Abstract
Sine-Gordon field as an effective description of a system of coupled pendulums in a constant gravitational field. Sine-Gordon solitons. The electromagnetic field, gauge potentials and gauge transformations. The Klein–Gordon equation and its solutions.
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Notes
- 1.
Here this means that all derivatives of the fields with respect to the Cartesian coordinates \(x^i\) also vanish at the spatial infinity.
- 2.
We adhere to the convention that vectors denoted by the arrow have components with upper indices.
- 3.
\(\Theta (x)=1\) for \(x>1\), \(\Theta (x)=0\) for \(x<0\). The value of \(\Theta (0)\) does not have to be specified because the step function is used under the integral. Formally, the step function is a generalized function, and for such functions their values at a given single point are not defined. Therefore, the question, “what is the value of \(\Theta (0)\)?” is meaningless.
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Arodź, H., Hadasz, L. (2017). Introduction. In: Lectures on Classical and Quantum Theory of Fields. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-55619-2_1
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DOI: https://doi.org/10.1007/978-3-319-55619-2_1
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