Common empirical basis
Relativistic quantum equations contain positive- and negative-energy branches. Standard quantum field theory describes observed particle and antiparticle processes with exceptional accuracy.
Standard
Until now: standard interpretation
- Negative-energy solutions are reinterpreted as antiparticles with positive physical energy.
- Particles and antiparticles are described through the standard Fock-space creation and annihilation construction.
- Vacuum and quantum fields are central elements of conventional QFT.
- CPT is usually treated as the fundamental combined discrete symmetry of local Lorentz-invariant QFT.
CTPA
CTPA formulation
- Both energy branches are retained as sectors of one relativistic particle theory.
- For E>0 the state evolves forward in ordinary time; for E<0 it evolves backward in ordinary time.
- Two Hilbert sectors with their own vacua are used; transitions occur through interactions.
- T-ordering is used for E>0 and anti-T-ordering for E<0.
- At the one-particle level the negative-energy branch is interpreted as the same particle with opposite time orientation rather than a new fundamental species.
- With both branches and induced contact terms consistently included, the program is intended to reproduce successful low-energy S-matrix results.
| Criterion | Standard | CTPA |
|---|
| Energy branches | Negative branch → antiparticles | E>0 and E<0 retained as physical sectors |
|---|
| Time orientation | Standard single interpretation | E<0 has opposite orientation in ordinary time |
|---|
| Hilbert space | Standard Fock construction | Two energy-sign sectors |
|---|
| Vacuum | Standard QFT vacuum | Separate sector vacua; no physical vacuum energy in CTPA |
|---|
| Discrete symmetry | CPT central | PT and full Lorentz O(1,3), including T, emphasized |
|---|
| Observables | Standard renormalized QFT | Same low-energy results should follow from the two-branch construction |
|---|
Possible checks and consequences
Kinematics and thresholdsCheck conservation laws and relativistic thresholds.
One-loop calculationsCompare QED, electroweak and QCD corrections with standard results.
Discrete symmetriesIdentify processes that organize P, T, PT and CPT differently.
This is a CTPA research program, not present mainstream consensus. It should be assessed through mathematical consistency and observables.