Definition of a scalar). In other words, if you change your coordinate system, a value of the scalar field at a given point in spacetime (now described by the new coordinates) is still the same number. Whereas a vector will, in general, have different components.
(Also, isn’t the wavefunction also a scalar in QFT?)
No. To quote wikipedia, “probability conservation is not a relativistically covariant concept”, because the particle number is neither conserved, nor is a covariant quantity. I.e., different observers can disagree on the number of particles, which violates the definition of a scalar. Thus the wavefunction (from which probability is derived) is not a useful concept in QFT and is replaced by fields living in the Fock space, not in the Hilbert space.
Definition of a scalar). In other words, if you change your coordinate system, a value of the scalar field at a given point in spacetime (now described by the new coordinates) is still the same number. Whereas a vector will, in general, have different components.
No. To quote wikipedia, “probability conservation is not a relativistically covariant concept”, because the particle number is neither conserved, nor is a covariant quantity. I.e., different observers can disagree on the number of particles, which violates the definition of a scalar. Thus the wavefunction (from which probability is derived) is not a useful concept in QFT and is replaced by fields living in the Fock space, not in the Hilbert space.