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Journal articles on the topic 'Number Theory and Field Theory'

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Published: 4 June 2021
Last updated: 2 February 2022

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1

Albu, Toma. "Field Theoretic Cogalois Theory via Abstract Cogalois Theory." Journal of Pure and Applied Algebra 208, no. 1 (January 2007): 101–6. http://dx.doi.org/10.1016/j.jpaa.2005.11.008.

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2

Ikeda, Kâzim Ilhan, and Erol Serbest. "Ramification theory in non-abelian local class field theory." Acta Arithmetica 144, no. 4 (2010): 373–93. http://dx.doi.org/10.4064/aa144-4-4.

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3

Dunne, Gerald V., and Christian Schubert. "Bernoulli number identities from quantum field theory and topological string theory." Communications in Number Theory and Physics 7, no. 2 (2013): 225–49. http://dx.doi.org/10.4310/cntp.2013.v7.n2.a1.

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4

Niemi, A. J., and G. W. Semenoff. "Fermion number fractionization in quantum field theory." Physics Reports 135, no. 3 (April 1986): 99–193. http://dx.doi.org/10.1016/0370-1573(86)90167-5.

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5

Ershov, Yu L. "Local class field theory." St. Petersburg Mathematical Journal 15, no. 06 (November 16, 2004): 837–47. http://dx.doi.org/10.1090/s1061-0022-04-00834-9.

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6

Hess, Florian, and Maike Massierer. "Tame class field theory for global function fields." Journal of Number Theory 162 (May 2016): 86–115. http://dx.doi.org/10.1016/j.jnt.2015.10.004.

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7

Saito, Shuji. "Class field theory for curves over local fields." Journal of Number Theory 21, no. 1 (August 1985): 44–80. http://dx.doi.org/10.1016/0022-314x(85)90011-3.

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8

Poudel, Parashu Ram. "Unified Field Theory." Himalayan Physics 4 (December 23, 2013): 87–90. http://dx.doi.org/10.3126/hj.v4i0.9435.

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Unified field theory is the long-sought means of tying together all known phenomena to explain the nature and behaviour of all matter and energy in existence. The quest for unification has been the perennial theme of modern physics. The belief that all physical phenomena can be reduced to simple and explained by a smaller number of laws is the central tenet of physics. Such a theory could potentially unlock all the secrets of nature and make a myriad of wonders possible, including such benefits as time travel and an inexhaustible source of clean energy, among many others. This paper aims to explain unified theory and its development towards the unification of four interactions in brief.The Himalayan Physics Vol. 4, No. 4, 2013 Page:87-90 Uploaded date: 12/23/2013
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9

Hiranouchi, Toshiro. "Class field theory for open curves over local fields." Journal de Théorie des Nombres de Bordeaux 30, no. 2 (2018): 501–24. http://dx.doi.org/10.5802/jtnb.1036.

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10

Miura, Kei, and Hisao Yoshihara. "Field Theory for Function Fields of Plane Quartic Curves." Journal of Algebra 226, no. 1 (April 2000): 283–94. http://dx.doi.org/10.1006/jabr.1999.8173.

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11

Dong, Chongying, Xingjun Lin, and Siu-Hung Ng. "Congruence property in conformal field theory." Algebra & Number Theory 9, no. 9 (November 4, 2015): 2121–66. http://dx.doi.org/10.2140/ant.2015.9.2121.

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12

Ehrlich, Philip. "Number systems with simplicity hierarchies: a generalization of Conway's theory of surreal numbers." Journal of Symbolic Logic 66, no. 3 (September 2001): 1231–58. http://dx.doi.org/10.2307/2695104.

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Introduction. In his monograph On Numbers and Games [7], J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many other numbers including ω, ω, /2, 1/ω, and ω − π to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered “number” fields—be individually definable in terms of sets of von Neumann-Bernays-Gödel set theory with Global Choice, henceforth NBG [cf. 21, Ch. 4], it may be said to contain “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system of real numbers bears to Archimedean ordered fields. This can be made precise by saying that whereas the ordered field of reals is (up to isomorphism) the unique homogeneous universal Archimedean ordered field, No is (up to isomorphism) the unique homogeneous universal orderedfield [14]; also see [10], [12], [13].However, in addition to its distinguished structure as an ordered field, No has a rich hierarchical structure that (implicitly) emerges from the recursive clauses in terms of which it is defined. This algebraico-tree-theoretic structure, or simplicity hierarchy, as we have called it [15], depends upon No's (implicit) structure as a lexicographically ordered binary tree and arises from the fact that the sums and products of any two members of the tree are the simplest possible elements of the tree consistent with No's structure as an ordered group and an ordered field, respectively, it being understood that x is simpler than y just in case x is a predecessor of y in the tree.
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13

ITZHAKI, N. "ON FIELD THEORIES WITH AN INFINITE NUMBER OF FIELDS." International Journal of Modern Physics A 13, no. 04 (February 10, 1998): 625–34. http://dx.doi.org/10.1142/s0217751x98000275.

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A toy model with an infinite number of interacting fermions in four-dimensional space–time is analyzed. We find that the model is finite at any order in perturbation theory. However, perturbation theory is valid only for external momenta smaller than [Formula: see text], where λ is the coupling constant.
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14

Perucca, Antonella, and Pietro Sgobba. "Kummer theory for number fields and the reductions of algebraic numbers." International Journal of Number Theory 15, no. 08 (August 19, 2019): 1617–33. http://dx.doi.org/10.1142/s179304211950091x.

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For all number fields the failure of maximality for the Kummer extensions is bounded in a very strong sense. We give a direct proof (without relying on the Bashmakov–Ribet method) of the fact that if [Formula: see text] is a finitely generated and torsion-free multiplicative subgroup of a number field [Formula: see text] having rank [Formula: see text], then the ratio between [Formula: see text] and the Kummer degree [Formula: see text] is bounded independently of [Formula: see text]. We then apply this result to generalize to higher rank a theorem of Ziegler from 2006 about the multiplicative order of the reductions of algebraic integers (the multiplicative order must be in a given arithmetic progression, and an additional Frobenius condition may be considered).
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15

Uzun, Mecit Kerem. "Motivic homology and class field theory over p-adic fields." Journal of Number Theory 160 (March 2016): 566–85. http://dx.doi.org/10.1016/j.jnt.2015.09.004.

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16

UBRIACO, MARCELO R. "QUANTUM GROUP SCHRÖDINGER FIELD THEORY." Modern Physics Letters A 08, no. 23 (July 30, 1993): 2213–21. http://dx.doi.org/10.1142/s021773239300194x.

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We show that a quantum deformation of quantum mechanics given in a previous work is equivalent to quantum mechanics on a nonlinear lattice with step size ∆x=(1−q)x. Then, based on this, we develop the basic formalism of quantum group Schrödinger field theory in one spatial quantum dimension, and explicitly exhibit the SU q(2) covariant algebras satisfied by the q-bosonic and q-fermionic Schrödinger fields. We generalize this result to an arbitrary number of fields.
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17

Shiekh, A. Y. "Finite massless quantum field theory." Canadian Journal of Physics 70, no. 6 (June 1, 1992): 463–66. http://dx.doi.org/10.1139/p92-078.

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Massless quantum field theory is usually troubled by both ultraviolet and infrared divergences. With the help of analytic continuation, this fact can be exploited to eliminate, or at least reduce the overall number of divergences. This mechanism is investigated within the context of dimensional regularization for the case of massless [Formula: see text] theory in four dimensions.
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18

Cohen, S. D. "ADDITIVE NUMBER THEORY OF POLYNOMIALS OVER A FINITE FIELD." Bulletin of the London Mathematical Society 24, no. 6 (November 1992): 614–15. http://dx.doi.org/10.1112/blms/24.6.614.

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19

Ferrari, Franco, Marcin R. Pia̧tek, and Yani Zhao. "A topological field theory for Milnor's triple linking number." Journal of Physics A: Mathematical and Theoretical 48, no. 27 (June 16, 2015): 275402. http://dx.doi.org/10.1088/1751-8113/48/27/275402.

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20

Papenbrock, T., and T. H. Seligman. "A particle-number expansion beyond self-consistent field theory." Physics Letters A 218, no. 3-6 (August 1996): 229–34. http://dx.doi.org/10.1016/0375-9601(96)00363-5.

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21

Passos, E. J. V. de. "Number-conserving mean-field theory for Bose-Einstein condensates." Journal of Physics B: Atomic, Molecular and Optical Physics 32, no. 23 (November 18, 1999): 5619–28. http://dx.doi.org/10.1088/0953-4075/32/23/315.

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22

Cohen, Henri. "A survey of computational class field theory." Journal de Théorie des Nombres de Bordeaux 11, no. 1 (1999): 1–13. http://dx.doi.org/10.5802/jtnb.235.

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23

Ershov, Yu L. "Abstract class field theory (a finitary approach)." Sbornik: Mathematics 194, no. 2 (February 28, 2003): 199–223. http://dx.doi.org/10.1070/sm2003v194n02abeh000712.

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24

FERRARI, FRANCO, HAGEN KLEINERT, and IGNAZIO LAZZIZZERA. "FIELD THEORY OF N ENTANGLED POLYMERS." International Journal of Modern Physics B 14, no. 32 (December 30, 2000): 3881–95. http://dx.doi.org/10.1142/s0217979200002570.

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25

HSIEH, CHUN-CHUNG. "LINKING IN KNOT THEORY." Journal of Knot Theory and Its Ramifications 15, no. 08 (October 2006): 957–62. http://dx.doi.org/10.1142/s0218216506004889.

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In this talk, we will give an explicit/combinatorial formulae for Massey–Milnor first non-vanishing linking, and also express this linking in terms of Chern–Simons–Witten perturbative quantum field theory.
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26

Gracey, J. A. "Large Nf quantum field theory." International Journal of Modern Physics A 33, no. 35 (December 20, 2018): 1830032. http://dx.doi.org/10.1142/s0217751x18300326.

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We review the development of the large [Formula: see text] method, where [Formula: see text] indicates the number of flavours, used to study perturbative and nonperturbative properties of quantum field theories. The relevant historical background is summarized as a prelude to the introduction of the large [Formula: see text] critical point formalism. This is used to compute large [Formula: see text] corrections to [Formula: see text]-dimensional critical exponents of the universal quantum field theory present at the Wilson–Fisher fixed point. While pedagogical in part the application to gauge theories is also covered and the use of the large [Formula: see text] method to complement explicit high order perturbative computations in gauge theories is also highlighted. The usefulness of the technique in relation to other methods currently used to study quantum field theories in [Formula: see text]-dimensions is also summarized.
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27

Adachi, Takahide, Osamu Iyama, and Idun Reiten. "-tilting theory." Compositio Mathematica 150, no. 3 (December 3, 2013): 415–52. http://dx.doi.org/10.1112/s0010437x13007422.

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AbstractThe aim of this paper is to introduce $\tau $-tilting theory, which ‘completes’ (classical) tilting theory from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting module for any finite-dimensional algebra over a field $k$ is a direct summand of exactly one or two tilting modules. An important property in cluster-tilting theory is that an almost complete cluster-tilting object in a 2-CY triangulated category is a direct summand of exactly two cluster-tilting objects. Reformulated for path algebras $kQ$, this says that an almost complete support tilting module has exactly two complements. We generalize (support) tilting modules to what we call (support) $\tau $-tilting modules, and show that an almost complete support $\tau $-tilting module has exactly two complements for any finite-dimensional algebra. For a finite-dimensional $k$-algebra $\Lambda $, we establish bijections between functorially finite torsion classes in $ \mathsf{mod} \hspace{0.167em} \Lambda $, support $\tau $-tilting modules and two-term silting complexes in ${ \mathsf{K} }^{\mathrm{b} } ( \mathsf{proj} \hspace{0.167em} \Lambda )$. Moreover, these objects correspond bijectively to cluster-tilting objects in $ \mathcal{C} $ if $\Lambda $ is a 2-CY tilted algebra associated with a 2-CY triangulated category $ \mathcal{C} $. As an application, we show that the property of having two complements holds also for two-term silting complexes in ${ \mathsf{K} }^{\mathrm{b} } ( \mathsf{proj} \hspace{0.167em} \Lambda )$.
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28

Miura, Kei, and Hisao Yoshihara. "Field theory for the function field of the quintic fermat curve." Communications in Algebra 28, no. 4 (January 2000): 1979–88. http://dx.doi.org/10.1080/00927870008826940.

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29

Rivasseau, V. "Constructive Field Theory in Zero Dimension." Advances in Mathematical Physics 2009 (2009): 1–12. http://dx.doi.org/10.1155/2009/180159.

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Constructive field theory can be considered as a reorganization of perturbation theory in a convergent way. In this pedagogical note we propose to wander through five different methods to compute the number of connected graphs of the zero-dimensional field theory, in increasing order of sophistication and power.
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30

Takeuchi, Daichi. "Blow-ups and class field theory for curves." Algebra & Number Theory 13, no. 6 (August 18, 2019): 1327–51. http://dx.doi.org/10.2140/ant.2019.13.1327.

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31

Masuda, Ariane M., Luciane Quoos, and Benjamin Steinberg. "Character theory of monoids over an arbitrary field." Journal of Algebra 431 (June 2015): 107–26. http://dx.doi.org/10.1016/j.jalgebra.2015.02.017.

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32

Wójcik, J. "On a problem in algebraic number theory." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 2 (February 1996): 191–200. http://dx.doi.org/10.1017/s0305004100074090.

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Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’
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33

Brown, Francis, and Oliver Schnetz. "Modular forms in quantum field theory." Communications in Number Theory and Physics 7, no. 2 (2013): 293–325. http://dx.doi.org/10.4310/cntp.2013.v7.n2.a3.

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34

EHRLICH, PHILIP, and ELLIOT KAPLAN. "NUMBER SYSTEMS WITH SIMPLICITY HIERARCHIES: A GENERALIZATION OF CONWAY’S THEORY OF SURREAL NUMBERS II." Journal of Symbolic Logic 83, no. 2 (February 5, 2018): 617–33. http://dx.doi.org/10.1017/jsl.2017.9.

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AbstractIn [16], the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field ${\bf{No}}$ of surreal numbers was brought to the fore and employed to provide necessary and sufficient conditions for an ordered field to be isomorphic to an initial subfield of ${\bf{No}}$, i.e., a subfield of ${\bf{No}}$ that is an initial subtree of ${\bf{No}}$. In this sequel to [16], analogous results for ordered abelian groups and ordered domains are established which in turn are employed to characterize the convex subgroups and convex subdomains of initial subfields of ${\bf{No}}$ that are themselves initial. It is further shown that an initial subdomain of ${\bf{No}}$ is discrete if and only if it is a subdomain of ${\bf{No}}$’s canonical integer part ${\bf{Oz}}$ of omnific integers. Finally, making use of class models the results of [16] are extended by showing that the theories of nontrivial divisible ordered abelian groups and real-closed ordered fields are the sole theories of nontrivial densely ordered abelian groups and ordered fields all of whose models are isomorphic to initial subgroups and initial subfields of ${\bf{No}}$.
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35

Kanter, I., and H. Sompolinsky. "Mean-field theory of spin-glasses with finite coordination number." Physical Review Letters 58, no. 2 (January 12, 1987): 164–67. http://dx.doi.org/10.1103/physrevlett.58.164.

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36

Horvat, R. "Effective field theory, large number of particle species, and holography." Physics Letters B 674, no. 1 (April 2009): 1–3. http://dx.doi.org/10.1016/j.physletb.2009.02.057.

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37

BAR-NATAN, DROR. "PERTURBATIVE CHERN-SIMONS THEORY." Journal of Knot Theory and Its Ramifications 04, no. 04 (December 1995): 503–47. http://dx.doi.org/10.1142/s0218216595000247.

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We present the perturbation theory of the Chern-Simons gauge field theory and prove that to second order it indeed gives knot invariants. We identify these invariants and show that in fact we get a previously unknown integral formula for the Arf invariant of a knot, in complete agreement with earlier non-perturbative results of Witten. We outline our expectations for the behavior of the theory beyond two loops.
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38

Styer, Robert. "Hecke theory over arbitrary number fields." Journal of Number Theory 33, no. 2 (October 1989): 107–31. http://dx.doi.org/10.1016/0022-314x(89)90001-2.

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39

SANCHIS-LOZANO, MIGUEL-ANGEL, J. FERNANDO BARBERO G., and JOSÉ NAVARRO-SALAS. "PRIME NUMBERS, QUANTUM FIELD THEORY AND THE GOLDBACH CONJECTURE." International Journal of Modern Physics A 27, no. 23 (September 18, 2012): 1250136. http://dx.doi.org/10.1142/s0217751x12501369.

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Motivated by the Goldbach conjecture in number theory and the Abelian bosonization mechanism on a cylindrical two-dimensional space–time, we study the reconstruction of a real scalar field as a product of two real fermion (so-called prime) fields whose Fourier expansion exclusively contains prime modes. We undertake the canonical quantization of such prime fields and construct the corresponding Fock space by introducing creation operators [Formula: see text] — labeled by prime numbers p — acting on the vacuum. The analysis of our model, based on the standard rules of quantum field theory and the assumption of the Riemann hypothesis, allows us to prove that the theory is not renormalizable. We also comment on the potential consequences of this result concerning the validity or breakdown of the Goldbach conjecture for large integer numbers.
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40

Yoshida, Teruyoshi. "Finiteness theorems in the class field theory of varieties over local fields." Journal of Number Theory 101, no. 1 (July 2003): 138–50. http://dx.doi.org/10.1016/s0022-314x(03)00018-0.

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41

Campos, Cédric M. "Higher-order field theory with constraints." Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 106, no. 1 (March 26, 2011): 89–95. http://dx.doi.org/10.1007/s13398-011-0025-7.

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42

Ji, Qingzhong, and Hourong Qin. "Iwasawa Theory for K2n." Journal of K-Theory 12, no. 1 (May 2, 2013): 115–23. http://dx.doi.org/10.1017/is013004020jkt225.

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AbstractGiven a number field F and a prime number p; let Fn denote the cyclotomic extension with [Fn : F] = pn; and let $\mathematical script capital(O)_F_n\$ denote its ring of integers. We establish an analogue of the classical Iwasawa theorem for the orders of K2i ($\mathematical script capital(O)_F_n\$){p}.
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43

Mlinar, John R., and Arthur G. Erdman. "An Introduction to Burmester Field Theory." Journal of Mechanical Design 122, no. 1 (January 1, 2000): 25–30. http://dx.doi.org/10.1115/1.533553.

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This paper introduces the Burmester field for motion-generation dyads with four design positions. The Burmester field is the region swept by a Burmester curve as one or more of the design positions varies. The geometric features of the Burmester field are discussed and shown to be related to the poles. The most significant feature are anchor poles that remain stationary as the design positions are changed. The envelope of the Burmester field found with the variation of a single design parameter is developed. This work demonstrates that the envelope of the Burmester field consists of segments of Burmester curves and segments found using envelope theory. A number of examples are presented and discussed. [S1050-0472(00)00501-8]
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44

Perucca, Antonella, and Pietro Sgobba. "Kummer Theory for Number Fields and the Reductions of Algebraic Numbers II." Uniform distribution theory 15, no. 1 (June 1, 2020): 75–92. http://dx.doi.org/10.2478/udt-2020-0004.

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AbstractLet K be a number field, and let G be a finitely generated and torsion-free subgroup of K×. For almost all primes p of K, we consider the order of the cyclic group (G mod 𝔭), and ask whether this number lies in a given arithmetic progression. We prove that the density of primes for which the condition holds is, under some general assumptions, a computable rational number which is strictly positive. We have also discovered the following equidistribution property: if ℓe is a prime power and a is a multiple of ℓ (and a is a multiple of 4 if ℓ =2), then the density of primes 𝔭 of K such that the order of (G mod 𝔭) is congruent to a modulo ℓe only depends on a through its ℓ-adic valuation.
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45

Ayad, Mohamed, Rachid Bouchenna, and Omar Kihel. "Indices in a Number Field." Journal de Théorie des Nombres de Bordeaux 29, no. 1 (2017): 201–16. http://dx.doi.org/10.5802/jtnb.976.

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46

Mollin, Richard A. "Continued fractions and class number two." International Journal of Mathematics and Mathematical Sciences 27, no. 9 (2001): 565–71. http://dx.doi.org/10.1155/s0161171201010900.

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We use the theory of continued fractions in conjunction with ideal theory (often called the infrastructure) in real quadratic fields to give new class number 2 criteria and link this to a canonical norm-induced quadratic polynomial. By doing so, this provides a real quadratic field analogue of the well-known result by Hendy (1974) for complex quadratic fields. We illustrate with several examples.
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47

Kerz, Moritz, and Alexander Schmidt. "Covering data and higher dimensional global class field theory." Journal of Number Theory 129, no. 10 (October 2009): 2569–99. http://dx.doi.org/10.1016/j.jnt.2009.05.003.

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48

Guignard, Quentin. "On the ramified class field theory of relative curves." Algebra & Number Theory 13, no. 6 (August 18, 2019): 1299–326. http://dx.doi.org/10.2140/ant.2019.13.1299.

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49

GELCA, RĂZVAN. "SL(2, C)-TOPOLOGICAL QUANTUM FIELD THEORY WITH CORNERS." Journal of Knot Theory and Its Ramifications 07, no. 07 (November 1998): 893–906. http://dx.doi.org/10.1142/s0218216598000474.

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In this paper we define the sl(2, C) topological quantum field theory with corners that corresponds to the smooth theory of Reshetikhin and Turaev. We encounter a sign obstruction at the level of the modular functor, which we solve by making use of the Klein four group. We deduce the Moore-Seiberg equations in the new context.
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50

Spiess, Michael. "Class Formations and Higher Dimensional Local Class Field Theory." Journal of Number Theory 62, no. 2 (February 1997): 273–83. http://dx.doi.org/10.1006/jnth.1997.2048.

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