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How to correctly represent a quantum field? As something single that fills all space (and particles are excitations of the field just like waves are excitations of a single ocean), or as a set of particles, each of which creates its own field (and when there are no particles, there is no field)?

Арман Гаспарян
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    Possible duplicates: https://physics.stackexchange.com/q/155608, https://physics.stackexchange.com/q/337423, https://physics.stackexchange.com/q/48030 – Nihar Karve Jan 19 '21 at 16:36

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In quantum field theory, whether for particle physics or other frames , (for example nuclear physics,) the fields are the plane wave solutions, i.e. without a potential, of the corresponding quantum equation, filling all points (x,y,z,t), a kind of coordinate system, whether particles exist or not. Creation and annihilation differential operators create or destroy a particle according to the problem at hand. Feynman diagrams are used as a shorthand describing the interactions.

The field conceptually always exists, for the standard model of particle physics: each particle in the table and their antiparticles is expressed as a field over all space time, electron field,neutrino field etc.

anna v
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  • Every single particle or every type of particle? That is, are all electrons excitations of a single field, or does each individual electron have its own field? – Арман Гаспарян Jan 19 '21 at 16:11
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    @АрманГаспарян All electrons and positrons are excitations of a single electron-positron field. – G. Smith Jan 19 '21 at 17:49
  • @G. Smith Does the electron-positron field consist of a large number of individual interacting electrons and positrons? That is, which is more fundamental, a field or a particle? Do particles form a field or does a field create particles? – Арман Гаспарян Jan 19 '21 at 18:59
  • @АрманГаспарян We should not have an extended discussion in comments on Anna’s answer. – G. Smith Jan 19 '21 at 19:44
  • @АрманГаспарян It is mathematics. Your question is the same as asking : which is more fundamental, the (x,y,z,t) coordinates or the track of the rocket described . The field is not described by particles it is the "field" on which creation and annihilation operators create and annihilate particle states.. – anna v Jan 20 '21 at 04:30