![]() While most new materialists, including Thomas Nail, tend to distance themselves from Deleuze, this essay reads the encounter of Nail's ‘process materialism’ and Deleuzian philosophy as productive rather than contentious. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. ![]() Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription).
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