CPT symmetry

Source: Wikipedia, the free encyclopedia.
"CPT theorem" redirects here. For the album by Greydon Square, see
The C.P.T. Theorem
.

Charge, parity, and time reversal symmetry is a fundamental

Lorentz invariant local quantum field theory with a Hermitian Hamiltonian
must have CPT symmetry.

History

The CPT theorem appeared for the first time, implicitly, in the work of

Lorentz invariance and the principle of locality in the interaction of quantum fields. Subsequently, Res Jost gave a more general proof in 1958 using the framework of axiomatic quantum field theory
.

Efforts during the late 1950s revealed the violation of

CP-symmetry was believed to be preserved by all physical phenomena, but in the 1960s that was later found to be false too, which implied, by CPT invariance, violations of T-symmetry
as well.

Derivation of the CPT theorem

Consider a

Lorentz boost in a fixed direction z. This can be interpreted as a rotation of the time axis into the z axis, with an imaginary rotation parameter. If this rotation parameter were real
, it would be possible for a 180° rotation to reverse the direction of time and of z. Reversing the direction of one axis is a reflection of space in any number of dimensions. If space has 3 dimensions, it is equivalent to reflecting all the coordinates, because an additional rotation of 180° in the x-y plane could be included.

This defines a CPT transformation if we adopt the Feynman–Stueckelberg interpretation of antiparticles as the corresponding particles traveling backwards in time. This interpretation requires a slight analytic continuation, which is well-defined only under the following assumptions:

  1. The theory is
    Lorentz invariant
    ;
  2. The vacuum is Lorentz invariant;
  3. The energy is bounded below.

When the above hold,

Lorentz invariance implies rotational invariance
, so that any state can be rotated by 180 degrees.

Since a sequence of two CPT reflections is equivalent to a 360-degree rotation,

spin-statistics theorem
.

Consequences and implications

The implication of CPT symmetry is that a "mirror-image" of our universe — with all objects having their positions reflected through an arbitrary point (corresponding to a parity inversion), all momenta reversed (corresponding to a time inversion) and with all matter replaced by antimatter (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.[8] CPT symmetry is recognized to be a fundamental property of physical laws.

In order to preserve this symmetry, every violation of the combined symmetry of two of its components (such as CP) must have a corresponding violation in the third component (such as T); in fact, mathematically, these are the same thing. Thus violations in T-symmetry are often referred to as CP violations.

The CPT theorem can be generalized to take into account pin groups.

In 2002

Lorentz symmetry.[9]

CPT violations would be expected by some

compact dimension of cosmological size, could also lead to CPT violation. Non-unitary theories, such as proposals where black holes violate unitarity, could also violate CPT. As a technical point, fields with infinite spin could violate CPT symmetry.[10]

The overwhelming majority of experimental searches for Lorentz violation have yielded negative results. A detailed tabulation of these results was given in 2011 by Kostelecky and Russell.[11]

See also

References

  1. ^ Kostelecký, V. A. (1998). "The Status of CPT".
    arXiv:hep-ph/9810365
    .
  2. ^ "This is the One Symmetry That the Universe Must Never Violate". Forbes.
  3. ^ Schwinger, Julian (1951). "The Theory of Quantized Fields I".
    S2CID 121971249
    .
  4. ^ Lüders, G. (1954). "On the Equivalence of Invariance under Time Reversal and under Particle-Antiparticle Conjugation for Relativistic Field Theories".
    Kongelige Danske Videnskabernes Selskab, Matematisk-Fysiske Meddelelser
    . 28 (5): 1–17.
  5. ^ Pauli, W.; Rosenfelf, L.; Weisskopf, V., eds. (1955). Niels Bohr and the Development of Physics.
    LCCN 56040984
    .
  6. ISBN 978-0198742999
    .
  7. S2CID 123577175
    .
  8. ^ Our universe may have a twin that runs backward in time Paul Sutter, Live Science. March 16th, 2022
  9. ^ Greenberg, O. W. (2002). "CPT Violation Implies Violation of Lorentz Invariance".
    S2CID 9409237
    .
  10. ISSN 2073-8994
    .
  11. ^ Kostelecký, V. A.; Russell, N. (2011). "Data tables for Lorentz and CPT violation".
    S2CID 3236027
    .

Sources

External links
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