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Diffstat (limited to 'man/kondo_preprocess.1')
| -rw-r--r-- | man/kondo_preprocess.1 | 29 |
1 files changed, 28 insertions, 1 deletions
diff --git a/man/kondo_preprocess.1 b/man/kondo_preprocess.1 index 5ec1399..e6e5c59 100644 --- a/man/kondo_preprocess.1 +++ b/man/kondo_preprocess.1 @@ -1,5 +1,5 @@ .Dd $Mdocdate: April 14 2015 $ -.Dt kondo_preprocess 1.2.1 +.Dt kondo_preprocess 1.3 .Os .Sh NAME .Nm kondo_preprocess @@ -94,6 +94,30 @@ defines external fields for A and B, denoted by a and b. They can be used as fie .D1 <axb.h> .Pp .It +Scalar products of A's and B's may also be specified using the '<#.#>' syntax: +.D1 <An.An> +.D1 <Bn.Bn> +.D1 <An.Bn> +.D1 <An.h> +.D1 <Bn.h> +.Pp +The difference between '[f #.#]' and '<#.#>' is that the former corresponds to a '#!symbols' entry whereas the latter is replaced by its corresponding polynomial when +.Nm +reads it (see +.Sx meankondo Ns (1)). +.Pp +.It +A vector 't=(t1,t2,t3)' of Pauli matrices (satisfying the Pauli commutation relations [ti,tj]=\\delta_{i,j}1+\\epsilon_{i,j,k}tk) is introduced as a non-commuting object. It can be used in scalar producs: +.D1 <An.t> +.D1 <Bn.t> +.D1 <t.h> +.D1 <a.t> +.D1 <b.t> +.Pp +Note that the '<#,#>' must be used since these scalar products do not commute whereas '#!symbols' entries must commute (see +.Sx meankondo Ns (1)). +.Pp +.It Furthermore, in order to simplify writing products of polynomials over each box index, if the polynomial contains a '%', then .Nm multiplies the polynomial by itself as many times as there are boxes (2^dimension times), replacing '%' with the appropriate box index. For example, if dimension=1 @@ -118,6 +142,9 @@ in which the polynomial can use the fields .D1 <a.h> .D1 <b.h> .D1 <axb.h> +.D1 <t.h> +.D1 <a.t> +.D1 <b.t> defined above. .Pp Example: |