2023-11-12   09193

The Free Scalar Quantum Field: Unitary Spacetime Symmetries

In a model whose equations of motion are linear, we can solve them explicitly: we can express the time-dependent field operators in terms of a set of time-independent operators (creation and annihilation operators), analogous to expressing a solution of a classical equation of motion in terms of data on an initial spacelike hypersurface. This article shows how those time-independent operators are affected by the unitary transformations that implement some spacetime symmetries in relativistic models of a single scalar field. The relationship of those symmetries to the stress-energy tensor is also explained. Special attention is given to Lorentz boosts and (in the massless case) scale transformations.

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