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In a sigma-model quantum field theory a field history is a morphism $\phi \colon \Sigma \to X$ for $\Sigma$ an $n$-dimensional manifold or similar. One is to think of this as being the trajectory: of an $(n-1)$-brane propagating in the target space $X$.
For the case $n = 1$ (for instance the relativistic particle, a 0-brane) the term worldline for $\Sigma$ has a long tradition. Accordingly one calls $\Sigma$ the worldvolume of the given $(n-1)$-brane when $n \gt 1$. For the case $n=2$ (the case of relevance in string theory) one also says worldsheet.
Hence generally for any field theory defined on a worldvolume or spacetime $\Sigma$, and with type of fields determined by a field bundle $E \overset{fb}{\to} \Sigma$, one may think of a section of the field bundle as a field trajectory.
The space of all these is the space of trajectories (space of histories).
worldline formalism (for scattering amplitudes in QFT)
worldvolume
Last revised on January 3, 2018 at 01:59:02. See the history of this page for a list of all contributions to it.