quantum field

quantum field (plural quantum fields)

1. (quantum mechanics) A quantum operator-valued function of (any point in) space.
   • 2013, Robert D. Klauber, Student Friendly Quantum Field Theory, 2nd edition, Fairfield, IA: Sandtrove Press, published 2018, →ISBN, →OCLC, §7.2.1, page 186:

         In Chaps. 3, 4, and 5, we saw that for each spin type, the Schrödinger picture wave equation for a state and the Heisenberg picture wave equation for the associated quantum field had the same form. In the former case, the wave equation solution was a state, i.e., a particle wave function. In the latter, the wave equation solution was a quantum field, i.e., an operator that created and destroyed states. For free scalars, this equation was the Klein-Gordon equation; for spinors, it was the (no interactions) Dirac equation; and for massless vectors (photons), it was Maxwell’s equation (sourceless, in terms of ${\displaystyle A^{\mu }}$ ).

   • ibid., §7.3.1, page 190

         The result is zero expectation value for φ, and this would be true for whatever state, including the vacuum, that we choose. This effectively means that we would measure nothing if we tried to measure the quantum field φ. The field itself is unmeasurable.

• operator field

• quantum field theory

• Robert D. Klauber (2013) Student Friendly Quantum Field Theory, Second edition, Fairfield, Iowa: Sandtrove Press, published 2018, →ISBN, →OCLC, §3.6.5, page 60