Each creation operator [a.sup.[dagger].sub.i] is adjoint to the corresponding

annihilation operator [a.sub.i], and these operators obey the "canonical commutation relations":

The q-oscillator is a simple quantum mechanical system described by an

annihilation operator and a creation operator parameterized by a parameter q.

The lowest-weight vectors are defined by imposing the condition A[PSI].sub.lw] = 0, A being an

annihilation operator (in the present work A is the

annihilation operator defined in (52)).

respectively, in terms of the time-dependent

annihilation operator [[??].sub.[sigma]] (r, t) for an electron with spin [sigma] [member of] {[up arrow], [down arrow]} and its adjoint, the creation operator [[??].sup.[dagger].sub.[sigma]](r, t), in the Heisenberg picture.

The operator [[partial derivative].sub.k] and its adjoint [[partial derivative].sup.*.sub.k] are referred to as the

annihilation operator and creation operator at site k, respectively.

where u ([beta]) = cosh [theta]([beta]) and v'([beta]) = sinh [theta]([beta]), with [a.sup.[dagger].sub.p] and [a.sub.p] being creation and

annihilation operators, respectively.

I do not want to amble in relativistic fields of creation and

annihilation operators, and vacuum fluctuations, spontaneous emmission and Lamb shifts.

The equivalence principle thus becomes even more powerful by the fact that the size change derived geometrically in it via the laws of Special Relativity gets independently confirmed by the creation and

annihilation operators of quantum electrodynamics.

In this paper we describe one aspect of this interaction; namely, how well-known concepts in quantum physics such as creation and

annihilation operators, and ladder operators, translate to combinatorial "counting" ideas as exemplified by Stirling numbers, which may find their expression in terms of infinite matrices.

So, the operators [a.sup.[dagger]](k, p) and a(k,p) are interpreted as creation and

annihilation operators of particles, respectively.

where [s.sup.[dagger]] (s) and [d.sup.[dagger]]([??]) are the creation and

annihilation operators of the s and d bosons.

The creation and

annihilation operators of the third order for H' are described by expressions [s.sub.+] = [b.sub.+][a.sub.+][b.sub.-], = [b.sub.+][a.sub.-][b.sub.-], where [a.sub.+] and [a.sub.-] are the creation and

annihilation operators for [H.sub.2].