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Symmetries in quantum mechanics describe features of spacetime and particles which are unchanged under some transformation, in the context of quantum mechanics, relativistic quantum mechanics and quantum field theory, and with applications in the mathematical formulation of the standard model and condensed matter physics.
Weyl noted that Paul Dirac's relativistic quantum mechanics implied that the electron should have a positively charged anti-particle. The only known particle with a positive charge was the proton , but Weyl was convinced that the anti-electron had to have the same mass as the electron, and physicists had already established that protons are ...
CPT is the only combination of C, P, and T that is observed to be an exact symmetry of nature at the fundamental level. [1] [2] The CPT theorem says that CPT symmetry holds for all physical phenomena, or more precisely, that any Lorentz invariant local quantum field theory with a Hermitian Hamiltonian must have CPT symmetry.
Each theory of quantum gravity uses the term "quantum geometry" in a slightly different fashion. String theory, a leading candidate for a quantum theory of gravity, uses it to describe exotic phenomena such as T-duality and other geometric dualities, mirror symmetry, topology-changing transitions [clarification needed], minimal possible distance scale, and other effects that challenge intuition.
The free fields care for particles in isolation, whereas processes involving several particles arise through interactions. The idea is that the state vector should only change when particles interact, meaning a free particle is one whose quantum state is constant. This corresponds to the interaction picture in quantum mechanics.
In nonrelativistic quantum mechanics, an account can be given of the existence of mass and spin (normally explained in Wigner's classification of relativistic mechanics) in terms of the representation theory of the Galilean group, which is the spacetime symmetry group of nonrelativistic quantum mechanics.
In summary, gauge symmetry attains its full importance in the context of quantum mechanics. In the application of quantum mechanics to electromagnetism, i.e., quantum electrodynamics, gauge symmetry applies to both electromagnetic waves and electron waves. These two gauge symmetries are in fact intimately related.
It was eventually realized that special relativity was inconsistent with single-particle quantum mechanics, so that all particles are now described relativistically by quantum fields. When the canonical quantization procedure is applied to a field, such as the electromagnetic field, the classical field variables become quantum operators .