In quantum field theory (QFT), space-time is not constructed from quantum fields; rather, it provides the framework within which quantum fields exist and interact. Space-time is a fundamental concept that combines the three dimensions of space with the dimension of time into a four-dimensional continuum.
In QFT, each point in space-time is associated with a field that describes a quantum mechanical entity. These fields, such as the electron field or the Higgs field, exist throughout space-time and interact with each other according to the principles of quantum mechanics. The behavior and dynamics of these fields are governed by the equations of the specific quantum field theory being considered.
The meaning of space-time in QFT is twofold. First, it serves as the stage or backdrop upon which the quantum fields evolve and interact. It provides the arena in which particles are created and annihilated, and their interactions are described. Second, space-time plays a role in determining the causal structure and symmetries of the theory.
In QFT, space-time is treated as a continuous manifold with a particular geometry, often described by the principles of general relativity. The curvature of space-time, as described by general relativity, influences the behavior of quantum fields and particles. Additionally, space-time symmetries, such as translation symmetry (the invariance of physical laws under spatial translations) and Lorentz symmetry (the invariance under Lorentz transformations), play important roles in QFT.
It's worth noting that the nature of space-time and its relationship with quantum fields is a topic of ongoing research and investigation, especially in attempts to reconcile general relativity and quantum mechanics in a theory of quantum gravity.