PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1997 | 39 | 1 | 287-299
Tytuł artykułu

The singularity structureοf the Yang-Mills configuration space

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The geometric description of Yang–Mills theories and their configuration space $\cal M$ is reviewed. The presence of singularities in M is explained and some of their properties are described. The singularity structure is analysed in detail for structure group SU(2). This review is based on [28].
Słowa kluczowe
Rocznik
Tom
39
Numer
1
Strony
287-299
Opis fizyczny
Daty
wydano
1997
Twórcy
  • NIKHEF-H, Kruislaan 409, NL-1098 SJ Amsterdam, The Netherlands
Bibliografia
  • [1] A. Yu. Alekseev and V. Schomerus, Representation theory of Chern–Simons observables, preprint q-alg/9503016.
  • [2] L. Alvarez-Gaumé and P. Ginsparg, The topological meaning of non-abelian anomalies, Nuclear Phys. B 243 (1984), 449.
  • [3] J. M. Arms, The structure of the solution set for the Yang–Mills equations, Math. Proc. Cambridge Philos. Soc. 90 (1981), 361.
  • [4] J. M. Arms, J. E. Marsden and V. Moncrief, Symmetry and bifurcations of momentum mappings, Comm. Math. Phys. 78 (1981), 455.
  • [5] A. Ashtekar and J. Lewandowski, Differential geometry on the space of connections via graphs and projective limits, preprint hep-th/9412073.
  • [6] A. Ashtekar, D. Marol f and J. Mourão, Integration on the space of connections modulo gauge transformations, preprint gr-qc/9403042.
  • [7] M. Asorey, F. Falceto, J. L. López and G. Luzón, Nodes, monopoles and confinement in 2+1-dimensional gauge theories, Phys. Lett. B 349 (1995), 125.
  • [8] M. Asorey and P. K. Mitter, Regularized, continuum Yang–Mills process and Feynman–Kac functional integral, Comm. Math. Phys. 80 (1981), 43.
  • [9] M. Asorey and P. K. Mitter, Cohomology of the Yang–Mills gauge orbit space and dimensional reduction, Ann. Inst. H. Poincaré Phys. Théor. A45 (1986), 61.
  • [10] M. Atiyah and J. Jones, Topological aspects of Yang–Mills theory, Comm. Math. Phys. 61 (1978), 97.
  • [11] M. Audin, The Topology of Torus Actions on Symplectic Manifolds, Birkhäuser, Basel 1991.
  • [12] P. van Baal, More (thoughts on) Gribov copies, Nuclear Phys. B 369 (1992), 259.
  • [13] P. van Baal and B. van den Heuvel, Zooming in on the SU(2) fundamental domain, Nuclear Phys. B 417 (1994), 215.
  • [14] O. Babelon and C. M. Viallet, The geometrical interpretation of the Faddeev–Popov determinant, Phys. Lett. B 85 (1979), 246.
  • [15] O. Babelon and C. M. Viallet, On the Riemannian geometry of the configuration space of gauge theories, Comm. Math. Phys. 81 (1981), 515.
  • [16] J. C. Baez, Generalized measures in gauge theory, Lett. Math. Phys. 31 (1994), 213.
  • [17] R. Bott, Morse theory and the Yang–Mills equations, in: Differential geometrical methods in mathematical physics, Lecture Notes in Math. 836, Springer, Berlin, 1980, p. 269.
  • [18] J. P. Brasselet and M. Ferrarotti, Regular differential forms on stratified spaces, preprint Pisa, Sept. 1992.
  • [19] A. Chodos, Canonical quantization of non-Abelian gauge theories in the axial gauge, Phys. Rev. D (3) 17 (1978), 2624.
  • [20] M. Daniel and C. M. Viallet, The gauge fixing problem around classical solutions of the Yang–Mills theory, Phys. Lett. B 76 (1978), 458.
  • [21] G. Dell’Antonio and D. Zwanziger, Every gauge orbit passes inside the Gribov horizon, Comm. Math. Phys. 138 (1991), 291.
  • [22] S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), 257.
  • [23] S. K. Donaldson and P. B. Kronheimer, The Geometry of Four-Manifolds, Clarendon Press, Oxford 1990.
  • [24] J. Eichhorn, T. Friedrich, Seiberg–Witten theory, this volume.
  • [25] M. Ferrarotti, Some results about integration on regular stratified sets, Ann. Mat. Pura Appl. (4) CL (1988), 263.
  • [26] A. E. Fischer, Resolving the singularities in the space of Riemannian geometries, J. Math. Phys. 27 (1986), 718.
  • [27] D. S. Freed, On determinant line bundles, in: Mathematical Aspects of String Theory, S. T. Yau, ed., World Scientific, Singapore, 1987, p. 189.
  • [28] J. Fuchs, M. G. Schmidt and C. Schweigert, On the configuration space of gauge theories, Phys. B 426 (1994), 107.
  • [29] H. B. Gao and H. Römer, Some features of blown-up non-linear σ-models, Classical Quantum Gravity 12 (1995), 17.
  • [30] M. J. Gotay, Reduction of homogeneous Yang–Mills fields, J. Geom. Phys. 6 (1989), 349.
  • [31] V. Gribov, Quantization of nonabelian gauge theories, Nuclear Phys. B 139 (1978), 1.
  • [32] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Wiley Interscience, New York 1978.
  • [33] A. Heil, A. Kersch, N. Papadopoulos, B. Reifenhäuser and F. Scheck, Anomalies from nonfree action of the gauge group, Ann. Physics 200 (1990), 206.
  • [34] A. Heil, A. Kersch, N. Papadopoulos, B. Reifenhäuser and F. Scheck, Structure of the space of reducible connections for Yang–Mills theories, J. Geom. Phys. 7 (1990), 489.
  • [35] W. Kondracki and J. S. Rogulski, On the stratification of the orbit space for the action of automorphisms on connections, Dissertationes Math. (Rozprawy Mat.) CCL (1986), 1.
  • [36] W. Kondracki and P. Sadowski, Geometric structure on the orbit space of gauge connections, J. Geom. Phys. 3 (1986), 421.
  • [37] E. Langmann, M. Salmhofer and A. Kovner, Consistent axial-like gauge fixing on hypertori, Modern Phys. Lett. A 9 (1994), 2913.
  • [38] P. K. Mitter and C. M. Viallet, On the bundle of connections and the gauge orbit manifold in Yang–Mills theory, Comm. Math. Phys. 79 (1981), 457.
  • [39] V. Moncrief, Reduction of the Yang–Mills equations, in: Differential geometrical methods in mathematical physics, Lecture Notes in Math. 836, Springer, Berlin, 1980, p. 276.
  • [40] M. Narasimhan and T. Ramadas, Geometry of SU(2) gauge fields, Comm. Math. Phys. 67 (1979), 121.
  • [41] L. Rozansky, A contribution of the trivial connection to the Jones polynomial and Witten’s invariant of 3d manifolds I. and II., preprints hep-th/9401069 and hep-th/9403021.
  • [42] N. Seiberg, Exact results on the space of vacua of four-dimensional SUSY gauge theories, Phys. Rev. D (3) 49 (1994), 6857.
  • [43] M. A. Semenov-Tyan-Shanskiĭ and V. A. Franke, A variational principle for the Lorentz condition and restriction of the domain of path integration in non-abelian gauge theory (Russian), Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 120 (1982), 159; transl. J. Soviet. Math. 34 (1986), 1999.
  • [44] I. M. Singer, Some remarks on the Gribov ambiguity, Comm. Math. Phys. 60 (1978), 7.
  • [45] I. M. Singer, The geometry of the orbit space for nonabelian gauge theories, Phys. Scripta T 24 (1981), 817.
  • [46] K. K. Uhlenbeck, Removable singularities in Yang–Mills fields, Comm. Math. Phys. 83 (1982), 11.
  • [47] E. Witten, Monopoles and four manifolds, Math. Res. Lett. 1 (1994), 769.
  • [48] C. N. Yang and R. M. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. (2) 96 (1954), 191.
  • [49] D. Zwanziger, Non-perturbative modification of the Faddeev–Popov formula and banishment of the naive vacuum, Nuclear Phys. B 209 (1982), 336.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv39z1p287bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.