SCIENTIFIC ABSTRACT KADYSHEVSKIY, V. - KADZIELA, W.

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December 31, 1967
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SCIENTIFIC ABSTRACT
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KADYSHEVSKIY, V.G,.---- (Model for the scnlar field theory in quantizcA spae-time] Eodell skaliarnoi teorii, polia v kviintovannom prostvanstye- vremeni. Dubna, Ob"edineruVi. in-t iadernykh isel., Ic)62. 8 p. Offm 15..10) (Quantum field theory) (Mathematical models) (Hyperspace) S/020/62/147/005/016/027 B104/Bla6 AUTHORs Kadyshevskiy, V. G. TITLEs Various Para-aetrizations in the theory of quantized space- time PERIODICALs Akademiya nauk SIJI)R., Doklady, v. 1117, no- 3, 1962, 508 - 591 TUT i In this continuation of an earlier-paper (V. G. Kadvshevskiy, Zhi;'A"F, 41, 1865 (1961)) problems are discussed which arise from the ambiguous definition of the four-momentura vector in Snyder's theory (Phys. Rev., 71, 38 (1947); V. L. AvErbakh, B. V. Mledvedevp DAN, 54, 41 (1949); Yu. A. Gollfand, ZhETF, 57, 504 (1959)). This ambig-aity is due to the fact that an infinite set of relativistically covariant syslezis of coordi- nates can be introduced on the five-dimensional hyperaphere. Each of these systems turns into the Cartesian system on transition to thie ordinary pseudoeuclidean p-space. In the-papers mentioned above, the four-momentum Pm is the coordinate projection of n point of the hypersphere to th'r. tang'ent plane 1. With the aid of 14 one obtains Card 1/3 4?/ -ij 5/c,,,6,~'02 7 Various parammcllriz~,tiom in thu. 31(14/31136 Thu projuction:j (,)), ("), und (5) %re studied. -From t,,ii: tne prt-viow; papers in unt., in orthoeowtl -vojc,,;t,,t:n 4t~ iz; in- ferred tha'_ Ih-,- pz-ob*~~. ~jf t?,c rieht definition of thtl 1~o n to searchinLz tn,- corrQct form of the shift p(+)k, th-E., :orrect x tc. In relativintic sL;ace with Lob-achevskiy geometrj one h%s to f-ica a similar situation. AS'JOCIATIGNs Obllyvdinc-nnyy in.~tltat yadurn1kh ijslcdov)iniy 1".7rint ? R 6 NT _~, 1) June 25, by A"'. N. Bogolyubov, Academician 5 UBM ITT i,,Lk sJune 1~), 1962 Card 3/1 S/020/62/147/006/015/034 MOM AUTHOR: ZadyshgvekiY_'V --_G-- TITLE: A scalar field theory model in the quantized space - time continuum PERIODICAL; Akademiya nauk SSSR. Doklady, v. 14T, no. 6, 1962, 1336-1339 TEXT: Using the results of previous studies (H. Shyder, Fbys. Rev., 71, 38 (1947), V. G. Kadyshevskiyj DAN, 147, no- 3 (1962)) and the example of the simple scalar model, some generalizations of the quantum field theory are investigated, which are possible in'the formalism of the .quantized space - time continuum. Essentially,, the generalizations consist in substituting the function 6(p(-)q) defihed by the author,for 6(p-q). In the new scheme all xn coordinates are non-commutative operatori and all constructions are carried out in the p-space, which hae ponetant curvature. The four-momentum p is defined by the author. In the m interaction representation S = Texp [i (P) ,p (_ (P (+) k)) tp (k) dQpdgk (4) Card 1/2 B/02 62/147/006/015/034 A scalar field theory model B104YI3180 is obtained for the S-matrix, yvhere the symbol T indicates that (4) was reduced to the normal form in accordance with the Wick theoren. From investigation of the divereence of the integrals.on expansion the author concludes that the scatterin& matrix must here b? generalized by the form of normal S-matrix in which all inner integrations are carried out in tfie 0iolidean R 4 The functional S' = e,'+E exp V+ (P) V (-(p (-F') k)),p (k) dQpdQh 11 1 (15) d0, FT -0) 610" P) 4,t k,2 (k)T!P (- replaces the new S-matrix. The matrix elements are found by variation of S' through the arguments li(,*t~-' + ~ with subsequent leyelling of these arguments zero and analytical c ontinuation (type P4 --.P' -ip.) of the expressions into the physical region. ASSOCIATION: Ob"yedinennyy inatitut yadernykh isaledovaniy (Joint Institute of Nuclear Research) PRESENTED: June 23, 1962, by N. N. Bogolyubov, Academician SUBMITT7D: June 19, 1962 2 Car 2 ACCESSION NR; AP4019232 S/0056/64/046/002/0654/0662 AUTHOR: Kady*shevskiy, V. G. TITLE: A relativistic equation for the S-matrix In the p-represent-.. ation.I.tunitarity and causality conditions SOURCE: Zhurnalleksper. I teor. fiz.' v. 46, no. 2, 1964, 654-662 TOPIC TAGS: ---scattering matrix, S matrix, relativistic scattering matrix, p representation, unitarity condition, causality, conditIonp covariant formulation I ABSTRACT: This Is the first artlele In a series, and It deals with unitarity and causality of the S-matrix, which are rather diftioult to prove in general form In the p-representatilon. Consistent co- variant formulation of the theory of ihe scattering matrix Is devel- oped in the p-representation # such 4~ way that the unitarity and causality conditions have a compact form and are easy to demonstrate.. All the derivations are in the interaction presentation, with the self-interaotion, of a scalar field with a mass used as an example* The result Is a four dImensional, aquaiion of motion for the scatter-' 1/2 ACOESSION NR: AP4019232 Ing matrix in p-spaoe which is analogbus to the corresponding equa- tion In the E-representation. ~'It is-proposed to solve this equation by means of a diagram teohniqub In th~ next paper. "The author Is deeply grateful to B. A. Arbuzbv, N.-N. Bogolyubov, Yu. A.-Gollfa- nd, A. V. Yefremov, D. A, Kirzknits,,A. A. Logunov, L. D. Solov.'- yev, -I. Yo. Taxom, I.. Todorov, tind A. T. Filippov for numerous use- ful,disoubsioiisl. Orig. art. he:s: 1 figure and 65 tomlas. ASSOCIATION: 'Ob"yedinenny*y institut.yaderny*3ch Iss,ledovaniy (Joint Institute.of Nuclear Research), SUBMITTED: 10ju163 MATE A0Q: 27max64 ENOL; 00' SUB CODE: PH ~10. REY ~,SOV; 004 OTMM: 005 2/2 Card;---- ACCESSION NRs AP4025920 6/0056/64/046/003/0872/0883 AUTHORs Kady*shevskiv, V. G. A TITLE: Relativistic equation for the 6 matrix in-the p-representa- tion. 11. Perturbation theory SOURCE: Zhurnal eksperimentallnoy i teoreticbeskoy fizikit v. 46t no. 3, 1964j. 872-883 TOPIC TAGS: S matrix, p representation, relativistic equatione co- variant motion equation, scattering matrix, perturbation theory, diagram technique, particle quasiparticle multiple exchange# conser-I vation laws, integral equation singularity, real particle, quasipar- ticle ABSTRACT: The covariant equation of motion for the acattering ma- trix, obtained in the first part of the paper (ZhETF va 46, 654* 1964) is investigated by means of perturbation theory. A specific Card 1/3 ACCESSION NR: AP4025920 diagram technique, differing from the Feynman technique, is devel- oped for the purpose. Application of this technique to some specif- ic examples shows that the mechanism of interaction of real physical quantities can be represented as multiple exchange of both real par- ticles and quasiparticles. 4-momentum is not conserved if the qua- siparticles have mass, but energy-momentum is conserved if real particles interact with massless quasiparticles, 'rho use of "heavy" quasiparticles for exchange with real particles corresponds to the study of short-range action of the real particles, while the use of light quasiparticles corresponds to long-range action. A uni4ue fea-~-. ture of the new diagram technique is tbat-the divergences obtained 'I are contained only in the one-dimensional integrals with respect to the mass-like parameters, whereas the integrals with respect to.the momenta converges A proof of the latter statement is presented "The author expresses deep gratitude to Be A# Arbuzovo Be 14. Ba; baahov, U. Me 13agolyubovo Yu, A. Gallfand, V. he Xtremomp D* As Kirzhnits, A. A* Logunov, L. D. Solovlyovo 1. Yoe Twm, 1. Todorove Card 2/3 ACCESSION NR:, AP4025920 and A. T. Filippov for numerous useful discussions," Orig. art. bass! 5 figures and 46 formulas* ASSOCIATIONt Ob"yedinenny*y institut yaderny*kh issledovaniy (Joint Institute of Nuclear Research) !SUBMITTED: 10JU163 DATE ACQ& 16Apr64 ENCL& 00 SUB CODE: PH NO REP SOV: 004 OTHERs 000 'Card ,i 3/3 K-~-!)Y. ~ 111.1 .%lKlY ) Re pro 3 on ta t i on f c r a a t tc r i i ~ ir i;,~i L - ix I n (4 uw i ,,, , t f I u ! : t'! ~ (: or-'r. Dokl. AN SSSH 160 rio.3:573-5'*,14 Jit 165. (:.!I oll -19. 3), 1. Ob"yedinemnyy irotitut. y,,Aernykh tlugimt 3, 296-41. KADYSHNIKOV, V.M. Use of the method of integral relatlonijhip~v in 3olving~ complelle prognostic equations of meteorolofy. Izv.AN ';SL;R.,S-ar.j;eofiz. m.8:1083-1092 Ag 162. (14IRA 15:8) 1. Glaviloye upravlaniye gidrometeorologiciximkoy 3luzlib., SSSR, Vychislitelin;yy meteorologichoskly tsentr. (Numrical weather forecastingg) L 8578-66--EVI I /FCC Gil; ACC NR3 AT50080 2 SOURCE CODE: URi66-6616ii;~obolooolut~,11100,~i AUTHOR% Kadyshnikov, V. H. 4'Y' ,I:- dXG: none TITLE: Using a systen of general equations for short-range unathor forecasting SOURCE: Simpozium po chislennym m,1et0daA_proVcLza__po od Leningrad, d1drome6oizdi_f,_ 1964, 41-51 TOPIC TAGS: weather forecasting, mathematic method, mathematic prediction ABSTRAM: A. A. Dorodnitsyn's method'of integral x*lationsMps i-il mood for solvimg a t,,stem of general equations in hydrothermodynamics within the frMiawork of th;e quasi- static bypothesis. Conditions of stability are detemined 1'rom bitial data of a: finite-difference analog for linearized forecast equations. An eXample of foTecast by the proposed system is given. The relative error in this exatq)lip, calculated from 324 internal points, was 0.85, 0.59 and 0.59 for the 1000, $00 anti 000 mb surfav~s respectively. An explanation is given for the high relative. arror at sea la%n~l' and it is suggested that prognosis could be improved by taking ihccount of friction. Qrig art. has: 9 figures, 8 formulas. SUB CODE: ES/ SUBM DATE: 060ct64/ ORIG REF: 0101 OTH REr: ool 1: fo,~iq_66 EVP(e)/EIYT(m)/E',VP(t)/ETI/ENP(k) IJP(C) JD/JG ACC NR. AP6020738 SOURCE CODE: Uri /013 6 /06/000/006/0065/0067 AUTHOR: Kolchin, 0. P.; Chuveleva, N. _P.,-. Sqmar(~~oya V.; 1,7111penko, V. V.; 0- Men'shchik* ~:_VTW, --K-adyshevskly, V. S.; Bellmov, N. I.; A ~r an io'v"'I E. B. ORG: none TITLE: Manufacture of powdered n1oblum and its alloys by hydrogenating compacted metals and alloys SOURCE: Tsvetnyye metally, no. 6, 1966, 65-67 TOPIC TAGS: metal powder, powder metal production, n1oblum, powder metallurgy, hydrogenation, n1oblum alloy ABSTRACT: The report presents a method for manufacturing bighpuri-ty powders by hydro- 1 genating n1obluni or Its alloys at lower temperatures (360 to 400C) and lesser excess hydrogen I pressures (up to 0.7 atm) than those commonly required. The process Is even faster at tho reduced temperature levels. Hydrogenation and milling technIques are given in dotail for source materials derived by electron beam smelting or carbide heatinir processes. For the latter, direct yield of dehydrogenated powder was 91.4%, total yield 9;.3%, unaccountable lossli; es 1.1%. The Impurity content In niobium powders obtained from different compacted metals Is' UDC- 669.293-492.2 Pip U I HVIII 1144 C It I III I" I I UT 'I ."4 ~.4oqi~-66 ACC NR, AP6020738 ihren in Table 1. Table 1. Impurity content by man) in niobitim powdors Ckained from different compacted metals. hifflal material 11"owd- r (-0. 147 mm) F-C N N 0 C Reduced Nretal 0.0.1 0.27 0.15 0.0.; 0.2.1 0.05 0.127 O-Og 0.01 0.05 0.20 0-09 0.65 - 0.11 0.05 0.20 0.10 0.03 - 011.1 0.1.13 0.01 0.65 0,0,1 0.13 0.0c, 0.01) 0.07 0.24 0.05 0.65 10.32 0.05 0.20 0.07 0.04 0.30 0.05 0.15 0-06 0.65 - Ends of rods of a sintered Metal* 0.05 - 0.12 0.08 0.16 0.15-,,-. 0.04 0.45 0.20 0.02 0.46 0.26 0.05 0.25 0.12 0.05 - 0.11 0.04 0.27 0.08 0.05 0.30 0.11 - - - 0.0.5 0.35 0.36, 0.05 - - 0.06 1 0.40 0.10 *T~c sintered rods contain 0.02%N. 0.02%0;