Quantum Field Theory and the Molecular Hypothesis for Chemical Substances

2 Quantum Field Theory and the Molecular Hypothesis for Chemical Substances 

3 The logical distinction between substance and molecule is obvious, but easily overlooked 

The basic building blocks of the theory are Heisenberg operators (x) which create and destroy respectively, particles of type m at the space-time point x = x, (x. For the purposes of chemistry we can take the index nzs e for electrons and a for nuclei only. Of course when energies are much larger than chemical energies, nuclei appear to be composite particles, and we must then introduce fields for their constituents (quarks, rishons). We shall not make any explicit reference to the spins carried by these fields beyond noting that odd-integral spins require fermi statistics, so that for fermi fields we have canonical anticommutation relations (CARS) 

The Hamiltonian for the coupled electron and nuclear fields can then be written in the usual way as a sum of kinetic (it) and potential 0T) energy terms, 

This Hamiltonian is Galilean invariant, as is appropriate for chemical phenomena, rather than Lorentz invariant. 

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