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Journal articles on the topic 'Nonperturbative'

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Author: Grafiati

Published: 4 June 2021

Last updated: 20 February 2023

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1

DIEGO, OSCAR. "NONPERTURBATIVE STOCHASTIC DEFINITIONS OF 2-D QUANTUM GRAVITY." Modern Physics Letters A 09, no. 26 (August 30, 1994): 2445–59. http://dx.doi.org/10.1142/s021773239400232x.

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I construct the ground state, up to first nonperturbative order, of the stochastic stabilization of the zero-dimensional matrix model which defines 2-D quantum gravity. It is given by the linear combination of a perturbative wave function and a nonperturbative one. The nonperturbative behavior which arise from the stabilized model and from the string equation are similar. I show the modification of the loop equation by nonperturbative contribution.

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2

Emelin, Maxim, and Radu Tatar. "Axion hilltops, Kahler modulus quintessence and the swampland criteria." International Journal of Modern Physics A 34, no. 28 (October 10, 2019): 1950164. http://dx.doi.org/10.1142/s0217751x19501641.

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We study the interplay among extrema of axion potentials, Kahler moduli stabilization and the swampland criteria. We argue that moving away from the minima of nonperturbatively generated axion potentials can lead to a runaway behavior of moduli that govern the couplings in the effective field theory. The proper inclusion of these degrees of freedom resolves the conflict between periodic axion potentials and the gradient de Sitter criterion, without the need to invoke the refined de Sitter criterion. We investigate the possibility of including this runaway direction as a model of quintessence that satisfies the swampland criteria. Using a single nonperturbative effect, the maximum along the axion direction provides such a runaway direction, which is unstable in the axion directions, sensitive to initial conditions and too steep to allow for a Hubble time of expansion without violating the field excursion criterion. Adding a second nonperturbative effect generates a saddle point in the potential satisfying the refined de Sitter criterion, which solves the steepness problem and improves the initial conditions problem although some fine-tuning remains required.

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3

Caracciolo, Sergio, and Andrea Pelissetto. "Nonperturbative lattice gravity." Nuclear Physics B - Proceedings Supplements 4 (April 1988): 78–82. http://dx.doi.org/10.1016/0920-5632(88)90086-2.

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4

Bender, Carl M. "Nonperturbative perturbation theory." Nuclear Physics B - Proceedings Supplements 11 (October 1989): 316–24. http://dx.doi.org/10.1016/0920-5632(89)90018-2.

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5

Ambjørn, J., A. Görlich, J. Jurkiewicz, and R. Loll. "Nonperturbative quantum gravity." Physics Reports 519, no. 4-5 (October 2012): 127–210. http://dx.doi.org/10.1016/j.physrep.2012.03.007.

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6

Chaudhuri, S., J. Lykken, and T. R. Morris. "Bigeneric nonperturbative strings." Physics Letters B 251, no. 3 (November 1990): 393–98. http://dx.doi.org/10.1016/0370-2693(90)90724-k.

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7

Pumplin, Jon. "Nonperturbative effects inτdecay." Physical Review D 41, no. 3 (February 1, 1990): 900–905. http://dx.doi.org/10.1103/physrevd.41.900.

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8

Badalyan, A. M., and V. P. Yurov. "Nonperturbative calculations ofhcandhbmasses." Physical Review D 42, no. 9 (November 1, 1990): 3138–41. http://dx.doi.org/10.1103/physrevd.42.3138.

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9

Jacobson, Ted, and Lee Smolin. "Nonperturbative quantum geometries." Nuclear Physics B 299, no. 2 (April 1988): 295–345. http://dx.doi.org/10.1016/0550-3213(88)90286-6.

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10

Neuberger, Herbert. "Nonperturbative BRS invariance." Physics Letters B 175, no. 1 (July 1986): 69–72. http://dx.doi.org/10.1016/0370-2693(86)90333-3.

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11

Shaparau, V. A., and V. I. Kuvshinov. "Nonperturbative Squeezed and Entangled Collinear Gluon States." Nonlinear Phenomena in Complex Systems 23, no. 4 (December 4, 2020): 435–41. http://dx.doi.org/10.33581/1561-4085-2020-23-4-435-441.

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We consider for the first time nonperturbative gluon state evolution up to the second order of smallness in time. Investigating gluon fluctuations at the nonperturbative stage we have proved theoretically the possibility of the existence of both single- and two-mode gluon squeezed states. The emergence of such remarkable states becomes pоssible owing to threeand four-gluon self-interactions. The three-gluon self-interaction leads to the squeezing effect at the next time stage of nonperturbative evolution.We have shown that the nonperturbative evolution during a short time leads both to colour squeezing and entanglement of gluons.

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12

Mariño, Marcos. "Nonperturbative effects and nonperturbative definitions in matrix models and topological strings." Journal of High Energy Physics 2008, no. 12 (December 30, 2008): 114. http://dx.doi.org/10.1088/1126-6708/2008/12/114.

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13

DIEGO, OSCAR, and JOSÉ GONZÁLEZ. "ON THE NATURE OF NONPERTURBATIVE EFFECTS IN STABILIZED 2-D QUANTUM GRAVITY." Modern Physics Letters A 09, no. 24 (August 10, 1994): 2253–64. http://dx.doi.org/10.1142/s0217732394002112.

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We remark that the weak coupling regime of the stochastic stabilization of 2-D quantum gravity has a unique perturbative vacuum. By means of Monte-Carlo simulations we show that the nonperturbative vacuum has no bounded eigenvalues around the local minimum of the stabilized potential. Nonperturbative effects can be assessed in the loop equation. This can be derived from the Ward identities of the stabilized model and is shown to be modified by nonperturbative terms.

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14

Takaura, Hiromasa. "Determination of HQET nonperturbative matrix elements with renormalon subtraction using Fourier transform." EPJ Web of Conferences 274 (2022): 03003. http://dx.doi.org/10.1051/epjconf/202227403003.

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As higher order perturbative series are available, it is becoming necessary to include nonperturbative effects in QCD calculations using the OPE. In order to systematically determine nonperturbative effects and to incorporate them into theoretical calculations, the renormalon problem should be resolved. We use a renormalon subtraction method utilizing Fourier transform to determine nonperturbative matrix elements of HQET, ⊼ and μ2π. This is the first determination performed with subtraction of the u = 1 renormalon.

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15

Guzzi, Marco, Tie-Jiun Hou, Sayipjamal Dulat, Jun Gao, Joey Huston, Pavel Nadolsky, Carl Schmidt, Jan Winter, Keping Xie, and C. P. Yuan. "CTEQ-TEA parton distribution functions with intrinsic charm." EPJ Web of Conferences 192 (2018): 00003. http://dx.doi.org/10.1051/epjconf/201819200003.

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We present a study in which the possibility of a (sizable) nonperturbative contribution to the charm parton distribution function (PDF) in a nucleon is investigated together with theoretical issues arising in its interpretation. The separation of the universal component of the nonperturbative charm from the rest of the radiative contributions is also discussed. We illustrate the potential impact of a nonperturbative charm PDF on LHC scattering processes. An estimate of nonperturbative charm magnitude in the CT14 and CT14HERA2 global QCD analyses at the next-to-next-to leading order (NNLO) in the QCD coupling strength is given by including the latest experimental data from HERA and the Large Hadron Collider. We show a comparison between different models of intrinsic charm and illustrate prospects for standard candle observables at the LHC.

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16

ALEKSEEV, A. I., and B. A. ARBUZOV. "AN INVARIANT CHARGE MODEL FOR ALL q2>0 IN QCD AND GLUON CONDENSATE." Modern Physics Letters A 20, no. 02 (January 20, 2005): 103–16. http://dx.doi.org/10.1142/s0217732305016439.

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Under assumption of singular behavior of invariant charge αs(q2) at q2≃0 and of large q2 behavior, corresponding to the perturbation theory up to four loops, a procedure is considered of smooth matching the β-function at a boundary of perturbative and nonperturbative regions. The procedure results in a model for αs for all q2>0 with dimensionless parameters being fixed and dimensional parameters being expressed in terms of only one quantity Λ QCD . The gluon condensate which is defined by the nonperturbative part of the invariant charge is calculated for two variants of "true perturbative" invariant charge, corresponding to freezing option and to analytic one in nonperturbative region. Dimensional parameters are fixed by varying normalization condition [Formula: see text]. It is obtained that on the boundary of perturbative region [Formula: see text], the procedure results in nonperturbative Coulomb component α Coulomb ≃0.25, the nonperturbative region scale q0≃1 GeV , the model parameter σ≃(0.42 GeV )2 which suits as string tension parameter, the gluon condensate appears to be close for two variants considered, K≃(0.33–0.36 GeV )4 (for [Formula: see text]).

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17

Yang, Jian-Jun, Hong-Qing Shen, and Guang-Lie Li. "Zero-Point Problem in Fixed-Point Gauge of Nonperturbative QCD." Modern Physics Letters A 12, no. 27 (September 7, 1997): 1983–89. http://dx.doi.org/10.1142/s021773239700203x.

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We discuss the essence of the zero-point in fixed-point gauge of nonperturbative QCD and describe how to set the zero-point appropriately in deriving the nonperturbative quark–gluon three-point vertex functions including gluon condensates.

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18

Mastropietro, Vieri. "Nonperturbative Adler-Bardeen theorem." Journal of Mathematical Physics 48, no. 2 (February 2007): 022302. http://dx.doi.org/10.1063/1.2436731.

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19

ADAMS, J., N. TETRADIS, J. BERGES, F. FREIRE, C. WETTERICH, and S. BORNHOLDT. "SOLVING NONPERTURBATIVE FLOW EQUATIONS." Modern Physics Letters A 10, no. 31 (October 10, 1995): 2367–79. http://dx.doi.org/10.1142/s0217732395002520.

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Nonperturbative exact flow equations describe the scale dependence of the effective average action. We present a numerical solution for an approximate form of the flow equation for the potential in a three-dimensional N-component scalar field theory. The critical behavior, with associated critical exponents, can be inferred with good accuracy.

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20

FERRARI, FRANK. "NONPERTURBATIVE DOUBLE SCALING LIMITS." International Journal of Modern Physics A 18, no. 04 (February 10, 2003): 577–91. http://dx.doi.org/10.1142/s0217751x03012424.

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Recently, the author has proposed a generalization of the matrix and vector models approach to the theory of random surfaces and polymers. The idea is to replace the simple matrix or vector (path)-integrals by gauge theory or nonlinear σ model (path)-integrals. We explain how this solves one of the most fundamental limitations of the classic approach: we automatically obtain nonperturbative definitions in non-Borel summable cases. This is exemplified in the simplest possible examples involving O (N) symmetric nonlinear σ models with N-dimensional target spaces, for which we construct (multi)critical metrics. The nonperturbative definitions of the double scaled, manifestly positive, partition functions rely on remarkable identities involving (path)-integrals.

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21

HÜBNER, MATTHIAS, and HERBERT SPOHN. "RADIATIVE DECAY: NONPERTURBATIVE APPROACHES." Reviews in Mathematical Physics 07, no. 03 (April 1995): 363–87. http://dx.doi.org/10.1142/s0129055x95000165.

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In radiative decay the coupled system, electron bound by some external potential plus radiation field, relaxes to the ground state in the long time limit. Our central issue is to prove such a behaviour on the basis of the corresponding Schrödinger equation. We argue that the spin-boson Hamiltonian is a simple, but physically still acceptable test case. We relate radiative decay to scattering theory and prove the existence of wave operators. Other approaches are reviewed and compared. Some challenging open problems are listed.

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22

Zhao, Xingbo, Anton Ilderton, Pieter Maris, and James P. Vary. "Nonperturbative Quantum Field Evolution." Few-Body Systems 55, no. 5-7 (February 4, 2014): 555–60. http://dx.doi.org/10.1007/s00601-014-0824-4.

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23

Gleiser, Marcelo, and Andrew F. Heckler. "Nonperturbative Effects on Nucleation." Physical Review Letters 76, no. 2 (January 8, 1996): 180–83. http://dx.doi.org/10.1103/physrevlett.76.180.

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24

Grunberg, Georges. "Nonperturbative unification of technicolor." Physical Review D 38, no. 3 (August 1, 1988): 1012–15. http://dx.doi.org/10.1103/physrevd.38.1012.

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25

Lepage, G. Peter. "High-precision nonperturbative QCD." Annals of Physics 315, no. 1 (January 2005): 193–212. http://dx.doi.org/10.1016/j.aop.2004.09.018.

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26

Solovtsov, I. L. "Nonperturbative expansion in QCD." Physics Letters B 340, no. 4 (December 1994): 245–49. http://dx.doi.org/10.1016/0370-2693(94)01260-1.

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27

Dimm, W., G. Peter Lepage, and Paul B. Mackenzie. "Nonperturbative “lattice perturbation theory”." Nuclear Physics B - Proceedings Supplements 42, no. 1-3 (April 1995): 403–5. http://dx.doi.org/10.1016/0920-5632(95)00263-9.

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28

Hamber, Herbert W., and Ruth M. Williams. "Nonperturbative simplicial quantum gravity." Physics Letters B 157, no. 5-6 (July 1985): 368–74. http://dx.doi.org/10.1016/0370-2693(85)90382-x.

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29

COURTOY, A., and SIMONETTA LIUTI. "ANALYSIS OF αsFROM THE REALIZATION OF QUARK-HADRON DUALITY." International Journal of Modern Physics: Conference Series 25 (January 2014): 1460046. http://dx.doi.org/10.1142/s2010194514600465.

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We present an analysis of the role of the running coupling constant at the intersection of perturbative and nonperturbative QCD in the context of the quark-hadron duality à la Bloom-Gilman. Our framework will be the unpolarized structure function of the proton in the resonance region. We suggest that the realization of duality is related to the inclusion of nonperturbative effects at the level of the coupling constant. The outcome of our analysis is a smooth transition from perturbative to nonperturbative QCD physics, embodied in the running of the coupling constant at intermediate scales.

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30

Dzhunushaliev, Vladimir. "Cosmological constant and Euclidean space from nonperturbative quantum torsion." International Journal of Geometric Methods in Modern Physics 12, no. 01 (December 28, 2014): 1550008. http://dx.doi.org/10.1142/s0219887815500085.

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Heisenberg's nonperturbative quantization technique is applied to the nonperturbative quantization of gravity. An infinite set of equations for all Green's functions is obtained. An approximation is considered where: (a) the metric remains as a classical field; (b) the affine connection can be decomposed into classical and quantum parts; (c) the classical part of the affine connection is the Christoffel symbols; (d) the quantum part is the torsion. Using a scalar and vector fields approximation it is shown that nonperturbative quantum effects give rise to a cosmological constant and an Euclidean solution.

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31

Simonov, Yu A. "Nonperturbative approach to the parton model." International Journal of Modern Physics A 31, no. 06 (February 24, 2016): 1650016. http://dx.doi.org/10.1142/s0217751x16500160.

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In this paper, the nonperturbative parton distributions, obtained from the Lorentz contracted wave functions, are analyzed in the formalism of many-particle Fock components and their properties are compared to the standard perturbative distributions. We show that the collinear and IR divergencies specific for perturbative evolution treatment are absent in the nonperturbative version, however for large momenta [Formula: see text] (string tension), the bremsstrahlung kinematics is restored. A preliminary discussion of possible nonperturbative effects in DIS and high energy scattering is given, including in particular a possible role of multihybrid states in creating ridge-type effects.

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32

WARNER, ROLAND C., and G. C. JOSHI. "INTERACTION BETWEEN COLOUR-SINGLET HADRONS FROM NONPERTURBATIVE QCD." International Journal of Modern Physics A 05, no. 19 (October 10, 1990): 3787–99. http://dx.doi.org/10.1142/s0217751x90001616.

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We present a nonperturbative QCD contribution to interactions between separated coloursinglet hadrons, arising from the nontrivial topology of the QCD vacuum. We have calculated the effect of the structure of the vacuum (modelled here as a dilute gas of instantons) on hadron propagation, as a way of studying at least some nonperturbative effects. We find that a nonperturbative interaction arises which is familiar to us from our earlier studies of many-body potentials in multiquark systems. This interaction is distinct from those earlier perturbative QCD calculations which bear a direct analogy to the van der Waals interaction of atomic physics.

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33

DZHUNUSHALIEV, VLADIMIR. "DYNAMICAL F(R) GRAVITIES." International Journal of Modern Physics D 21, no. 05 (May 2012): 1250042. http://dx.doi.org/10.1142/s0218271812500423.

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It is offered that F(R) modified gravities can be considered as nonperturbative quantum effects arising from Einstein gravity. It is assumed that nonperturbative quantum effects gives rise to the fact that the connection becomes incompatible with the metric, the metric factors and the square of the connection in Einstein–Hilbert Lagrangian have nonperturbative additions. In the simplest approximation both additions can be considered as functions of one scalar field. The scalar field can be excluded from the Lagrangian obtaining F(R) gravity. The essence of quantum correction to the affine connection as a torsion is discussed.

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34

CIVITARESE, O., P. O. HESS, and D. A. AMOR-QUIROZ. "GENERALIZED VARIATIONAL PROCEDURE: AN APPLICATION TO NONPERTURBATIVE QCD." International Journal of Modern Physics E 22, no. 09 (September 2013): 1350071. http://dx.doi.org/10.1142/s0218301313500717.

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We present a generalized variational procedure oriented to the algebraic solution of many-body Hamiltonians expressed in bosonic and fermionic variables. The method specializes in the nonperturbative regime of the solutions. As an example, we focus on the application of the method to nonperturbative QCD.

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35

CVETIČ, G., and JI-YOUNG YU. "NONPERTURBATIVE DISPERSIVE SECTOR IN STRONG (QUASI-)ABELIAN FIELDS." International Journal of Modern Physics A 16, no. 01 (January 10, 2001): 57–82. http://dx.doi.org/10.1142/s0217751x01002853.

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In strong (quasi-)Abelian fields, even at the one-loop level of the coupling constant, quantum fluctuations of fermions induce an effective Lagrangian density whose imaginary (absorptive) part is purely nonperturbative and known to be responsible for the fermion–antifermion pair creation. On the other hand, the induced real (dispersive) part has perturbative and nonperturbative contributions. In the one-loop case, we argue how to separate the two contributions from each other for any strength of the field. We show numerically that the nonperturbative contributions are in general comparable with or larger than the induced perturbative ones. We arrive at qualitatively similar conclusions also for the induced energy density. Further, we investigate numerically the quasianalytic continuation of the perturbative results into the nonperturbative sector, by employing (modified) Borel–Padé. It turns out that in the case at hand, we have to integrate over renormalon singularities, but there is no renormalon ambiguity involved.

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36

ALVAREZ-GAUMÉ, L., and J. L. F. BARBÓN. "NONLINEAR VACUUM PHENOMENA IN NONCOMMUTATIVE QED." International Journal of Modern Physics A 16, no. 06 (March 10, 2001): 1123–46. http://dx.doi.org/10.1142/s0217751x01002750.

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We show that the classic results of Schwinger on the exact propagation of particles in the background of constant field-strengths and plane waves can be readily extended to the case of nocommutative QED. It is shown that nonperturbative effects on constant backgrounds are the same as their commutative counterparts, provided the on-shell gauge-invariant dynamics are referred to a nonperturbatively related space–time frame. For the case of the plane wave background, we find evidence of the effective extended nature of noncommutative particles, producing retarded and advanced effects in scattering. Besides the known "dipolar" character of noncommutative neutral particles, we find that charged particles are also effectively extended, but they behave instead as "half-dipoles."

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37

LAUSCHER, O., and M. REUTER. "TOWARDS NONPERATURBATIVE RENORMALIZABILITY OF QUANTUM EINSTEIN GRAVITY." International Journal of Modern Physics A 17, no. 06n07 (March 20, 2002): 993–1002. http://dx.doi.org/10.1142/s0217751x02010418.

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We summarize recent evidence supporting the conjecture that four-dimensional Quantum Einstein Gravity (QEG) is nonperturbatively renormalizable along the lines of Weinberg's asymptotic safety scenario. This would mean that QEG is mathematically consistent and predictive even at arbitrarily small length scales below the Planck length. For a truncated version of the exact flow equation of the effective average action we establish the existence of a non-Gaussian renormalization group fixed point which is suitable for the construction of a nonperturbative infinite cutoff-limit. The cosmological implications of this fixed point are discussed, and it is argued that QEG might solve the horizon and flatness problem of standard cosmology without an inflationary period.

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38

Gingrich, Douglas M. "Collider searches for nonperturbative low-scale gravity states." International Journal of Modern Physics A 30, no. 34 (December 9, 2015): 1530061. http://dx.doi.org/10.1142/s0217751x15300616.

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The possibility of producing nonperturbative low-scale gravity states in collider experiments was first discussed in about 1998. The ATLAS and CMS experiments have searched for nonperturbative low-scale gravity states using the Large Hadron Collider with a proton–proton center-of-mass energy of 8 TeV. These experiments have now seriously confronted the possibility of producing nonperturbative low-scale gravity states which were proposed over 17 years ago. I will summarize the results of the searches, give a personal view of what they mean, and make some predictions for 13 TeV center-of-mass energy. I will also discuss early ATLAS 13 TeV center-of-mass energy results.

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39

Dzhunushaliev, Vladimir, and Vladimir Folomeev. "Dipole-like Field Configurations in Nonperturbative Vacuum." Symmetry 14, no. 12 (December 15, 2022): 2659. http://dx.doi.org/10.3390/sym14122659.

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A model of nonperturbative vacuum in SU(2) Yang–Mills theory coupled to a nonlinear spinor field is suggested. By analogy with Abelian magnetic monopole dominance in quantum chromodynamics, it is assumed that the dominant contribution to such a vacuum comes from dipole-like field configurations existing in this theory. Using an assumption of the behavior of the number density of dipole-like field configurations whose energy approaches infinity, we derive an approximate expression for the energy density of such nonperturbative vacuum symmetrical under translation that turns out to be finite, unlike the infinite energy density of perturbative vacuum. Using characteristic values of the parameters appearing in the expression for the nonperturbative energy density, it is shown that this density may be of the order of the energy density associated with Einstein’s cosmological constant. The physical interpretation of the spinor field self-coupling constant as a characteristic distance between dipole-like field configurations is suggested. The questions of experimental verification of the nonperturbative vacuum model under consideration and of determining its pressure are briefly discussed.

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40

Fried, H. M., T. Grandou, and R. Hofmann. "Casimir operator dependences of nonperturbative fermionic QCD amplitudes." International Journal of Modern Physics A 31, no. 20n21 (July 27, 2016): 1650120. http://dx.doi.org/10.1142/s0217751x16501207.

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In eikonal and quenched approximations, it is argued that the strong coupling fermionic QCD Green’s functions and related amplitudes depart from a sole dependence on the [Formula: see text] quadratic Casimir operator, [Formula: see text], evaluated over the fundamental gauge group representation. Noted in nonrelativistic quark models and in a nonperturbative generalization of the Schwinger mechanism, an additional dependence on the cubic Casimir operator shows up, in contradistinction with perturbation theory and other nonperturbative approaches. However, it accounts for the full algebraic content of the rank-2 Lie algebra of [Formula: see text]. Though numerically subleading effects, cubic Casimir dependences, here and elsewhere, appear to be a signature of the nonperturbative fermionic sector of QCD.

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41

SCHNITTGER, JENS, and ULRICH ELLWANGER. "NONPERTURBATIVE CONDITIONS FOR LOCAL WEYL INVARIANCE ON A CURVED WORLD-SHEET." International Journal of Modern Physics A 09, no. 11 (April 30, 1994): 1821–48. http://dx.doi.org/10.1142/s0217751x94000789.

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We investigate Weyl anomalies on a curved world-sheet to the second order in a weak field expansion. Using a local version of the exact renormalization group equations, we obtain nonperturbative results for the tachyon/graviton/dilaton system. We discuss the elimination of redundant operators, which play a crucial role for the emergence of target space covariance. Performing the operator product expansion on a curved world-sheet allows us to obtain the nonperturbative contributions to the dilaton β function. We find the β functions, after suitable field redefinitions, to be related to a target space effective action through a κ function involving derivatives. Also, we can establish a nonperturbative Curci-Paffuti relation including the tachyon β function.

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42

MIRAMONTES, J. LUIS, and JOAQUÍN SÁNCHEZ GUILLÉN. "UNIVERSALITY AND NONPERTURBATIVE DEFINITIONS OF 2D QUANTUM GRAVITY FROM MATRIX MODELS." International Journal of Modern Physics A 07, no. 26 (October 20, 1992): 6457–72. http://dx.doi.org/10.1142/s0217751x92002957.

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The universality of the nonperturbative definition of Hermitian one-matrix models following the quantum, stochastic, or d=1-like stabilization is discussed in comparison with other procedures. We also present another alternative definition, which illustrates the need of new physical input for d=0 matrix models to make contact with 2D quantum gravity at the nonperturbative level.

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43

Dzhunushaliev, V., and A. Makhmudov. "Scalar model of glueball in nonperturbative quantisation à la heisenberg." International Journal of Mathematics and Physics 6, no. 2 (2015): 74–79. http://dx.doi.org/10.26577/2218-7987-2015-6-2-74-79.

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44

Dzhunushaliev, Vladimir. "Toy Models of a Nonassociative Quantum Mechanics." Advances in High Energy Physics 2007 (2007): 1–10. http://dx.doi.org/10.1155/2007/12387.

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Toy models of a nonassociative quantum mechanics are presented. The Heisenberg equation of motion is modified using a nonassociative commutator. Possible physical applications of a nonassociative quantum mechanics are considered. The idea is discussed that a nonassociative algebra could be the operator language for the nonperturbative quantum theory. In such approach the nonperturbative quantum theory has observables and unobservables quantities.

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45

KONISHI, K. "RENORMALIZATION GROUP AND DYNAMICS OF SUPERSYMMETRIC GAUGE THEORIES." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1861–73. http://dx.doi.org/10.1142/s0217751x01004529.

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We discuss questions related to renormalization group and to nonperturbative aspects of non-Abelian gauge theories with N=2 and/or N=1 supersymmetry. Results on perturbative and nonperturbative β functions of these theories are reviewed, and new mechanisms of confinement and dynamical symmetry breaking recently found in a class of SU(nc), USp(2nc) and SO(nc) theories are discussed.

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46

Shojaei-Fard, Ali. "The Complexities of Nonperturbative Computations." Russian Journal of Mathematical Physics 28, no. 3 (July 2021): 358–76. http://dx.doi.org/10.1134/s1061920821030092.

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47

Suganuma, H., S. Umisedo, S. Sasaki, H. Toki, and O. Miyamura. "Monopole Dominance for Nonperturbative QCD." Australian Journal of Physics 50, no. 1 (1997): 233. http://dx.doi.org/10.1071/p96045.

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Abstract:

Monopole dominance for the nonperturbative features in QCD is studied both in the continuum and the lattice gauge theories. First, we study the dynamical chiral-symmetry breaking (DχSB) in the dual Higgs theory using the effective potential formalism. We find that the main driving force for DχSB is brought from the confinement part in the nonperturbative gluon propagator rather than the short-range part, which means monopole dominance for DχSB. Second, the correlation between instantons and QCD–monopoles is studied. In the Polyakov-like gauge, where A4(x) is diagonalized, the QCD–monopole trajectory penetrates the centre of each instanton, and becomes complicated in the multi-instanton system. Finally, using the SU(2) lattice gauge theory with 164 and 163 × 4, the instanton number is measured in the singular (monopole-dominating) and regular (photon-dominating) sectors, respectively. Instantons and anti-instantons only exist in the monopole sector both in the maximally abelian gauge and in the Polyakov gauge, which means monopole dominance for the topological charge.

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48

Gross, David J., and Alexander A. Migdal. "Nonperturbative two-dimensional quantum gravity." Physical Review Letters 64, no. 2 (January 8, 1990): 127–30. http://dx.doi.org/10.1103/physrevlett.64.127.

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Puig, Joaquim. "A nonperturbative Eliasson's reducibility theorem." Nonlinearity 19, no. 2 (December 9, 2005): 355–76. http://dx.doi.org/10.1088/0951-7715/19/2/007.

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Novikov, Viktor A. "Nonperturbative QCD and supersymmetric QCD." Physics-Uspekhi 47, no. 2 (February 28, 2004): 109–16. http://dx.doi.org/10.1070/pu2004v047n02abeh001632.

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