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Journal articles on the topic 'Operator renormalization'

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Published: 10 December 2022

Last updated: 28 January 2023

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1

Kawamura, Hiroyuki, Tsuneo Uematsu, Yoshiaki Yasui, and Jiro Kodaira. "Renormalization of Twist-Four Operators in QCD Bjorken and Ellis–Jaffe Sum Rules." Modern Physics Letters A 12, no. 02 (January 20, 1997): 135–43. http://dx.doi.org/10.1142/s0217732397000133.

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The QCD effects of twist-four operators on the first moment of nucleon spin-dependent structure function g1(x,Q2) are studied in the framework of operator product expansion and renormalization group method. We investigate the operator mixing through renormalization of the twist-four operators including those proportional to the equation of motion by evaluating off-shell Green's functions in the usual covariant gauge as well as in the background gauge. Through this procedure we extract the one-loop anomalous dimension of the spin-1 and twist-four operator which determines the logarithmic correction to the 1/Q2 behavior of the contribution from the twist-four operators to the first moment of g1(x,Q2).

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2

Horn, D., W. G. J. Langeveld, H. R. Quinn, and M. Weinstein. "Operator renormalization group." Physical Review D 38, no. 10 (November 15, 1988): 3238–47. http://dx.doi.org/10.1103/physrevd.38.3238.

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3

SAKAI, KENJI. "HANDLE OPERATOR AND QUANTUM STRING EQUATION FROM WILSON’S RENORMALIZATION GROUP." Modern Physics Letters A 04, no. 22 (October 30, 1989): 2185–93. http://dx.doi.org/10.1142/s0217732389002458.

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We show explicitly a relationship between string one-loop amplitudes obtained by using a handle operator and those obtained by using a usual trace formula in the operator formalism on the sphere. Using this relationship we construct the handle operator as a product of two local operators. As a quantum (loop corrected) string equation we derive Wilson’s equation for the general partition function with handle operators.

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4

NAKAYAMA, YU. "VECTOR BETA FUNCTION." International Journal of Modern Physics A 28, no. 31 (December 19, 2013): 1350166. http://dx.doi.org/10.1142/s0217751x13501662.

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We propose various properties of renormalization group beta functions for vector operators in relativistic quantum field theories. We argue that they must satisfy compensated gauge invariance, orthogonality with respect to scalar beta functions, Higgs-like relation among anomalous dimensions and a gradient property. We further conjecture that nonrenormalization holds if and only if the vector operator is conserved. The local renormalization group analysis guarantees the first three within power counting renormalization. We verify all the conjectures in conformal perturbation theories and holography in the weakly coupled gravity regime.

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5

HAZARD, P. E. "Hénon-like maps with arbitrary stationary combinatorics." Ergodic Theory and Dynamical Systems 31, no. 5 (March 9, 2011): 1391–443. http://dx.doi.org/10.1017/s0143385710000398.

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AbstractWe extend the renormalization operator introduced in [A. de Carvalho, M. Martens and M. Lyubich. Renormalization in the Hénon family, I: universality but non-rigidity. J. Stat. Phys.121(5/6) (2005), 611–669] from period-doubling Hénon-like maps to Hénon-like maps with arbitrary stationary combinatorics. We show that the renormalization picture also holds in this case if the maps are taken to be strongly dissipative. We study infinitely renormalizable maps F and show that they have an invariant Cantor set 𝒪 on which F acts like a p-adic adding machine for some p>1. We then show, as for the period-doubling case in the work of de Carvalho, Martens and Lyubich [Renormalization in the Hénon family, I: universality but non-rigidity. J. Stat. Phys.121(5/6) (2005), 611–669], that the sequence of renormalizations has a universal form, but that the invariant Cantor set 𝒪 is non-rigid. We also show that 𝒪 cannot possess a continuous invariant line field.

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6

CHANDRAMOULI, V. V. M. S., M. MARTENS, W. DE MELO, and C. P. TRESSER. "Chaotic period doubling." Ergodic Theory and Dynamical Systems 29, no. 2 (April 2009): 381–418. http://dx.doi.org/10.1017/s0143385708080371.

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AbstractThe period doubling renormalization operator was introduced by Feigenbaum and by Coullet and Tresser in the 1970s to study the asymptotic small-scale geometry of the attractor of one-dimensional systems that are at the transition from simple to chaotic dynamics. This geometry turns out not to depend on the choice of the map under rather mild smoothness conditions. The existence of a unique renormalization fixed point that is also hyperbolic among generic smooth-enough maps plays a crucial role in the corresponding renormalization theory. The uniqueness and hyperbolicity of the renormalization fixed point were first shown in the holomorphic context, by means that generalize to other renormalization operators. It was then proved that, in the space ofC2+αunimodal maps, forα>0, the period doubling renormalization fixed point is hyperbolic as well. In this paper we study what happens when one approaches from below the minimal smoothness thresholds for the uniqueness and for the hyperbolicity of the period doubling renormalization generic fixed point. Indeed, our main result states that in the space ofC2unimodal maps the analytic fixed point is not hyperbolic and that the same remains true when adding enough smoothness to geta prioribounds. In this smoother class, calledC2+∣⋅∣, the failure of hyperbolicity is tamer than inC2. Things get much worse with just a bit less smoothness thanC2, as then even the uniqueness is lost and other asymptotic behavior becomes possible. We show that the period doubling renormalization operator acting on the space ofC1+Lipunimodal maps has infinite topological entropy.

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7

MAGGIORE, NICOLA. "ALGEBRAIC RENORMALIZATION OF N=2 SUPER YANG-MILLS THEORIES COUPLED TO MATTER." International Journal of Modern Physics A 10, no. 26 (October 20, 1995): 3781–801. http://dx.doi.org/10.1142/s0217751x95001789.

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We study the algebraic renormalization of N=2 supersymmetric Yang-Mills theories coupled to matter. A regularization procedure preserving both the BRS invariance and the supersymmetry is not known yet, so it is necessary to adopt the algebraic method of renormalization, which does not rely on any regularization scheme. The whole analysis is reduced to the solution of cohomology problems arising from the generalized Slavnov operator which summarizes all the symmetries of the model. Besides unphysical renormalizations of the quantum fields, we find that the only coupling constant of N=2 supersymmetric Yang-Mills theories can get quantum corrections. Moreover, we prove that all the symmetries defining the theory are algebraically anomaly-free.

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8

Antusch, Stefan, Manuel Drees, Jörn Kersten, Manfred Lindner, and Michael Ratz. "Neutrino mass operator renormalization revisited." Physics Letters B 519, no. 3-4 (November 2001): 238–42. http://dx.doi.org/10.1016/s0370-2693(01)01127-3.

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9

FRÖHLICH, JÜRG, MARCEL GRIESEMER, and ISRAEL MICHAEL SIGAL. "ON SPECTRAL RENORMALIZATION GROUP." Reviews in Mathematical Physics 21, no. 04 (May 2009): 511–48. http://dx.doi.org/10.1142/s0129055x09003682.

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The operator-theoretic renormalization group (RG) methods are powerful analytic tools to explore spectral properties of field-theoretical models such as quantum electrodynamics (QED) with non-relativistic matter. In this paper, these methods are extended and simplified. In a companion paper, our variant of operator-theoretic RG methods is applied to establishing the limiting absorption principle in non-relativistic QED near the ground state energy.

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10

Ishikawa, Tomomi. "Perturbative matching of continuum and lattice quasi-distributions." EPJ Web of Conferences 175 (2018): 06028. http://dx.doi.org/10.1051/epjconf/201817506028.

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Matching of the quasi parton distribution functions between continuum and lattice is addressed using lattice perturbation theory specifically withWilson-type fermions. The matching is done for nonlocal quark bilinear operators with a straightWilson line in a spatial direction. We also investigate operator mixing in the renormalization and possible O(a) operators for the nonlocal operators based on a symmetry argument on lattice.

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11

Huang, Xing, and Binchao Zhang. "Growth of a Renormalized Operator as a Probe of Chaos." Advances in High Energy Physics 2022 (October 10, 2022): 1–8. http://dx.doi.org/10.1155/2022/9216427.

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We propose that the size of an operator evolved under holographic renormalization group flow shall grow linearly with the scale and interpret this behavior as a manifestation of the saturation of the chaos bound. To test this conjecture, we study the operator growth in two different toy models. The first one is a MERA-like tensor network built from a random unitary circuit with the operator size defined using the integrated out-of-time-ordered correlator (OTOC). The second model is an error-correcting code of perfect tensors, and the operator size is computed using the number of single-site physical operators that realize the logical operator. In both cases, we observe linear growth.

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12

DOLAN, BRIAN P. "SYMPLECTIC GEOMETRY AND HAMILTONIAN FLOW OF THE RENORMALIZATION GROUP EQUATION." International Journal of Modern Physics A 10, no. 18 (July 20, 1995): 2703–32. http://dx.doi.org/10.1142/s0217751x95001273.

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It is argued that renormalization group flow can be interpreted as a Hamiltonian vector flow on a phase space which consists of the couplings of the theory and their conjugate “momenta,” which are the vacuum expectation values of the corresponding composite operators. The Hamiltonian is linear in the conjugate variables and can be identified with the vacuum expectation value of the trace of the energy-momentum operator. For theories with massive couplings the identity operator plays a central role and its associated coupling gives rise to a potential in the flow equations. The evolution of any quantity, such as N-point Green functions, under renormalization group flow can be obtained from its Poisson bracket with the Hamiltonian. Ward identities can be represented as constants of the motion which act as symmetry generators on the phase space via the Poisson bracket structure.

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13

ERCOLESSI, E., P. TEOTONIO-SOBRINHO, and G. BIMONTE. "DISCRETIZED LAPLACIANS ON AN INTERVAL AND THEIR RENORMALIZATION GROUP." International Journal of Modern Physics A 09, no. 25 (October 10, 1994): 4485–509. http://dx.doi.org/10.1142/s0217751x94001783.

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The Laplace operator admits infinite self-adjoint extensions when considered on a segment of the real line. They have different domains of essential self-adjointness characterized by a suitable set of boundary conditions on the wave functions. In this paper we show how these extensions can be recovered by studying the continuum limit of certain discretized versions of the Laplace operator on a lattice. Associated to this limiting procedure, there is a renormalization flow in the finite-dimensional parameter space describing the discretized operators. This flow is shown to have infinite fixed points, corresponding to the self-adjoint extensions characterized by scale-invariant boundary conditions. The other extensions are recovered by looking at the other trajectories of the flow.

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14

HOLLANDS, STEFAN. "RENORMALIZED QUANTUM YANG–MILLS FIELDS IN CURVED SPACETIME." Reviews in Mathematical Physics 20, no. 09 (October 2008): 1033–172. http://dx.doi.org/10.1142/s0129055x08003420.

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We present a proof that the quantum Yang–Mills theory can be consistently defined as a renormalized, perturbative quantum field theory on an arbitrary globally hyperbolic curved, Lorentzian spacetime. To this end, we construct the non-commutative algebra of observables, in the sense of formal power series, as well as a space of corresponding quantum states. The algebra contains all gauge invariant, renormalized, interacting quantum field operators (polynomials in the field strength and its derivatives), and all their relations such as commutation relations or operator product expansion. It can be viewed as a deformation quantization of the Poisson algebra of classical Yang–Mills theory equipped with the Peierls bracket. The algebra is constructed as the cohomology of an auxiliary algebra describing a gauge fixed theory with ghosts and anti-fields. A key technical difficulty is to establish a suitable hierarchy of Ward identities at the renormalized level that ensures conservation of the interacting BRST-current, and that the interacting BRST-charge is nilpotent. The algebra of physical interacting field observables is obtained as the cohomology of this charge. As a consequence of our constructions, we can prove that the operator product expansion closes on the space of gauge invariant operators. Similarly, the renormalization group flow is proved not to leave the space of gauge invariant operators. The key technical tool behind these arguments is a new universal Ward identity that is formulated at the algebraic level, and that is proven to be consistent with a local and covariant renormalization prescription. We also develop a new technique to accomplish this renormalization process, and in particular give a new expression for some of the renormalization constants in terms of cycles.

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15

Stubbins, Calvin. "Operator renormalization group and spin systems." Physical Review D 44, no. 2 (July 15, 1991): 488–503. http://dx.doi.org/10.1103/physrevd.44.488.

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16

Babu, K. S., C. N. Leung, and J. Pantaleone. "Renormalization of the neutrino mass operator." Physics Letters B 319, no. 1-3 (December 1993): 191–98. http://dx.doi.org/10.1016/0370-2693(93)90801-n.

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17

Capri, M. A. L., S. P. Sorella, R. C. Terin, and H. C. Toledo. "Renormalizability of pure 𝒩 = 1 super-Yang–Mills in the Wess–Zumino gauge in the presence of the local composite operators A2 and λ̄λ." International Journal of Modern Physics A 33, no. 28 (October 9, 2018): 1850161. http://dx.doi.org/10.1142/s0217751x18501610.

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The [Formula: see text] super-Yang–Mills theory in the presence of the local composite operator [Formula: see text] is analyzed in the Wess–Zumino gauge by employing the Landau gauge fixing condition. Due to the supersymmetric structure of the theory, two more composite operators, [Formula: see text] and [Formula: see text], related to the SUSY variations of [Formula: see text] are also introduced. A BRST invariant action containing all these operators is obtained. An all-order proof of the multiplicative renormalizability of the resulting theory is then provided by means of the algebraic renormalization setup. Though, due to the nonlinear realization of the supersymmetry in the Wess–Zumino gauge, the renormalization factor of the gauge field turns out to be different from that of the gluino.

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18

CHATURVEDI, S., A. K. KAPOOR, and V. SRINIVASAN. "RENORMALIZATION OF STOCHASTICALLY QUANTIZED FIELD THEORIES." International Journal of Modern Physics A 03, no. 01 (January 1988): 163–85. http://dx.doi.org/10.1142/s0217751x88000047.

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We discuss the renormalizability of stochastically quantized ϕ4 theory in four dimensions using the operator formalism of the Langevin equation developed by Namiki and Yamanaka. The operator formalism casts the Parisi Wu stochastic quantization scheme into a five-dimensional field theory. The usefulness of this approach over the one based directly on the Langevin equation is brought out for discussion of renormalization. We propose a new regularization scheme for the stochastic diagrams and use it to compute the renormalization constants and counter terms for the ϕ4 theory to second order in the coupling constant.

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19

Dragos, Jack, Thomas Luu, Andrea Shindler, and Jordy de Vries. "Electric Dipole Moment Results from lattice QCD." EPJ Web of Conferences 175 (2018): 06018. http://dx.doi.org/10.1051/epjconf/201817506018.

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We utilize the gradient flow to define and calculate electric dipole moments induced by the strong QCD θ-term and the dimension-6 Weinberg operator. The gradient flow is a promising tool to simplify the renormalization pattern of local operators. The results of the nucleon electric dipole moments are calculated on PACS-CS gauge fields (available from the ILDG) using Nf = 2+1, of discrete size 323×64 and spacing a ≃ 0.09 fm. These gauge fields use a renormalization-group improved gauge action and a nonperturbatively O(a) improved clover quark action at β = 1.90, with cSW = 1.715. The calculation is performed at pion masses of mπ ≃ 411, 701 MeV.

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20

ALEXANIAN, GARNIK G., and E. F. MORENO. "RENORMALIZATION OF HAMILTONIAN." International Journal of Modern Physics A 16, no. 11 (April 30, 2001): 1983–88. http://dx.doi.org/10.1142/s0217751x01004608.

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In this talk we describe a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group1. By a series of unitary transformations that successively decouple the high-frequency degrees of freedom and partially diagonalizes the high-energy part, we obtain the effective Hamiltonian for the low energy degrees of freedom. Using this technique we study λϕ4 theory at two loops and QED and Yang-Mills theory at one loop.

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21

Seke, J. "Development of a Novel Renormalization Technique in Nonrelativistic QED Based on a New Theoretical Concept." Modern Physics Letters B 11, no. 04 (February 10, 1997): 155–60. http://dx.doi.org/10.1142/s0217984997000219.

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A new renormalization concept is introduced. By using this new concept and a novel technique based on the resolvent-operator method, it is shown, for the first time to our knowledge, that an unambiquous renormalization to all orders of the interaction can be carried out in nonrelativistic QED.

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22

Yampolsky, Michael. "On the eigenvalues of a renormalization operator." Nonlinearity 16, no. 5 (June 20, 2003): 1565–71. http://dx.doi.org/10.1088/0951-7715/16/5/301.

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23

Yampolsky, M. "On the eigenvalues of a renormalization operator." Nonlinearity 17, no. 2 (January 27, 2004): 743. http://dx.doi.org/10.1088/0951-7715/17/2/c01.

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24

Levitov, L. S. "Renormalization group for a quasiperiodic Schrödinger operator." Journal de Physique 50, no. 7 (1989): 707–16. http://dx.doi.org/10.1051/jphys:01989005007070700.

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25

Caracciolo, Sergio, Andrea Montanari, and Andrea Pelissetto. "Operator product expansion and non-perturbative renormalization." Nuclear Physics B - Proceedings Supplements 73, no. 1-3 (March 1999): 273–75. http://dx.doi.org/10.1016/s0920-5632(99)85045-2.

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26

Robertson, David G. "Composite operator renormalization and the trace anomaly." Physics Letters B 253, no. 1-2 (January 1991): 143–48. http://dx.doi.org/10.1016/0370-2693(91)91375-6.

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27

Glasko, A. V. "One Property of the Renormalization Group Operator." Theoretical and Mathematical Physics 138, no. 1 (January 2004): 59–66. http://dx.doi.org/10.1023/b:tamp.0000010633.34984.43.

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28

Ji, Hao Yang, and Si Min Li. "The Attractor of Fibonacci-like Renormalization Operator." Acta Mathematica Sinica, English Series 36, no. 11 (November 2020): 1256–78. http://dx.doi.org/10.1007/s10114-020-9185-8.

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29

GORBOVICKIS, IGORS, and MICHAEL YAMPOLSKY. "Rigidity, universality, and hyperbolicity of renormalization for critical circle maps with non-integer exponents." Ergodic Theory and Dynamical Systems 40, no. 5 (September 25, 2018): 1282–334. http://dx.doi.org/10.1017/etds.2018.82.

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We construct a renormalization operator which acts on analytic circle maps whose critical exponent $\unicode[STIX]{x1D6FC}$ is not necessarily an odd integer $2n+1$, $n\in \mathbb{N}$. When $\unicode[STIX]{x1D6FC}=2n+1$, our definition generalizes cylinder renormalization of analytic critical circle maps by Yampolsky [Hyperbolicity of renormalization of critical circle maps. Publ. Math. Inst. Hautes Études Sci.96 (2002), 1–41]. In the case when $\unicode[STIX]{x1D6FC}$ is close to an odd integer, we prove hyperbolicity of renormalization for maps of bounded type. We use it to prove universality and $C^{1+\unicode[STIX]{x1D6FC}}$-rigidity for such maps.

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30

Gattringer, Christof, M. Göckeler, Philipp Huber, and C. B. Lang. "Renormalization of bilinear quark operators for the chirally improved lattice Dirac operator." Nuclear Physics B 694, no. 1-2 (August 2004): 170–86. http://dx.doi.org/10.1016/j.nuclphysb.2004.06.013.

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31

JHA, P. K., and K. C. TRIPATHY. "SYMMETRIES OF THE RENORMALIZATION GROUP EQUATIONS AND THE SCALING LAW REVISITED." Modern Physics Letters A 08, no. 32 (October 20, 1993): 3017–23. http://dx.doi.org/10.1142/s0217732393001975.

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The symmetry associated with the renormalization group equation satisfied by the Wilson coefficients in the operator product expansion of the electromagnetic current in deep inelastic scattering is re-examined using Blueman-Cole-Obsiannikov-Olver program. It is shown that the system exhibits infinite-dimensional symmetry. From the characteristics, we derive the detailed solutions of the renormalization group equation and the scaling laws for Wilson moments.

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32

Costa, M., G. Panagopoulos, H. Panagopoulos, and G. Spanoudes. "Gauge-invariant renormalization of the gluino-glue operator." Physics Letters B 816 (May 2021): 136225. http://dx.doi.org/10.1016/j.physletb.2021.136225.

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33

Khan, Subrata. "Renormalization group evolution of the non-unitary operator." Nuclear Physics B 864, no. 1 (November 2012): 38–51. http://dx.doi.org/10.1016/j.nuclphysb.2012.06.005.

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34

Blossier, B., A. Le Yaouanc, V. Morénas, and O. Pène. "Lattice renormalization of the static quark derivative operator." Physics Letters B 632, no. 2-3 (January 2006): 319–25. http://dx.doi.org/10.1016/j.physletb.2005.10.026.

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35

Bagan, E., R. B. Mann, T. G. Steele, and U. Sarkar. "Renormalization-group evolution of the gluonicCP-violating operator." Physical Review D 43, no. 7 (April 1, 1991): 2233–35. http://dx.doi.org/10.1103/physrevd.43.2233.

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36

PAZ, GIL. "AN EFFECTIVE FIELD THEORY LOOK AT DEEP INELASTIC SCATTERING." Modern Physics Letters A 25, no. 24 (August 10, 2010): 2039–49. http://dx.doi.org/10.1142/s0217732310033803.

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This talk discusses the effective field theory view of deep inelastic scattering. In such an approach, the standard factorization formula of a hard coefficient multiplied by a parton distribution function arises from matching of QCD onto an effective field theory. The DGLAP equations can then be viewed as the standard renormalization group equations that determines the cutoff dependence of the nonlocal operator whose forward matrix element is the parton distribution function. As an example, the non-singlet quark splitting function is derived directly from the renormalization properties of the nonlocal operator itself. This approach, although discussed in the literature, does not appear to be well known to the larger high energy community. In this talk we give a pedagogical introduction to this subject.

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37

SYROS, C. "QUANTUM CHRONOTOPOLOGY AND TIME ASYMMETRY IN FIELD THEORY." International Journal of Modern Physics A 13, no. 32 (December 30, 1998): 5477–501. http://dx.doi.org/10.1142/s0217751x98002493.

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A new, physical definition of the time elements is mathematically given. Their union constitutes a disconnected time topological space, [Formula: see text]. Based on the properties of this time–space and using the theory of random quantum fields previously developed, a nonunitary evolution operator, [Formula: see text], is derived. [Formula: see text] breaks down into two disjunct, spontaneously renormalized evolution operators by quantizing the random field action integral: one operator is unitary, [Formula: see text], and the other non-measure-preserving, [Formula: see text]. [Formula: see text] coincides, apart from the renormalization, with the evolution operator of the standard QFT. U ump (τ) breaks time symmetry in QFT. It reconciles the time reversal invariance of the basic equations of quantum theory with the irreversibility of the macroscopic, and some microscopic, phenomena. It provides a basis for the CP violation in the neutral K0 meson decay. Functional integrals arising in the theory have in the limit countably additive measures.

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38

KIM, SANG-YOON. "RENORMALIZATION ANALYSIS OF INTERMITTENCY IN TWO COUPLED MAPS." International Journal of Modern Physics B 13, no. 03 (January 30, 1999): 283–92. http://dx.doi.org/10.1142/s0217979299000175.

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The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvalue associated with the scaling of the control parameter of the uncoupled one-dimensional map. However, the relevant "coupling eigenvalue" associated with coupling perturbation varies depending on the fixed maps. These renormalization results are also confirmed for a linearly-coupled case.

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39

MANN, R. B., and H. B. ZHENG. "PERTURBED W3 CONFORMAL THEORIES AND SPIN-4/3 PARAFERMIONIC COSET MODELS." Modern Physics Letters A 06, no. 25 (August 20, 1991): 2281–87. http://dx.doi.org/10.1142/s0217732391002670.

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40

Morinelli, Vincenzo, Gerardo Morsella, Alexander Stottmeister, and Yoh Tanimoto. "Scaling Limits of Lattice Quantum Fields by Wavelets." Communications in Mathematical Physics 387, no. 1 (August 14, 2021): 299–360. http://dx.doi.org/10.1007/s00220-021-04152-5.

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AbstractWe present a rigorous renormalization group scheme for lattice quantum field theories in terms of operator algebras. The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We construct scaling maps for scalar lattice fields using Daubechies’ wavelets, and show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field, with the continuum action of spacetime translations. In particular, lattice fields are identified with the continuum field smeared with Daubechies’ scaling functions. We compare our scaling maps with other renormalization schemes and their features, such as the momentum shell method or block-spin transformations.

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41

PANAT, P. V., B. DEY, D. G. KANHERE, and R. E. AMRITKAR. "WAVEFUNCTION RENORMALIZATION OF ONE HOLE IN A STRONGLY CORRELATED SYSTEM." Modern Physics Letters B 09, no. 25 (October 30, 1995): 1685–91. http://dx.doi.org/10.1142/s0217984995001704.

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The wavefunction renormalization factor Zk of a hole injected in a half-filled band in a strongly correlated system in two dimensions is evaluated analytically using the extended quasiparticle operator introduced by Dagotto and Schrieffer. A model Hamiltonian for such an extended hole is proposed. We analytically calculate Zk for different parameter values and observe that the Zk value increases as compared with what it would be if a bare hole operator is used. This is in conformity with the numerical observation of Dagotto and Schrieffer.

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42

Tanaka, Kazuhiro. "Spin Structure Functions of the Nucleon and Twist-3 Operators in QCD." Australian Journal of Physics 50, no. 1 (1997): 79. http://dx.doi.org/10.1071/p96048.

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We investigate the twist-3 spin-dependent parton distribution functions hL(x; Q2) and gT (x; Q2). We discuss the physical relevance of the parton distributions from the view point of the factorization theorem in QCD. A unique feature of the ‘measurable’ higher-twist distributions hL and gT is emphasized. We investigate the Q2 -evolution of hL and gT in the framework of the renormalization group and standard QCD perturbation theory. We calculate the anomalous dimension matrix for the twist-3 operators for hL and gT in the one-loop order. The operator mixing among the relevant twist-3 operators, including the operators proportional to the QCD equations of motion, is treated properly in a consistent scheme. Implications for future experiments are also discussed.

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43

Goto, Shin-itiro, and Kazuhiro Nozaki. "Liouville operator approach to symplecticity-preserving renormalization group method." Physica D: Nonlinear Phenomena 194, no. 3-4 (July 2004): 175–86. http://dx.doi.org/10.1016/j.physd.2004.02.004.

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44

Bach, Volker, Thomas Chen, Jürg Fröhlich, and Israel Michael Sigal. "Smooth Feshbach map and operator-theoretic renormalization group methods." Journal of Functional Analysis 203, no. 1 (September 2003): 44–92. http://dx.doi.org/10.1016/s0022-1236(03)00057-0.

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45

Browne, R. E., D. Dudal, J. A. Gracey, V. E. R. Lemes, M. S. Sarandy, R. F. Sobreiro, S. P. Sorella, and H. Verschelde. "Renormalization group aspects of the local composite operator method." Journal of Physics A: Mathematical and General 39, no. 25 (June 7, 2006): 7889–99. http://dx.doi.org/10.1088/0305-4470/39/25/s06.

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46

SYROS, C. "DERIVATION OF GIBBS STATES FORM QUANTUM FIELD THEORY." Modern Physics Letters B 04, no. 17 (September 20, 1990): 1089–98. http://dx.doi.org/10.1142/s0217984990001379.

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Abstract:

A Lorentz invariant and Hermitian statistical field theory is presented. Its derivation is based on the random field theory, the evolution operator and the path integration. It yields the density matrix, the Gibbs states and the temperatures for equilibrium, nonequilibrium and variable particles numbers states. The chemical potential follows from a spontaneous energy renormalization of the Hamiltonian in the evolution operator. The generalization to any field other than scalar fields is straightforward.

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47

BIEŃKOWSKA, JADWIGA. "THE RENORMALIZATION GROUP FLOW IN 2D N=2 SUSY LANDAU-GINSBURG MODELS." International Journal of Modern Physics A 08, no. 22 (September 10, 1993): 3945–64. http://dx.doi.org/10.1142/s0217751x93001600.

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We investigate the renormalization of N=2 SUSY Landau-Ginsburg models with central charge c=3p/(2+p) perturbed by an almost marginal chiral operator. We calculate the renormalization of the chiral fields up to the gg* order and of the nonchiral fields up to the g(g*) order. We propose a formulation of the nonrenormalization theorem and show that it holds in the lowest nontrivial order. It turns out that, in this approximation, the chiral fields cannot get renormalized: [Formula: see text]. The β function then remains unchanged: β=∈g.

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48

Ettaieb, Aymen, Habib Ouerdiane, and Hafedh Rguigui. "Powers of quantum white noise derivatives." Infinite Dimensional Analysis, Quantum Probability and Related Topics 17, no. 03 (August 5, 2014): 1450018. http://dx.doi.org/10.1142/s0219025714500180.

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We introduce a new operator obtained from the quantum white noise (QWN) derivatives which satisfies new important commutation relations generalizing those of the renormalized power white noise Lie algebra introduced by Accardi, Boukas and Franz (see Ref. 5) without using renormalization conditions.

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49

Sonoda, H. "The operator algebra at the Gaussian fixed-point." International Journal of Modern Physics A 36, no. 16 (June 2, 2021): 2150106. http://dx.doi.org/10.1142/s0217751x21501062.

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We consider the multiple products of relevant and marginal scalar composite operators at the Gaussian fixed-point in [Formula: see text] dimensions. This amounts to perturbative construction of the [Formula: see text] theory where the parameters of the theory are momentum-dependent sources. Using the exact renormalization group (ERG) formalism, we show how the scaling properties of the sources are given by the short-distance singularities of the multiple products.

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50

Freitas, Gabriel, and Marc Casals. "A novel method for renormalization in quantum-field theory in curved spacetime." International Journal of Modern Physics D 27, no. 11 (August 2018): 1843001. http://dx.doi.org/10.1142/s0218271818430010.

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In quantum-field theory in curved spacetime, two important physical quantities are the expectation value of the stress-energy tensor [Formula: see text] and of the square of the field operator [Formula: see text]. These expectation values must be renormalized, which is usually performed via the so-called point-splitting prescription. However, the renormalization method that is usually implemented in the literature, in principle, only applies to static, spherically-symmetric spacetimes, and does not readily generalize to other types of spacetime. We present a novel implementation of the renormalization procedure which may be used in the future for more general spacetimes, such as Kerr black hole spacetime. As an example, we apply our method to the renormalization of [Formula: see text] for a massless scalar field in Bertotti–Robinson spacetime.

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