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Franz Gross; Cetin Savkli; John Tjon

Thomas Jefferson National Accelerator Facility, Newport News, VA (United States). Funding organisation: USDOE Office of Energy Research (ER) (United States)

Thomas Jefferson National Accelerator Facility, Newport News, VA (United States). Funding organisation: USDOE Office of Energy Research (ER) (United States)

AbstractAbstract

[en] A scalar field theory with a χ†χφ interaction is known to be unstable. Yet it has been used frequently without any sign of instability in standard text book examples and research articles. In order to reconcile these seemingly conflicting results, we show that the theory is stable if the Fock space of all intermediate states is limited to a finite number of χ| χ loops associated with field χ that appears quadradically in the interaction, and that instability arises only when intermediate states include these loops to all orders

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16 Feb 2001; 124 Kilobytes; DOE/ER--40150-1811; NUCL-TH--0102041; WM--01-103; AC05-84ER40150; Available from PURL: https://www.osti.gov/servlets/purl/775029-eTkfs4/native/; No journal information given for this preprint

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Miscellaneous

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Jaekel, C.D.

Vienna Univ. (Austria). Inst. fuer Theoretische Physik

Vienna Univ. (Austria). Inst. fuer Theoretische Physik

AbstractAbstract

[en] In 1989 Prof H. Narnhofer and Prof. W. Thirring established a (nonlocal) model of fermions with pair interactions. The existence of equilibrium states and the appearance of mixing properties was proofed. If this model reflects the basic facts of nature, one has to expect and to require that at high temperatures there is a unique equilibrium state and at low temperatures there are many different equilibrium states. Uniqueness of the equilibrium state at high temperatures is the topic of this dissertation. One may be astonished, that the proof of the uniqueness requires such a huge machinery, while the existence of KMS-states followes from fairly general conditions. Two states differ, if they can be distinguished by experiment. If one considers now that we have to show that two KMS-states at high temperatures result into the same value in all experiments one can think of, one might get an idea how unhandy this problem is. Even a conscious numeration of all experiments was a problem. Surprisingly only a few principal ideas of the treatment of spin-models survive. The temperature is the leading parameter and therefore it is a good idea to make a high temperature perturbation expansion for the KMS-condition, which fixes an equilibrium state in mathematical terms. But when we choose a generating vector for the perturbation expansion the similarities end. We better use physical considerations: at high temperatures we expect that chemical bounds will be broken up and the interacting equilibrium state will differ only slightly from the equilibrium state for the free time evolution. Roughly spoken, one can expect that high-energetic particles neglect interactions and fly in a straight line. In chapter 2.4 the whole machinery is presented in an easy-to-survey manner on a simple interaction. But in the case of pair interactions every particle interacts with each other and so the author was not able to find an easily accessible form of the developed method for this case. Starting from bounded local interactions we release the spatial limit and prove the uniqueness of the KMS-state (with a momentum cutoff). (author)

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Jan 1993; 73 p; Available from Universitaetsbibliothek der Universitaet Wien, Dr. Karl Lueger-Ring 1, A-1010 Vienna (AT); Reference number D 27820.; Thesis (Dr. rer.nat.).

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Miscellaneous

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[en] Using results previously developed for non-perturbative description of persistent self-interactions in spin zero meson theories the pi-pi scattering cross section is calculated. The integrals which appear in the amplitude are convergent. (author)

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Journal Article

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Lettere al Nuovo Cimento; ISSN 0024-1318; ; v. 28(1); p. 5-7

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AbstractAbstract

[en] The work is devoted to the problem of solving a set of asymptotic equations describing the model hardon interaction. More specifically an interactive procedure consisting of two stages is proposed and the first stage is exhaustively studied here. The principle of contracting transformations has been applied for this purpose. Under rather general and natural assumptions, solutions in a series of metric spaces suitable for physical applications have been found. For each of these spaces a solution with unique definiteness is found. (authors)

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Journal Article

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Bulg. J. Phys; ISSN 0323-9217; ; v. 10 (1); p. 3-12

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[en] A method based upon the expansion of the wave function of few interacting particles onto a complete set of basis functions constructed by including a correlation factor into the harmonic-oscillator basis is developed. The results for three nucleons interacting via the Malflet-Tjon potential are presented and compared with Faddeev and Green's function Monte Carlo results. Preliminary results of the application of the method to more realistic nucleon-nucleon interactions and to the 3α system are briefly discussed

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[en] On the basis of a modified definition of the K-matrix we construct amplitudes for low-energy ππ, K K-bar and πK scatterings. An iteration scheme allows us to account for crossing symmetry and coupled-channel unitarity. We find that we have to include information on the masses and widths of the possible resonances - they cannot be predicted in this framework. As a result we present partial-wave amplitudes that agree well with experiments. Conclusions on several features of meson-meson scattering can be drawn. (author)

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55 refs.

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Journal Article

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Nuovo Cimento. A; ISSN 0369-3546; ; v. 41(1); p. 73-95

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[en] A class of optimal formalisms is derived to describe in the simplest possible way the relationship between the amplitudes of an arbitrary four-particle reaction and the experimental observables for that reaction. Within the optimal class (which includes none of the currently used formalisms) there are an infinite number of realizations depending on coordinate systems and quantization axes. The matrix connecting the bilinear combinations of amplitudes and the experimental observables (the X-matrix) for the optimal class consists only of small submatrices along the main diagonal, the maximum sizes of which are independent of the values of the spins involved. Two examples are worked out in detail: 1/2+0→1/2+0 and 1+1/2→0+1/2, and it is shown that the optimal prescription in conjunction with quantization along the normal of the reaction plane gives an unprecedentedly simple X-matrix as well as constraints among the observables imposed by parity conservation, which are also maximally simple. The advantages of the new class of formalisms are enumerated for the purposes of studies of high energy and nuclear reactions

Original Title

P invariance constraints

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Journal Article

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Annals of Physics (New York); v. 98(1); p. 128-159

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[en] Some considerations are presented in favour of the hypothesis on baryon charge nonconservation at the fundamental particle level provided strong gravitational interaction at short distances is taken into account. An estimation of the probability for one or two elementary particles to annihilate into energy is attempted. The value obtained is of the order of (10

^{45}grs.)^{-1}. Experimental verification of the decay proposed is noted to be a highly complicated one for pulse values required are of the order of 10^{28}eVOriginal Title

Novy tip radioaktivnogo raspada: gravitatsionnaya annigilyatsiya barionov

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10 refs.; for English translation see the journal Sov. Phys. - JETP.

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Journal Article

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Zhurnal Ehksperimental'noj i Teoreticheskoj Fiziki; v. 72(1); p. 18-21

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[en] A Comment on the Letter by E. Fischback et al., Phys. Rev. Lett. 60, 74 (1988)

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[en] We have extended a recent calculation of the nucleon-nucleon large angle elastic scattering amplitudes to the meson-baryon case. Comparison with the available experimental information indicates that we have an accurate description of hadronic interactions at short distances. (orig.)

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Phys. Lett., B; ISSN 0370-2693; ; v. 93(1/2); p. 187-190

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