A finite-action solution to generalized Yang-Mills-Higgs theory

Monopole-instanton in topologically massive gauge theories in 2+1 dimensions with a Chern–Simons mass term have been studied by Pisarski some years ago. He investigated the SU(2) Yang–Mills–Higgs model with an additional Chern–Simons mass term in the action. Pisarski argued that there is a monopole-instanton solution that is regular everywhere, but found that it does not possess finite action. There were no exact or numerical solutions being presented by Pisarski. Hence it is our purpose to further investigate this solution in more detail. We obtained numerical regular solutions that smoothly interpolates between the behavior at small and large distances for different values of Chern–Simons term strength and for several fixed values of Higgs field strength. The monopole-instanton's action is real but infinite. The action vanishes for large Chern–Simons term only when the Higgs field expectation value vanishes.

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Vortex configurations with finite action per unit plane in pure Yang-Mills theory

Physics Letters B ◽

10.1016/0370-2693(81)90874-1 ◽

1981 ◽

Vol 102 (4) ◽

pp. 273-276 ◽

Cited By ~ 1

Author(s):

B. Bunk ◽

P. Jacob

Keyword(s):

Yang Mills ◽

Finite Action

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INVESTIGATION OF A THEORY WITH SOLITON-LIKE CONFIGURATIONS

International Journal of Modern Physics A ◽

10.1142/s0217751x88001004 ◽

1988 ◽

Vol 03 (10) ◽

pp. 2349-2369 ◽

Cited By ~ 2

Author(s):

A. WIEDEMANN ◽

H.J.W. MÜLLER-KIRSTEN ◽

D.H. TCHRAKIAN

Keyword(s):

Simple Model ◽

Green's Function ◽

Schrodinger Equation ◽

Zero Mode ◽

Finite Energy ◽

Higher Order ◽

Scalar Theory ◽

Yang Mills ◽

Field Fluctuations ◽

Finite Action

Motivated by the study of classical finite-action field configurations of higher order Yang-Mills-Higgs theories, we construct the Lagrangian of a scalar theory in one space and one time dimensions which can serve as a relatively simple model for the investigation of the properties of theories with finite energy or action classical configurations. The condition of stability of the classical configuration, the zero mode and the significance of the latter in connection with constraints which ensure the existence of the Green’s function, are studied in detail. It is then shown how a Schrödinger equation can be established and solved whose eigenfunctionals determine the probability of field fluctuations in the neighborhood of the classical configuration.

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Finite-action solutions of higher-order yang-mills-higgs theory in four dimensions

Il Nuovo Cimento A ◽

10.1007/bf02730430 ◽

1986 ◽

Vol 92 (1) ◽

pp. 107-115 ◽

Cited By ~ 4

Author(s):

J. Burzlaff ◽

D. H. Tchrakian

Keyword(s):

Higher Order ◽

Four Dimensions ◽

Yang Mills ◽

Finite Action

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Moduli space metrics for axially symmetric instantons

Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences ◽

10.1098/rspa.1994.0116 ◽

1994 ◽

Vol 446 (1928) ◽

pp. 479-497 ◽

Cited By ~ 2

Keyword(s):

Lie Algebras ◽

Moduli Space ◽

Axial Symmetry ◽

Axially Symmetric ◽

Toda Equation ◽

Vortex System ◽

Yang Mills ◽

Self Duality ◽

Finite Action ◽

Arbitrary Gauge

Under an axial symmetry the Yang–Mills self-duality equations for an arbitrary gauge group reduce to the Toda equation for that particular group, from which the finite action instantons (hyperbolic vortices) may be constructed. The space of such finite action instantons, with gauge equivalent solutions identified, is known as the moduli space, and carries a naturally defined Kähler metric. This metric is studied for the simply laced Lie algebras, and explicit examples are constructed for the 2-vortex system.

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