Restoration of Many Electron Wave Functions from One-Electron Density

General theorem describing a relation between diagonal of one-electron density matrix and a certain class of many-electron ensembles of determinant states is proved. As a corollary to this theorem a constructive proof of sufficiency of Coleman's representability conditions is obtained. It is shown that there exist rigorous schemes for construction of energy of many-electron system as functionals of one-electron density.Comment: LaTex, 10 page

N=4 Super Yang-Mills Low-Energy Effective Action at Three and Four Loops

We investigate the low-energy effective action in N=4 super Yang-Mills theory with gauge group SU(n) spontaneously broken down to its maximal torus. Using harmonic superspace technique we prove an absence of any three- and four-loop corrections to non-holomorphic effective potential depending on N=2 superfield strengths. A mechanism responsible for vanishing arbitrary loop corrections to low-energy effective action is discussed.Comment: LaTeX, 12 pages; minor correction

Grothendieck-Serre conjecture for adjoint groups of types E_6 and E_7 and for certain classical groups

Assume that R is a semi-local regular ring containing an infinite perfect field, or that R is a semi-local ring of several points on a smooth scheme over an infinite field. Let K be the field of fractions of R. Let H be a strongly inner adjoint simple algebraic group of type E_6 or E_7 over R, or any twisted form of one of the split groups of classical type O^+_{n,R}, n>=4; PGO_{n,R}, n>=4; PSp_{2n,R}, n>=2; PGL_{n,R}, n>=2. We prove that the kernel of the map H^1_{et}(R,H)-> H^1_{et}(K,H) induced by the inclusion of R into K is trivial. This continues the recent series of papers by the authors and N. Vavilov on the Grothendieck--Serre conjecture.Comment: 3 page

Quantum dynamics of N=1, D=4 supergravity chiral compensator

A new four-dimensional $N=1$ superfield model is suggested. The model is induced by supertrace anomaly of matter superfields in curved superspace and leads to effective theory of supergravity chiral compensator. A renormalization structure of this model is studied, one-loop counterterms are calculated and renormalization group equations are investigated. It is shown that the theory under consideration is infrared free

On quantum model of supergravity compensator

A new $N=1$ superfield model in $D=4$ flat superspace is suggested. This model describes dynamics of chiral compensator and can be treated as a low-energy limit of $D=4$, $N=1$ quantum superfield supergravity. Renormalization structure of this model is studied and one-loop counterterms are calculated. It is shown that the theory is infrared free. An effective action for the model under consideration is investigated in infrared domain. The lower contributions to the one-loop effective action are computed in explicit form.Comment: LaTeX, 9 page

On S.L. Tabachnikov's conjecture

S. L. Tabachnikov's conjecture is proved: for any closed curve $\Gamma$ lying inside convex closed curve $\Gamma_1$ the mean absolute curvature $T(\Gamma)$ exceeds $T(\Gamma_1)$ if $\Gamma\ne k\Gamma_1$. An inequality $T(\Gamma)\ge T(\Gamma_1)$ is proved for curves in a hemisphere

Generalized RECPs accounting for Breit effects: uranium, plutonium and superheavy elements 112, 113, 114

The Generalized Relativistic Effective Core Potential (GRECP) method is described which allows one to simulate Breit interaction and finite nuclear models by an economic way and with high accuracy. The corresponding GRECPs for the uranium, plutonium, eka-mercury (E112), eka-thallium (E113) and eka-lead (E114) atoms are generated. The accuracy of these GRECPs and of the RECPs of other groups is estimated in atomic numerical SCF calculations with Coulomb two-electron interactions and point nucleus as compared to the corresponding all-electron Hartree-Fock-Dirac-Breit calculations with the Fermi nuclear charge distribution. Different nuclear models and contributions of the Breit interaction between different shells are studied employing all-electron four-component methods.Comment: 16 pages, 10 tables, revtex4 styl

Lambda_b lifetime puzzle in heavy-quark expansion

Lifetime differences of heavy hadrons can be consistently computed in heavy-quark expansion. The leading effects appear through spectator interactions at order 1/m_b^3. We compute a well-defined subset of 1/m_b^4 corrections to the lifetime ratio of Lambda_b baryon and B_d meson. We find that these corrections are large and should be taken into account in the systematic analysis of heavy hadron lifetimes. We claim that they could shift the ratio \tau_{\Lambda_b}/\tau_{B_d} by as much as -4.5%, significantly reducing the discrepancy between the theoretical predictions and experimental observations.Comment: 4 pages, 2 figures, LaTeX2

Implications of decoupling effects for one-loop corrected effective actions from superstring theory

We study the decoupling effects in one-loop corrected N=1 supersymmetric theory with gauge neutral chiral superfields, by calculating the one-loop corrected effective Lagrangian that involves light and heavy fields with the mass scale M, and subsequently eliminating heavy fields by their equations of motion. In addition to new non-renormalizable couplings, we determine the terms that grow as log(M) and renormalize the fields and couplings in the effective field theory, in accordance with the decoupling theorem. However, in a theory derived from superstring theory, these terms can significantly modify low energy predictions for the effective couplings of light fields. For example, in a class of heterotic superstring vacua with an anomalous U(1) the vacuum restabilization introduces such decoupling effects which in turn correct the low energy predictions for certain couplings by 10-50%.Comment: 11 pages, Late

Accounting for Breit interaction in actinide and superheavy element compounds: 1. General remarks

The incorporation of the Breit interaction in atomic and molecular calculations is discussed in the framework of four-component all-electron and two-component relativistic effective core potential (RECP)formalisms. Contributions of the Breit interaction between different core and valence shells are studied in the Dirac-Fock approximation for the uranium, plutonium, ekathallium (Z=113), ekalead (Z=114) and other heavy atoms. It is shown that the two-electron Breit effects between the valence electrons can be neglected for "chemical accuracy" (1 kcal/mol) of calculation of spectroscopic properties of systems containing superheavy elements and actinides whereas large core-core and core-valence Breit contributions can be efficiently described by one-electron RECP operators. Different versions of the generalized RECPs with the Breit interaction taken into account are constructed for uranium and plutonium and tested in comparison with the corresponding all-electron four-component calculations.Comment: 15 pages, 2 figures, REVTeX4 style, submitted to Pthys.Rev.