Abstract
We now analyze the particles that appear in the theory described by the Lagrangian (12.2). As usual, we must expand the Lagrangian in the neighborhood of a classical vacuum φ 0, having lifted the degeneracy of the classical vacuum by imposing a gauge condition. A natural gauge condition is
where σ, as before, is the map taking a point in R n to the nearest point in R. We recall that, in general, σ is one-to-one and continuous only in a neighborhood of R, say R, so that the gauge condition (13.1) is only meaningful for fields that are near the vacuum manifold. Generally, the fields considered here satisfy this condition only for |x| large enough, so we will consider gauge transformations defined outside a certain ball, rather than on the whole of R 3. (Also, the gauge transformation can depend on time, but this is not important to the current discussion.)
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© 1993 Springer-Verlag Berlin Heidelberg
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Schwarz, A.S. (1993). Particles in Gauge Theories. In: Quantum Field Theory and Topology. Grundlehren der mathematischen Wissenschaften, vol 307. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02943-5_15
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DOI: https://doi.org/10.1007/978-3-662-02943-5_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-08130-9
Online ISBN: 978-3-662-02943-5
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