While checking whether the elementary particle reaction is possible, we multiply parity of each particle on left hand side and right hand side and check whether they are equal or not whereas we add energy on left hand side and right hand side and check whether they are equal or not. What determines whether we have to add or multiply ?
Energy is additive; parity is additive mod 2 which turns out to be the same as ``multiplication''.
So the operation is addition, what changes is whether it's mod 2 or not. Parity is additive mod 2.
In elementary particle reactions, the parity of each particle and the energy conservation must be considered. Parity is a quantum mechanical property that describes how a particle behaves under spatial inversion, which is a reflection of the coordinates of the particle about a chosen origin.
When checking whether a reaction is possible or not based on parity, we multiply the parity of each particle on the left-hand side by the parity of each particle on the right-hand side of the reaction. This is because parity is a multiplicative quantum number, meaning that the total parity of the system is obtained by multiplying the parities of the individual particles.
On the other hand, energy conservation is a conservation law that requires the total energy of the system before the reaction to be equal to the total energy of the system after the reaction. In this case, we add the energy on the left-hand side of the reaction to the energy on the right-hand side of the reaction and check whether they are equal or not.
Therefore, the decision to add or multiply depends on the property being considered. Parity is a multiplicative property and energy conservation is an additive property.
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