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Just as the position states I'it) are defined as eigenstates of 7,the coherent states are defind as eigenstates of the annihilation operators. To see why annihilation operators are selected rather than creation operators. it is usdui t o consider the dstcnca! sf dgenstates of the: crestton and annlhitation operators. If we denote by 14) a general vector of the Fock space. we can expand 14) as: 00 Thus,14) necessarily has a component with a mtnimum number of paeicles and 'rf we apply any creation operator t o 14).

Here. we pmsent an afternative prod. 168) (ax a & % f B*pm) b . = (a1 a,[#l... L> ... . 26iJwt? obtain and the analagous adjornt equations. Thus Now consider the integrals which may arise in Eq. a,( and l&,. . h or ) unoccupied in both s t a b , which requires that n=n and {al. a%) fs some permutation I ) of (P1 PG). taIE:, . [G. and . . .. noting that an even number of antlcommutatians is requlred to bring the intwral over each state into the form of Eq. 1), so that the value is just The left hand side of Eq.

TaIE:, . [G. and . . .. noting that an even number of antlcommutatians is requlred to bring the intwral over each state into the form of Eq. 1), so that the value is just The left hand side of Eq. 168)thus yields the result previously derived in Eq. 50)for the right hand side, so the equality is established for any vectors in the Sack space. As in the ease af Bosons, this completeness relation provides a usdul expressiion for the trace of an operator. 172) Mm-. 'ff we deOine a eom@eteset of states (In)) i~ the h c k space, the trace of an operator A may be written ' R A=x ( n l ~ l n ) 11.

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Advansed plasma theory by Rosenbluth


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