit cycles are tilted ellipses with angular frequency $\text{}\text{?}$gw of the order of 10⁶ s^?1. In a realistic semiconductor situation G$\text{\$}\text{?}$10^?3.