CPT
Symmetry and Theorem| CPT
Symmetry and Theorem |
In General > s.a. anomalies;
C Conjugation;
M-theory; particle
statistics; QED;
quantum klein-gordon field.
* Remark: It is a symmetry
of any Lorentz-invariant, local quantum field theory, whether or not the individual
factors are.
* Operator: The operator 
=
PCT is anti-unitary; for a charged scalar field, –1
(x) = (–x)*.
* Proofs: Lüders
and Pauli proved it based on Lagrangian quantum field theory; Jost gave a more
general axiomatic quantum field theory proof.
@ Proofs of theorem: Lüders AP(57),
reprinted AP(00);
Streater & Wightman
64; in Feynman in(87) [topological]; Greenberg FP(06)hp/03.
@ Related topics: Norbury EJP(90)
[for electromagnetism]; Greenberg PLB(98)ht/97 [and
locality]; Duck & Sudarshan 98; Borchers & Yngvason mp/00;
Kostelecky ed-02; Socolovsky IJTP(04)mp [Dirac
field]; Scurek AJP(04)may
[group and reps]; Carballo & Socolovsky IJTP(09)-a0811 [CPT
from P and T subgroups of Lorentz group]; Carballo & Socolovsky a0906 [irreducible
representations of CPT group for QED].
@ Generalized: Grimus & Rebelo PRP(97)
[P and CP, in gauge theories]; Soloviev JMP(98)
[non-local quantum field theory]; Dastidar & Dastidar MPLA(99)
[non-local
gauge theories]; Chaichian et al PLB(03)ht/02,
Franco & Polito JMP(05)
[non-commutative field theory]; Jannussis et al NCB(05)
[non-Hermitian H].
Violation and Tests > s.a. CP violation;
early-universe cosmology; matter; Parity.
* Possible reasons: Extra
dimensions; Violation of Lorentz invariance; Quantum-gravity effects.
* For electrons: Relative difference for g of e+/e– is
less than 2 
10–12.
* For neutral kaons.
* For baryons: The relative
mass difference of p and p-bar is
less than 10–10 [@ news pn(98)may].
@ In quantum gravity: Mavromatos NIMB(04)hp/03, hp/03-in;
Mavromatos LNP(05)gq/04-ln
[review, emphasis on spacetime foam]; Klinkhamer & Rupp PRD(04);
Bernabeu et al PRD(06)ht [entangled
neutral mesons]; Mavromatos JPCS(09)-a0904 [stringy].
@ Other theory: Bertolami et al PLB(97)hp/96 [and
baryogenesis]; Colladay & Kostelecky
PRD(97)hp [string
theory]; Adam & Klinkhamer NPB(01)hp,
PLB(01)ht [abelian
Chern-Simons theory]; Klinkhamer ht/01-in,
PRD(02)ht/01,
hp/05-in
[chiral fermions and non-trivial spacetime topology]; > s.a. modified
lorentz symmetry and
QED.
@ CMB: Feng et al PRL(06);
Cabella et al PRD(07)-a0705 [WMAP
3-year data]; Auriemma a0711-in
[rev]; Xia et al a0908 [polarization].
@ Other tests: Commins AJP(93)sep-RL;
Colladay & Kostelecky
PLB(95)hp,
PRD(95)hp, hp/96-in
[hep]; Bluhm et al PRL(99);
Geer et APEX PRL(00);
Hughes et al PRL(01)
[muonium spectroscopy]; Murayama
PLB(04)
[Ks vs neutrinos]; Canè et al PRL(04)
[neutron, bound on boost effects]; Minataka & Uchinami PRD(05)hp [supernova
neutrinos]; Hooper et al PRD(05)hp [high-energy
neutrinos]; Bernabeu et al hp/06-in
[neutral kaons].
Time Reversal > s.a. arrow
of time; canonical general relativity; electromagnetism; entropy; finsler
geometry.
* Remarks: Distinguish
between irreversibility and T or CPT violation (Lüders:
T should be called "motion reversal"); Finding T violation
would be equivalent to finding CP violation, because of the CPT theorem.
* And experiment: One
of the ways of looking for T violation is to look for a neutron dipole moment;
The Hamiltonian would contain a term d 
· E,
and, under T, 
– and E E,
so H would not be invariant; So far, experimentally dN < 6 10–25 e · cm.
@ General references: Rosen AJP(73)apr
[for electromagnetic quantities]; Sachs Sci(72)may,
87; Price qp/96-in
[interactions and boundary conditions]; news pn(98)nov,
Mavromatos pw(98)dec
[experiment]; Kuenzi et al
cm/02 [in
solid state]; North PhSc(08)apr
[new view]; Arntzenius & Greaves BJPS(09)
[in classical electromagnetism].
@ Violation: Ryder CP(94); Gutkin JPA(07)
[dynamical, and chaos].
In Curved Spacetime > s.a. quantum
field theory effects in curved spacetime [Unruh
effect].
* Remark: It does not hold
for a black hole background metric, in the sense that there is no operator such
that $–1 = $
–1,
where $ is the superscattering matrix for pure and mixed states.
@ References: Brout & Englert NPB(81),
Anandan PRL(98)
[and cosmology]; Buchholz et al CQG(00)
[AdS]; Hollands CMP(04)gq/02 [and
operator product expansion];
Arntzenius SHPMP(04)
[Lorentz group reps, and t-orientation]; Varlamov PLB(05)mp [dS,
spinor fields].
In Quantum Gravity > s.a. non-commutative
field theory; time
in quantum gravity.
* Idea: The CPT theorem
is a consequence of usual quantum field theory; It uses special relativity
(in that it assumes the symmetries of Minkowski spacetime) and quantum mechanics,
and
therefore
it
need not hold in quantum gravity.
* Scenarios: It may arise
from modified uncertainty relations [@ Amelino-Camelia MPLA(97)gq],
or from geons.
@ Reviews: Mavromatos hp/04-in, hp/04-in
[tests with neutrinos]; Mavromatos PoS-a0707
[and decoherence].
@ General references: Penrose in(79), in(81); Page PRL(80);
Wald PRD(80);
Wald in(81); Hawking
CMP(82);
Page GRG(82);
Banks et al NPB(84);
Hawking NPB(84);
Gross NPB(84);
Neacsu IJTP(84);
Banks NPB(85).
@ Scenarios: Alexanian & Balachandran PLB(02)ht/01 [geons].
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sep 2009