Spherical shells of a classical gauge field and their topological charge as a perturbative expansion

Farhi, Edward; Khoze, Valentin V.; Rajagopal, Krishna; Singleton, Robert L.

doi:10.1103/physrevd.50.4162

Cited by 8 publications

(38 citation statements)

References 18 publications

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“…The classical evolution of certain gauge field configurations in Minkowski space was addressed in Refs. [7][8]. In this paper we study fermion number violation in the background of a gauge field in Minkowski space.…”

Section: Introductionmentioning

confidence: 99%

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Fermion number violation in the background of a gauge field in Minkowski space

Khoze

1995

Nuclear Physics B

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Anomalous fermion number violation is studied in the background of a pure SU (2) gauge field in Minkowski space using the method of N. Christ. It is demonstrated that the chiral fermion number is violated by at most an integer amount. Then the method is applied for a spherically symmetric Minkowski space classical gauge field in the background. These classical gauge fields are finite energy solutions to pure SU (2) equations of motion with in general non-integer topological charge. We show that in the classical background which during a finite time-interval matches such solutions the fermion number violation is integer and non-zero. In particular, we calculate the violation of the fermion number in the presence of Lüscher-Schechter solutions. The meaning of anomaly equation and applications to QCD and electroweak theory are briefly discussed. We also comment on the relation of the results of this paper to the previous work.

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Section: Introductionmentioning

confidence: 99%

“…On classical solutions in Minkowski space Q in general can take any value, not just an integer [7,8]. This is a consequence of the fact that classical Minkowski gauge fields do not approach just some pure gauges in the far past and future, but the finite energy radiation is always present.…”

Section: Introductionmentioning

confidence: 99%

Fermion number violation in the background of a gauge field in Minkowski space

Khoze

1995

Nuclear Physics B

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“…In a companion paper 9 we analyze fermion production in the background of a field which locally changes winding number. We work with a (1+1)-dimensional analogue.…”

Section: Discussionmentioning

confidence: 99%

“…In a companion paper 9 we study fermion number production in a (1+1)-dimensional theory with an arbitrary background gauge field. We arrange for the background field to change its winding number in local regions and we allow for these local changes to be non-integer.…”

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confidence: 99%

Minkowski space non-Abelian classical solutions with noninteger winding number change

1993

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Working in a spherically symmetric ansatz in Minkowski space we discover new solutions to the classical equations of motion of pure SU (2) gauge theory. These solutions represent spherical shells of energy which at early times move inward near the speed of light, excite the region of space around the origin at intermediate times and move outward at late times. The solutions change the winding number in bounded regions centered at the origin by non-integer amounts. They also produce non-integer topological charge in these regions. We show that the previously discovered solutions of Lüscher and Schechter also have these properties.

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“…First, we write the complex fields χ and φ in polar form 1 1 In Ref. [3] the phase of χ was called ϕ. In this paper we call it θ.…”

Section: Gauge Invariant Variablesmentioning

confidence: 99%

Gauge-invariant variables for spontaneously broken SU(2) gauge theory in the spherical ansatz

1995

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We describe classical solutions to the Minkowski space equations of motion of SU (2) gauge theory coupled to a Higgs field in the spatial spherical ansatz. We show how to reduce the equations to four equations for four gauge invariant degrees of freedom which correspond to the massive gauge bosons and the Higgs particle. The solutions typically dissipate at very early and late times. To describe the solutions at early and late times, we linearize and decouple the equations of motion, all the while working only with gauge invariant variables. We express the change in Higgs winding of a solution in terms of gauge invariant variables.

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Spherical shells of a classical gauge field and their topological charge as a perturbative expansion

Cited by 8 publications

References 18 publications

Fermion number violation in the background of a gauge field in Minkowski space

Fermion number violation in the background of a gauge field in Minkowski space

Minkowski space non-Abelian classical solutions with noninteger winding number change

Gauge-invariant variables for spontaneously broken SU(2) gauge theory in the spherical ansatz

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