CPT symmetry is a fundamental symmetry of physical laws under transformations that involve the inversions of charge, parity and time simultaneously. Symmetry in physics refers to features of a Physical system that exhibit the property of Symmetry —that is under certain transformations, aspects of these A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i In Mathematics a transform is an Operator applied to a function so that under the transform certain operations are simplified Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of

## History

Efforts in the late 1950s revealed the violation of P-symmetry by phenomena that involve the weak force, and there are well known violations of C-symmetry and T-symmetry as well. In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In Physics, C-symmetry means the symmetry of physical laws under a charge -conjugation transformation. T Symmetry is the symmetry of physical laws under a Time reversal transformation &mdash T t \mapsto -t For a short time, the CP-symmetry was believed to be preserved by all physical phenomena, but that was later found to be false too. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics On the other hand, there is a theorem that derives the preservation of CPT symmetry for all of physical phenomena assuming the correctness of quantum laws and Lorentz invariance. In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally Specifically, the CPT theorem states that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry. In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally In quantum field theory (QFT the forces between particles are mediated by other particles In Mathematics, on a finite-dimensional Inner product space, a self-adjoint operator is one that is its own adjoint, or equivalently one whose matrix In Quantum mechanics, the Hamiltonian H is the Observable corresponding to the Total energy of the system
The CPT theorem appeared for the first time, implicitly, in the work of Julian Schwinger in 1951 to prove the connection between spin and statistics. Julian Seymour Schwinger ( February 12, 1918 &ndash July 16, 1994) was an American Theoretical physicist. The spin-statistics theorem in Quantum mechanics relates the spin of a particle to the statistics obeyed by that particle In 1954 Gerhard Lüders and Wolfgang Pauli derived more explicit proofs so that the theorem is sometimes known as the Lüders-Pauli theorem. At about the same time and independently the theorem was also proved by John Stewart Bell. John Stewart Bell ( June 28 1928 &ndash October 1 1990) was a Physicist, and the originator of Bell's Theorem, one of the These proofs are based on the validity of Lorentz invariance and the Principle of locality in the interaction of quantum fields. In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally In Physics, the principle of locality is that distant objects cannot have direct influence on one another an object is influenced directly only by its immediate surroundings Subsequently Res Jost gave a more general proof in the framework of axiomatic quantum field theory.

## Derivation

Consider a Lorentz boost in a fixed direction z. In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to This can be interpreted as a rotation of the time axis into the z axis, but the rotation parameter is imaginary. If the rotation parameter were real, it would be possible to do a 180 degree rotation, and the rotation would reverse the direction of time and the direction of z. Reversing the direction of one axis is a reflection of space in any number of dimensions, and in three space dimensions it is equivalent to reflecting all the coordinates, because you can throw in an additional rotation of 180 degrees in the x-y plane for good measure.

This defines a CPT transformation when the antiparticles are interpreted as particles travelling backwards in time. to most kinds of particles, there is an associated antiparticle with the same Mass and opposite Electric charge. This interpretation requires a slight analytic continuation, which is only well-defined under the following assumptions:

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

When this is true, the quantum theory can be extended to a Euclidean theory, which is defined by translating all the operators to imaginary time using the Hamiltonian. The commutation relations of the Hamiltonian and Lorentz generators guarantee that the Lorentz invariance implies rotation invariance, and any state can be rotated by 180.

Since two CPT-reflections in a sequence are equivalent to a 360 degree rotation, fermions change by a sign under two CPT reflections, while bosons do not. This can be used to prove the spin-statistics theorem. The spin-statistics theorem in Quantum mechanics relates the spin of a particle to the statistics obeyed by that particle

## Consequences and Implications

A consequence of this derivation is that a violation of CPT automatically indicates a Lorentz violation. In standard Physics, Lorentz covariance is a key property of Spacetime that follows from the Special theory of relativity, where it applies globally

The implication of CPT symmetry is that a mirror-image of our universe — with all objects having momenta and positions reflected by an imaginary plane (corresponding to a parity inversion), with all matter replaced by antimatter (corresponding to a charge inversion)— would evolve exactly like our universe. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product In Physics, a parity transformation (also called parity inversion) is the flip in the sign of one Spatial Coordinate. Matter is commonly defined as being anything that has mass and that takes up space. In Particle physics and Quantum chemistry, antimatter is the extension of the concept of the Antiparticle to Matter, where antimatter is composed Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. At any moment of corresponding times, the two universes would be identical, and the CPT transformation would simply turn one into the other. 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. In Particle physics, CP violation is a violation of the postulated CP symmetry of the laws of physics

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