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The quantum theory of fields is largely based on studying perturbations around non-interacting, or free, field theories, which correspond to a collection of quantum-mechanical harmonic oscillators.
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Those who read while in the bath will be able to verify this easily, by slowing stirring the water in circles of varying size
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In fact, Endlich et al
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If M M is a torus, for example, this can be arranged by ensuring that the Fourier modes above the EFT cut-off fall off faster than any polynomial
Cited in the paper.
These quantities are not all Poincaré invariant, so they are still really only proxies for observables
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S. Endlich, A. Nicolis, R. Rattazzi, and J. Wang, JHEP 1104
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Considering invariants was suggested in Endlich et al. 2011 , but was not followed up
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