Is CPT Symmetry Inherent in All Quantum Field Theories?

[wotanub]

I was looking at the wikipedia article on CPT and it starts with "Charge, Parity, and Time Reversal Symmetry is a fundamental symmetry of physical laws under the simultaneous transformations of charge conjugation (C), parity transformation (P), and time reversal (T)."

What does it mean that CPT is a symmetry of the "physical laws?" Is it obvious that a QFT has CPT symmetry from its Lagrangian? For example, if I had a Lagrangian for some QFT, and replaced the particle fields with anitparticle fields and vise versa, does C symmetry imply that the two conjugate Lagrangians will yield the same equations of motion? If so, how could a parity or time inversion operation be applied to a Lagrangian in the same way?

What is the precise meaning of "physical laws?"

 

[jedishrfu]

Here's the wikipedia article on it:

https://en.wikipedia.org/wiki/CPT_symmetry

The implication of CPT symmetry is that a "mirror-image" of our universe — with all objects having their positions reflected by an arbitrary plane (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced byantimatter (corresponding to a charge inversion)— would evolve under exactly our physical laws. The CPT transformation turns our universe into its "mirror image" and vice versa. CPT symmetry is recognized to be a fundamental property of physical laws.

 

[A. Neumaier]

What is the precise meaning of "physical laws?"

In this context, it means the Wightman axioms for quantum field theory, from which CPT symmetry is derivable with full rigor.