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Journal articles on the topic 'Chern-Simon'

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Published: 9 March 2023

Last updated: 10 March 2023

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1

SMOLIN, LEE. "INVARIANTS OF LINKS AND CRITICAL POINTS OF THE CHERN-SIMON PATH INTEGRALS." Modern Physics Letters A 04, no. 12 (June 20, 1989): 1091–112. http://dx.doi.org/10.1142/s0217732389001271.

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A method is given for evaluating the functional integrals of Chern-Simon field theories to first nontrivial order. The basis of this method is a background independent regularization which allows the factors associated with twists of the framing of loops to be computed. To first order, Witten’s result connecting the Jones polynomial to expectation values of the Chern-Simon theory is reproduced. Additionally, a method for constructing solutions to the classical field equations of the theory is described, and it is shown that a static solution to Einstein’s equations (in Ashtekar’s form) may be associated with every such solution.

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2

DESER, S., and Z. YANG. "A REMARK ON THE HIGGS EFFECT IN PRESENCE OF CHERN-SIMONS TERMS." Modern Physics Letters A 04, no. 22 (October 30, 1989): 2123–24. http://dx.doi.org/10.1142/s0217732389002380.

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3

HSIEH, CHUN-CHUNG. "COMBINATORIC AND DIAGRAMMATIC STUDY IN KNOT THEORY." Journal of Knot Theory and Its Ramifications 16, no. 09 (November 2007): 1235–53. http://dx.doi.org/10.1142/s0218216507005786.

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Motivated by Massey–Milnor linking and Chern–Simon–Witten perturbative quantum field theory, we developed some combinatorial and diagrammatic study in this paper, aiming at knot theory in the combinatoric aspect.

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4

ANEZIRIS, C., A. P. BALACHANDRAN, L. KAUFFMAN, and A. M. SRIVASTAVA. "NOVEL STATISTICS FOR STRINGS AND STRING “CHERN-SIMON” TERMS." International Journal of Modern Physics A 06, no. 14 (June 10, 1991): 2519–58. http://dx.doi.org/10.1142/s0217751x91001210.

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We study the statistics of identical strings in R3. Novel possibilities for string statistics are shown to exist at least in the absence of physical inputs such as the possibility of string pair creation. There are for instance strings which do not obey Bose, Fermi or parastatistics. There are also strings which violate the standard spin-statistics relation. The Abelian Chern-Simons Lagrangian which leads to anyons is generalized to strings. It leads to exotic phase changes of wave functions when strings are moved in homotopically nontrivial loops in the N-string configuration space. Non-Abelian generalizations of this Abelian string Lagrangian are also proposed.

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5

Amir, M. Jamil, and Sarfraz Ali. "Spherical Symmetric Gravitational Collapse in Chern-Simon Modified Gravity." International Journal of Theoretical Physics 55, no. 4 (November 7, 2015): 2040–52. http://dx.doi.org/10.1007/s10773-015-2844-3.

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6

NAKANISHI, N. "ASYMPTOTIC COMPLETENESS AND THE THREE-DIMENSIONAL GAUGE THEORY HAVING THE CHERN-SIMON TERM." International Journal of Modern Physics A 04, no. 05 (March 1989): 1055–64. http://dx.doi.org/10.1142/s0217751x89000480.

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The three-dimensional Abelian gauge theory having the Chern-Simon term is studied. When matter current is absent, the gauge field in covariant gauge is explicitly expressed in terms of asymptotic fields. It is shown that the mechanism of mass generation can be understood as a kind of the Higgs mechanism.

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7

Naschie, Mohamed S. El. "From Chern-Simon, Holography and Scale Relativity to Dark Energy." Journal of Applied Mathematics and Physics 02, no. 07 (2014): 634–38. http://dx.doi.org/10.4236/jamp.2014.27069.

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8

Helayël-Neto, J. A., Alireza Sepehri, and Tooraj Ghaffary. "The Origin of Chern-Simons Modified Gravity from an 11 + 3-Dimensional Manifold." Advances in High Energy Physics 2017 (2017): 1–13. http://dx.doi.org/10.1155/2017/6021419.

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It is our aim to show that the Chern-Simons terms of modified gravity can be understood as generated by the addition of a 3-dimensional algebraic manifold to an initial 11-dimensional space-time manifold; this builds up an 11+3-dimensional space-time. In this system, firstly, some fields living in the bulk join the fields that live on the 11-dimensional manifold, so that the rank of the gauge fields exceeds the dimension of the algebra; consequently, there emerges an anomaly. To solve this problem, another 11-dimensional manifold is included in the 11+3-dimensional space-time, and it interacts with the initial manifold by exchanging Chern-Simon fields. This mechanism is able to remove the anomaly. Chern-Simons terms actually produce an extra manifold in the pair of 11-dimensional manifolds of the 11+3-space-time. Summing up the topology of both the 11-dimensional manifolds and the topology of the exchanged Chern-Simons manifold in the bulk, we conclude that the total topology shrinks to one, which is in agreement with the main idea of the Big Bang theory.

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9

PAL, SHESANSU SEKHAR. "DERIVATIVE CORRECTIONS TO DIRAC–BORN–INFELD AND CHERN–SIMON ACTIONS FROM NONCOMMUTATIVITY." International Journal of Modern Physics A 17, no. 09 (April 10, 2002): 1253–71. http://dx.doi.org/10.1142/s0217751x0200993x.

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We show that the higher-order derivative α′ corrections to the Dirac–Born–Infeld (DBI) and Chern–Simon actions is derived from noncommutativity in the Seiberg–Witten limit, and is shown to agree with Wyllard's (hep-th/0008125) result, as conjectured by Das et al., (hep-th/0106024). In calculating the corrections, we have expressed [Formula: see text] in terms of F, Â in terms of A up to order [Formula: see text], and made use of it.

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10

Amir, M. Jamil, and Sarfraz Ali. "Ricci Dark Energy of Amended FRW Universe in Chern-Simon Modified Gravity." International Journal of Theoretical Physics 54, no. 4 (September 24, 2014): 1362–69. http://dx.doi.org/10.1007/s10773-014-2334-z.

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11

Ali, Sarfraz, and M. Jamil Amir. "A Study of Holographic Dark Energy Models in Chern-Simon Modified Gravity." International Journal of Theoretical Physics 55, no. 12 (September 6, 2016): 5095–105. http://dx.doi.org/10.1007/s10773-016-3131-7.

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12

Morales, Ivan, Bruno Neves, Zui Oporto, and Olivier Piguet. "Dimensionally Compactified Chern-Simon Theory in 5D as a Gravitation Theory in 4D." International Journal of Modern Physics: Conference Series 45 (January 2017): 1760005. http://dx.doi.org/10.1142/s2010194517600059.

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We propose a gravitation theory in 4 dimensional space-time obtained by compacting to 4 dimensions the five dimensional topological Chern-Simons theory with the gauge group SO(1,5) or SO(2,4) – the de Sitter or anti-de Sitter group of 5-dimensional space-time. In the resulting theory, torsion, which is solution of the field equations as in any gravitation theory in the first order formalism, is not necessarily zero. However, a cosmological solution with zero torsion exists, which reproduces the Lambda-CDM cosmological solution of General Relativity. A realistic solution with spherical symmetry is also obtained.

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13

Pis’mak, D. Yu, and Yu M. Pis’mak. "Chern-Simon potential in models of interaction of electromagnetic field with thin films." Physics of Particles and Nuclei 44, no. 3 (May 2013): 450–61. http://dx.doi.org/10.1134/s1063779613030118.

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14

Sheng, Dong-Ning, Zhao-Bin Su, and B. Sakita. "On the Constraint Equation for the Lowest Landau Level in Fractional Quantum Hall System." International Journal of Modern Physics B 05, no. 10 (June 1991): 1715–24. http://dx.doi.org/10.1142/s0217979291001619.

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In the framework of collective field theory, We apply the Chern-Simon field theory treatment to the constraint equation for the lowest Landau level to investigate the generic properties for the quasi-particles of the FQH system. It shows a transparent connection to the Laughlin's wave functions. If we take an average over the wave functional for the constraint equation, the resulted equation can be interpreted as the vortex equation for the fractionally charged quasi-particles. Introducing a generalized ρ (density)-ϑ (phase) transformation, not only the fractional statistics and the hierarchy scheme can be drawn from the constraint equation, it also gives rise an interesting picture that vortices condense as a Halperin like wave fuction on a Laughlin like background condensate of ν=1/m.

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15

Baulieu, Laurent, and Marc Bellon. "The anomaly cancellation mechanism in N=1, D=4 supergravity and distorted supergravity algebra with Chern-Simon forms." Physics Letters B 169, no. 1 (March 1986): 59–63. http://dx.doi.org/10.1016/0370-2693(86)90685-4.

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16

Jawad, Abdul, Shamaila Rani, and Nadeem Azhar. "Non-flat FRW universe version of Tsallis holographic dark energy in specific modified gravity." Modern Physics Letters A 34, no. 07n08 (March 12, 2019): 1950055. http://dx.doi.org/10.1142/s021773231950055x.

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Among various dark energy models, Tsallis holographic dark energy model shows the dynamical enthusiasm to describe the transition phase of the universe. In this paper, we consider Tsallis holographic dark energy with event and apparent horizon as an infrared cutoff in the framework of dynamical Chern–Simon modified gravity and non-flat FRW universe. We explore Hubble, equation of state and deceleration parameters and found that Hubble parameter lies in the range [Formula: see text] and [Formula: see text] for event and apparent horizon trajectories, respectively. It is mentioned here that the equation of state parameter lies within the range [Formula: see text] (event) and [Formula: see text] (apparent). Also, deceleration parameter for both cases show accelerated and decelerated phase of universe as well as cosmological constant. Moreover, we also checked the stability of our model through square speed of sound, which shows the positive behavior (exhibits the stability of the model). Finally, we observe that the generalized second law of thermodynamics remains valid in both cases of horizon.

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17

MAZHARIMOUSAVI, S. HABIB, O. GURTUG, and M. HALILSOY. "GENERATING STATIC, SPHERICALLY SYMMETRIC BLACK HOLES IN LOVELOCK GRAVITY." International Journal of Modern Physics D 18, no. 13 (December 15, 2009): 2061–82. http://dx.doi.org/10.1142/s0218271809015813.

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We present the generalization of a known theorem to generate static, spherically symmetric black hole solutions in higher-dimensional Lovelock gravity. Particular limits such as Gauss–Bonnet (GB) and Einstein–Hilbert (EH) in any dimension N yield all the solutions known to date with an energy–momentum. In our generalization, with special emphasis on third order Lovelock gravity, we have found two different class of solutions characterized by the matter field parameter. Several particular cases are studied and properties related to asymptotic behaviors are discussed. Our general solution, which covers topological black holes as well, splits naturally into distinct classes such as Chern–Simon (CS) and Born–Infeld (BI) in higher-dimensions. The occurence of naked singularities is studied and it is found that the space–time behaves nonsingularly in the quantum-mechanical sense when it is probed with quantum test particles. The theorem is extended to cover Bertotti–Robinson (BR) type solutions in the presence of the GB parameter alone. Finally, we prove also that extension of the theorem for a scalar–tensor source of higher dimensions (N > 4) fails to work.

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18

Ye, Jinwu. "The gauge-invariant Green function in 3+1 dimensional QED (QCD) and 2+1 dimensional Abelian (non-Abelian) Chern–Simon theory." Journal of Physics: Condensed Matter 16, no. 25 (June 8, 2004): 4465–76. http://dx.doi.org/10.1088/0953-8984/16/25/007.

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19

Baker, Anne C., and G. Jackson. "Lightweight tension structures – an aesthetic integration of geometry and mechanics. Part 1. The role of minimal surfaces and soap films. Part 2. Finding the form of a minimal surface, by W. J. Lewis, Mathematics Today 35 (1) pp. 10–16, (3) pp. 80–84, 1999. - Magic squares indeed!, by Arthur T. Benjamin and Kan Yasuda, American Mathematical Monthly 106 (2), pp. 152–156, 1999. - Pierre-Simon de Laplace: 1749–1827, by Roger Cook, Mathematical Spectrum 31 (3), pp. 49–51, 1998/9. - Unifying threads in Alfred Tarski’s work, by Steven Givant, The Mathematical Intelligencer 21 (1), pp. 47–58, 1999. - André Weil and algebraic topology, by Armand Borel, pp. 422–427. - André Weil as I knew him, by Goro Shimura, pp. 428–433. - André Weil: A prologue, by Anthony W. Knapp, pp. 434–439. - André Weil (1906-1998), by Armand Borel, Pierre Carrier, Komaravolu Chandrasekharan, Shiing-Shen Chern and Shokichi Iyanaga, pp. 440–447. - The apprenticeship of a mathematician – autobiography of André Weil, reviewed by V. S. Varadarajan, pp. 448–456. - Introduction to metric preserving functions, by Paul Corazza, The American Mathematical Monthly 106 (4) pp. 309–323, 1999. - Visual aspects of understanding group theory, by D. F. Almeida, Int. J. of Mathematical Education in Science and Technology 30 (2) pp. 159–166, 1999 - Marriage, Magic, and Solitaire, by David B. Leep and Gerry Myerson, The American Mathematical Monthly 106 (5) pp. 419–429, 1999. - Professional Development of Mathematics Teachers, by H. Wu, Notices of the American Mathematical Society 46 (5) pp. 535–541, 1999. - Mathematics Today 35 (4) pp. 118–122, 1999 contains three short articles under the heading Mathematics and Dyslexia. - Difficulties in Knowledge Integration: Revisiting Zeno’s Paradox with Irrational Numbers, by Irit Peled and Sara Hershkovitz, International Journal of Mathematical Education in Science and Technology 30 (1) pp. 39–46, 1999." Mathematical Gazette 83, no. 498 (November 1999): 529–32. http://dx.doi.org/10.1017/s0025557200165052.

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20

Herrmann, Joachim. "Towards a unified theory of the fundamental physical interactions based on the underlying geometric structure of the tangent bundle." European Physical Journal C 82, no. 10 (October 26, 2022). http://dx.doi.org/10.1140/epjc/s10052-022-10781-4.

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AbstractThis paper pursues the hypothesis that the tangent bundle (TB) with the central extended little groups of the SO(3,1) group as gauge group is the underlying geometric structure for a unified theory of the fundamental physical interactions. Based on this hypothesis as a first step, I recently presented a generalized theory of electroweak interaction (including hypothetical dark matter particles) (Herrmann in Eur Phys J C 79:779, 2019). The vertical Laplacian of the tangent bundle possesses the same form as the Hamiltonian of a 2D semiconductor quantum Hall system. This explains fractional charge quantization of quarks and the existence of lepton and quark families. As will be shown, the SU(3) color symmetry for strong interactions arises in the TB as an emergent symmetry similar to Chern–Simon gauge symmetries in quantum Hall systems. This predicts a signature of quark confinement as a universal large-scale property of the Chern–Simon fields and induces a new understanding of the vacuum as the ground state occupied by a condensate of quark–antiquark pairs. The gap for quark–antiquark pairing is calculated in the mean-field approximation, which allows a numerical estimation of the characteristic parameters of the vacuum such as its chemical potential, the quark condensation parameter and the vacuum energy. Note that a gauge theoretical understanding of gravity was previously achieved by considering the translation group T(3,1) in the TB as gauge group. Therefore, the theory presented here can be considered as a new type of unified theory for all known fundamental interactions linked with the geometrization program of physics.

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21

Sadovskii, Dmitri A., and Boris I. Zhilinskii. "Quaternionic Dirac oscillator." Journal of Physics A: Mathematical and Theoretical, August 4, 2022. http://dx.doi.org/10.1088/1751-8121/ac8708.

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Abstract We construct an elementary quaternionic slow-fast Hamiltonian dynamical system with one formal control parameter and two slow degrees of freedom as half-integer spin in resonance 1:1:2 with two slow oscillators. Invariant under spin reversal and having a codimension-5 crossing of its fast Kramers-degenerate semi-quantum eigenvalues, our system is the dynamical equivalent of the spin-quadrupole model by Avron, Sadun, Segert, and Simon [Commun. Math. Phys. 124(4), 595–627 (1989)], exhibiting non-Abelian geometric phases. The equivalence is uncovered through the equality of the spectral ﬂow between quantum superbands and Chern numbers c2 computed by Avron et al.

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