Ian Jauslin
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authorIan Jauslin <ian.jauslin@roma1.infn.it>2015-07-22 13:55:29 +0000
committerIan Jauslin <ian.jauslin@roma1.infn.it>2015-07-22 13:55:29 +0000
commitf13eacbc8e5ab714dd3544adab8189c313382c77 (patch)
treeefd35fca778e6e343206f48918898a8b4cda9977 /man/kondo_preprocess.1
parent3b591888b5dad7cef02170743a92e2bf9c5831db (diff)
Support for non-commuting fieldsv1.3
Diffstat (limited to 'man/kondo_preprocess.1')
-rw-r--r--man/kondo_preprocess.129
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: