# The singularity structureοf the Yang-Mills configuration space

Banach Center Publications (1997)

- Volume: 39, Issue: 1, page 287-299
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topFuchs, Jürgen. "The singularity structureοf the Yang-Mills configuration space." Banach Center Publications 39.1 (1997): 287-299. <http://eudml.org/doc/208668>.

@article{Fuchs1997,

abstract = {The geometric description of Yang–Mills theories and their configuration space $\mathcal \{M\}$ 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].},

author = {Fuchs, Jürgen},

journal = {Banach Center Publications},

keywords = {gauge transformations; space of connections; singular strata; Yang-Mills functional; connections},

language = {eng},

number = {1},

pages = {287-299},

title = {The singularity structureοf the Yang-Mills configuration space},

url = {http://eudml.org/doc/208668},

volume = {39},

year = {1997},

}

TY - JOUR

AU - Fuchs, Jürgen

TI - The singularity structureοf the Yang-Mills configuration space

JO - Banach Center Publications

PY - 1997

VL - 39

IS - 1

SP - 287

EP - 299

AB - The geometric description of Yang–Mills theories and their configuration space $\mathcal {M}$ 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].

LA - eng

KW - gauge transformations; space of connections; singular strata; Yang-Mills functional; connections

UR - http://eudml.org/doc/208668

ER -

## References

top- [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. Zbl0579.58038
- [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. Zbl0486.58008
- [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. Zbl0840.58058
- [8] M. Asorey and P. K. Mitter, Regularized, continuum Yang–Mills process and Feynman–Kac functional integral, Comm. Math. Phys. 80 (1981), 43. Zbl0476.58008
- [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. Zbl0596.55003
- [10] M. Atiyah and J. Jones, Topological aspects of Yang–Mills theory, Comm. Math. Phys. 61 (1978), 97. Zbl0387.55009
- [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. Zbl1007.81511
- [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. Zbl0495.58003
- [16] J. C. Baez, Generalized measures in gauge theory, Lett. Math. Phys. 31 (1994), 213. Zbl0798.58009
- [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. Zbl0486.58009
- [18] J. P. Brasselet and M. Ferrarotti, Regular differential forms on stratified spaces, preprint Pisa, Sept. 1992. Zbl0837.55003
- [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. Zbl0726.53067
- [22] S. K. Donaldson, Polynomial invariants for smooth four-manifolds, Topology 29 (1990), 257. Zbl0715.57007
- [23] S. K. Donaldson and P. B. Kronheimer, The Geometry of Four-Manifolds, Clarendon Press, Oxford 1990. Zbl0820.57002
- [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. Zbl0691.58017
- [26] A. E. Fischer, Resolving the singularities in the space of Riemannian geometries, J. Math. Phys. 27 (1986), 718. Zbl0604.58007
- [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. Zbl1049.81556
- [29] H. B. Gao and H. Römer, Some features of blown-up non-linear σ-models, Classical Quantum Gravity 12 (1995), 17. Zbl0817.53043
- [30] M. J. Gotay, Reduction of homogeneous Yang–Mills fields, J. Geom. Phys. 6 (1989), 349. Zbl0692.53041
- [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. Zbl0408.14001
- [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. Zbl0719.53064
- [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. Zbl0759.53019
- [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. Zbl0614.57025
- [36] W. Kondracki and P. Sadowski, Geometric structure on the orbit space of gauge connections, J. Geom. Phys. 3 (1986), 421. Zbl0624.53055
- [37] E. Langmann, M. Salmhofer and A. Kovner, Consistent axial-like gauge fixing on hypertori, Modern Phys. Lett. A 9 (1994), 2913. Zbl1020.58503
- [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. Zbl0474.58004
- [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. Zbl0489.58006
- [40] M. Narasimhan and T. Ramadas, Geometry of SU(2) gauge fields, Comm. Math. Phys. 67 (1979), 121. Zbl0418.53029
- [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. Zbl0379.53009
- [45] I. M. Singer, The geometry of the orbit space for nonabelian gauge theories, Phys. Scripta T 24 (1981), 817. Zbl1063.81623
- [46] K. K. Uhlenbeck, Removable singularities in Yang–Mills fields, Comm. Math. Phys. 83 (1982), 11. Zbl0491.58032
- [47] E. Witten, Monopoles and four manifolds, Math. Res. Lett. 1 (1994), 769. Zbl0867.57029
- [48] C. N. Yang and R. M. Mills, Conservation of isotopic spin and isotopic gauge invariance, Phys. Rev. (2) 96 (1954), 191. Zbl06538052
- [49] D. Zwanziger, Non-perturbative modification of the Faddeev–Popov formula and banishment of the naive vacuum, Nuclear Phys. B 209 (1982), 336.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.