Trace norm convergence of exponential product formula

LetH andK be lower-bounded self-adjoint operators whose form sum is denoted byH K. We show the norm inequality (e^–rH/2 e^–rK e^–rH/2)^1/r forr > 0 and any symmetric norm . WhenH +K is essentially self-adjoint and e^–K is of trace class, we prove that (e^–rH/2e^–rK e^–rH/2)^1/r converges asr 0 to e^–(H+K) in the trace norm.     

Symmetry transformations in Batalin-Vilkovisky formalism

Let us suppose that the functionalS on an odd symplectic manifold satisfies the quantum master equation e ^s = 0. We prove that in some sense every quantum observable (i.e. every functionH obeying _p (He ^s) = 0) determines a symmetry of the theory with the action functionalS. Research supported in part by NSF grant No. DMS-9201366.     

Search for lepton flavor violation in supersymmetric models via meson decays

Considering the constraints from the experimental data on μ→eγ$\mu \to e\gamma$, μ→3e$\mu \to 3e$, μ–e$\mu \text{–}e$ conversion, etc., we analyze the lepton flavor violating decays ?(J/Ψ,?(1S))→e⁺μ⁻(μ⁺τ⁻)$?(J/\Psi ,?(1S))\to e^{+}{\mu }^{-}({\mu }^{+}{\tau }^{-})$ in the scenarios of the minimal supersymmetric extensions of Standard Model with seesaw mechanism. Numerically, there is parameter space that the LFV processes of J/Ψ(?)→μ⁺τ⁻$J/\Psi (?)\to {\mu }^{+}{\tau }^{-}$ can reach the upper experimental bounds, meanwhile the theoretical predictions on μ→eγ$\mu \to e\gamma$, μ→3e$\mu \to 3e$, μ–e$\mu \text{–}e$ conversion satisfy the present experimental bounds. For searching of new physics, lepton flavor violating processes J/Ψ(?)→μ⁺τ⁻$J/\Psi (?)\to {\mu }^{+}{\tau }^{-}$ may be more promising and effective channels.     

Left regular representation and contraction of sl q (2) to e q (2)

The left regular representation of the quantum algebras sl _q (2) and e _q (2) are discussed and shown to be related by contraction. The reducibility is studied andq-difference intertwining operators are constructed.     

gl q (n) and quantum monodromy

A generalized Toda lattice based on gl(n) is considered. The Poisson brackets are expressed in terms of a Lax connection, L=–() and a classical r-matrix, {₁,₂}=[r,₁+₂}. The essential point is that the local lattice transfer matrix is taken to be the ordinary exponential, T=e; this assures the intepretation of the local and the global transfer matrices in terms of monodromy, which is not true of the T-matrix used for the sl(n) Toda lattice. To relate this exponential transfer matrix to the more manageable and traditional factorized form, it is necessary to make specific assumptions about the equal time operator product expansions. The simplest possible assumptions lead to an equivalent, factorized expression for T, in terms of operators in (an extension of) the enveloping algebra of gl(n). Restricted to sl(n), and to multiplicity-free representations, these operators satisfy the commutation relations of sl _q (n), which provides a very simple injection of sl _q (n) into the enveloping algebra of sl(n). A deformed coproduct, similar in form to the familiar coproduct on sl _q (n), turns gl(n) into a deformed Hopf algebra gl _q (n). It contains sl _q (n) as a subalgebra, but not as a sub-Hopf algebra.     

On the schwarz problem for the [^(\textsu)]\text2 \widehat{{\text{su}}}_{\text{2}} Knizhnik-Zamolodchikov equation

We study the monodromy representations ^k,Iof the mapping class group ₄ acting on 4-point blocks satisfying the Knizhnik-Zamolodchikov equation for the levelk su₂ current algebra. We classify all irreducible ^k,Iwhich are realized by finite groups; we also display finite irreducible components for the reducible representations corresponding tok = 10.Supported by the Federal Ministry of Science and Research, Austria.     

Experimental studies of few-body systems at MAMI

Few-body experiments at the Mainz Microtron were focused on a number of selected topics. Double-polarization experiments to determine the neutron electric form factor G_en have been performed using both deuterium and polarized helium-3 targets. The structure of ³He has been studied in the reactions ³H e⃗ e(e⃗e,e′n) and ³H e⃗ e(e⃗e,e′p) with large (transversal) missing momenta and in quasi-elastic electron scattering. Electromagnetically induced two-nucleon knockout has been investigated in order to study the role of correlated nucleon-nucleon motion in the nucleus. Measurements of the (e,e′pn) reaction on ³He and ¹⁶O were performed for the first time. A triple-polarization experiment of type ³H e⃗ e(e⃗e,e′e⃗p⃗)d has been performed, where, in addition, the spin of the knocked out proton is analyzed. This measurement provides information on the spin-dependent momentum distribution of proton-deuteron clusters in the ³He nucleus. Hence, by tagging the outgoing deuteron spin-polarized ³He might also serve as an effective polarized proton target for electron scattering experiments. Moreover, in inclusive ^3,4He(e,e′) measurements at low momentum transfer, the effect of 3-body-forces has been studied.     

Z 3-Graded exterior differential calculus and gauge theories of higher order

We present a possible generalization of the exterior differential calculus, based on the operator d such that d³=0, but d²0. The entities dx ⁱ and d² x ^k generate an associative algebra; we shall suppose that the products dx ⁱ dx ^k are independent of dx ^k dx ⁱ , while theternary products will satisfy the relation: dx ⁱ dx ^k dx ^m =jdx ^k dx ^m dx ⁱ =j ²dx ^m dx ^m dx ⁱ dx ^k , complemented by the relation dx ⁱ d² x ^k =jd² x ^k dx ⁱ , withj:=e^2i/3.We shall attribute grade 1 to the differentials dx ⁱ and grade 2 to the second differentials d² x ^k ; under the associative multiplication law the grades add up modulo 3.We show how the notion ofcovariant derivation can be generalized with a 1-formA so thatD:=d+A, and we give the expression in local coordinates of thecurvature 3-form defined as :=d² A+d(A ²)+AdA+A ³.Finally, the introduction of notions of a scalar product and integration of theZ ₃-graded exterior forms enables us to define the variational principle and to derive the differential equations satisfied by the 3-form . The Lagrangian obtained in this way contains the invariants of the ordinary gauge field tensorF _ik and its covariant derivativesD _i F _km .     

Accurate potential energy function and spectroscopic study of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical

This paper calculates the equilibrium internuclear separations, the harmonic frequencies and the potential energy curves of the X^2∑＋, A^2П and B^2∑＋ states of the CP radical by the highly accurate valence internally contracted multireference configuration interaction method with correlation-consistent basis sets （aug-cc-pV6Z for C atom and aug-cc-pVQZ for P atom）. The potential energy curves are all fitted with the analytic potential energy function by the least-square fitting. Employing the analytic potential energy function, we determine the spectroscopic constants （Be, αe and ωeχe） of these states. For the X2∑＋ state, the obtained values of De, Be, αe, ωeχe, Re and ωe are 5.4831 eV, 0.792119 cm-1, 0.005521 cm-1, 6.89653 cm-1, 0.15683 nm, 12535.11 cm-1, respectively. For the A2H state, the present values of De, Be,αe, ωeχe, Re and We are 4.586 eV, 0.703333 cm-1, 0.005458 cm-1, 6.03398 cm-1, 0.16613 nm, 1057.89 cm-1, respectively. For the B2E＋ state, the present values of De, Be, αe, ωeχe, Re and We are 3.506 eV, 0.677561 cm-1, 0.00603298 cm-1, 5.68809 cm-1, 0.1696 nm, 822.554 cm-1, respectively. For these states, the vibrational states with the rotational quantum number J equals zero （J = 0） are studied by solving the radial nuclear Schr6dinger equation using the Numerov method. For each vibrational state, the vibrational level, the classical turning points, the rotational inertial and the centrifugal distortion constants are calculated. Comparison is made with recent theoretical and experimental results.     

Fermion number creation via electromagnetism

Let an external current, whose support is confined to the space-like slab |x ⁰| < T in two-dimensional spacetime, build up a localized charge density which vanishes for times |x ⁰| > T. We show that the zero mass Dirac quantum field reacts to this current by a c-number shift of the fermion number, i.e. Q _out=Q _in+Q, with , where q(x ⁰) denotes the total external charge. For the shift of the axial charge we obtain an extension of existing results.     

Giant monopole resonances in the statistical model

The strength functions fore ⁺ e ^– pair decay of the isoscalar and isovector giant monopole resonances in highly excited nuclei are derived and used in a statistical model calculation of thee ⁺ e ^– pair energy spectrum from compound nuclear decay in¹¹⁰Sn following a fusion evaporation reaction. This result is then compared to thee ⁺ e ^– spectrum derived from internal pair decay of the giant dipole and giant quadrupole resonances. The computation shows that the pair decay from the excited-state GDR dominates the pair spectrum over the region of all giant resonances, exceedingL=0 transitions by at least a factor of ten. We also compute the angular correlations betweene ⁺ ande ^– for theL=0, L=1 andL=2 transitions and estimate their power to discriminate between the various multipolarities.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Update of the e + e − → π+π− cross section measured by the spherical neutral detector in the energy region 400 < √s < 1000 MeV

The corrected cross section of the e ⁺ e ⁻ → π⁺π⁻ process measured in the spherical neutral detector experiment at the VEPP-2M e ⁺ e ⁻ collider is presented. The update is necessary due to a flaw in the e ⁺ e ⁻ → π⁺π⁻ and e ⁺ e ⁻ → μ⁺μ⁻ Monte Carlo event generators used previously in data analysis. The text was submitted by the authors in English.     

Effect of in-medium parameters of ρ meson in its photoproduction reactions on nuclei

There exist model calculations showing the modification of the hadronic parameters of ρ meson in the nuclear environment. From these parameters, we extract the ρ-meson-nucleus optical potential and show the medium effect due to this potential on the ρ-meson mass distribution spectra in the photonuclear reactions. The calculated results reproduced reasonably the measured e ⁺ e ⁻ invariant mass, i.e., ρ-meson mass, distribution spectra in γ, ρ ⁰ → e ⁺ e ⁻ reactions on nuclei.

     

Theoretical investigations of spectroscopic parameters and molecular constants for electronic ground state of Cl2 and its isotopes

The potential energy curve of the Cl 2(X1Σg+) is investigated by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the largest correlation-consistent basis set, aug-cc-pV6Z, in the valence range. The theoretical spectroscopic parameters and the molecular constants of three isotopes, 35Cl2, 35Cl37Cl and 37Cl2, are studied. For the 35Cl2 (X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are obtained to be 2.3921 eV, 2.4264 eV, 0.19939 nm, 555.13 cm-1 , 2.6772 cm-1 , 0.001481 cm-1 and 0.24225 cm-1 , respectively. For the 35Cl37Cl(X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are calculated to be 2.3918 eV, 2.4257 eV, 0.19939 nm, 547.68 cm-1 , 2.6234 cm-1 , 0.00140 cm-1 and 0.23572 cm-1 , respectively. And for the 37C2 (X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are obtained to be 2.3923 eV, 2.4257 eV, 0.19939 nm, 540.06 cm-1 , 2.5556 cm-1 , 0.00139 cm-1 and 0.22919 cm-1 , respectively. These spectroscopic results are in good agreement with the available experimental data. With the potential of Cl2 molecule determined at the MRCI/aug-cc-pV6Z level of theory, the total of 59 vibrational states is predicted for each isotope when the rotational quantum number J equals zero (J = 0). The theoretical vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0, which are in excellent accordance with the available experimental findings.     

A possible way to promote antihydrogen formation via metastable antiprotonic helium atoms

A new way to promote antihydrogen formation via the recently discovered long-lived metastable states of antiprotonic helium atoms is discussed. Recombination processes such ase ^– ¯pHe⁺⁺ +e ⁺ e ^– e ⁺ ¯p + He⁰ are possible in this respect.Dedicated to Prof. Dr. P. Kienle on the occasion of his 60th birthday     

Resolved photon processes

We review high-energy scattering processes that are sensitive to the hadronic structure of the photon, describing theoretical predictions as well as recent experimental results. These processes include deep-inelastic electron-photon scattering ate ⁺ e ⁻ colliders; and the production of jets, heavy quarks and isolated photons in the collision of real photons ate ⁺ e ⁻ colliders, as well as in photon-photon collisions atep colliders. We also comment on minijet based calculations of totalγp andγγ cross-sections, and discuss the possibility that future lineare ⁺ e ⁻ colliders might produce very large photon fluxes due to the beamstrahlung phenomenon; in the most extreme cases, we predict more than one hadronicγγ event to occur at every bunch crossing.     

Probing anomalous Higgs couplings at an <Emphasis Type="Italic">eγ</Emphasis> collider using unpolarised beams

We examine the sensitivity of eγ colliders (based on e ⁺ e ⁻ linear colliders of c.m. energy 500 GeV) to the anomalous couplings of the Higgs to W-boson via the process e ⁻ γ → νWH. This has the advantage over e ⁺ e ⁻ collider in being able to dissociate WWH vertex from ZZH. We are able to construct several dynamical variables which may be used to constrain the various couplings in the WWH vertex.      

Unitary equivalence between a spin 1/2 charged particle in a two-dimensional magnetic field and a spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electric field

We prove the unitary equivalence between the Dirac HamiltonianH _D for a relativistic spin 1/2 neutral particle with an anomalous magnetic moment in a two-dimensional electrostatic fieldE = (E ₁,E ₂) and the direct sum of the Dirac-Weyl operatorsD(±A) for a spin 1/2 charged particle in two-dimensional magnetic fields ±dA with the vector potentialA =E ₂ dx ¹ -E ₁ dx ², (x ¹,x ²) ². As applications, we investigate the ground state and the spectra ofH _D.     

Electron cooling in three‐dimensional Dirac fermion systems at low temperature: Effect of screening

Hot electron cooling rate P, due to acoustic phonons, is investigated in three‐dimensional Dirac fermion systems at low temperature taking account of the screening of electron–acoustic phonon interaction. P is studied as a function of electron temperature T_e and electron concentration n_e. Screening is found to suppress P very significantly for about T_e < 0.5 K and its effect reduces considerably for about T_e > 1 K in Cd₃As₂. In Bloch–Grüneisen (BG) regime, for screened (unscreened) case the T_e dependence is P ～ T_e⁹(T_e⁵) and the n_e dependence gives P ～ n_e^–5/3 (n_e^–1/3). The T_e dependence is characteristic of 3D phonons and n_e dependence is characteristics of 3D Dirac fermions. The plot of P /T_e⁴ vs. T_e shows a maximum at temperature T_em which shifts to higher values for larger n_e. Interestingly, the maximum is nearly same for different n_e and T_em/n_e^1/3 being nearly constant. More importantly, we propose, the n_e dependent measurements of P would provide a clearer signature to identify 3D Dirac semimetal phase. (© 2016 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)