quantum field theory In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles a ...

, multiplicative quantum numbers are conserved quantum numbers of a special kind. A given quantum number ''q'' is said to be additive if in a particle reaction the sum of the ''q''-values of the interacting particles is the same before and after the reaction. Most conserved quantum numbers are additive in this sense; the

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respecti ...

is one example. A multiplicative quantum number ''q'' is one for which the corresponding product, rather than the sum, is preserved. Any conserved quantum number is a symmetry of the Hamiltonian of the system (see Noether's theorem). Symmetry groups which are examples of the abstract group called Z₂ give rise to multiplicative quantum numbers. This group consists of an operation, P, whose square is the identity, P² = 1. Thus, all symmetries which are mathematically similar to parity (physics) give rise to multiplicative quantum numbers. In principle, multiplicative quantum numbers can be defined for any

abelian group In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is com ...

. An example would be to trade the

, Q, (related to the abelian group U(1) of

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...

), for the new quantum number exp(2''i''π ''Q''). Then this becomes a multiplicative quantum number by virtue of the charge being an additive quantum number. However, this route is usually followed only for discrete subgroups of U(1), of which Z₂ finds the widest possible use.

References

*''Group theory and its applications to physical problems, by M. Hamermesh'' (Dover publications, 1990) Quantum field theory Nuclear physics {{quantum-stub

See also

References