Tables of supersymmetric evolutionary equations with higher order symmetries
Supersymmetric evolution equations
Preliminary Comments
All weights mentioned in the tables below are based on a
weight of x equal 2.
If casses are labeled as having weight(t)=n
then this means that each term of the right hand side of f_t=...
has the same weight as f_(n/2)x. Odd integer n weights
can be obtained through the supersymmetric D derivative which
has half of the weight of one x derivative. The highest
x derivative may be lower than
n/2 but each term has to have exactly this weight.
In the evolutionary equations the weight is called weight(t)
whereas in the symmetry it is called weight(s).
Only evolution equations and their symmetries are
computed which satisfy the following non-triviality conditions:
- None of the right hand sides of any equation or symmetry should
vanish identically.
- None of the evolution equations should involve only one field.
- At least one evolutionary equation should be non-linear.
- In order not to have a purely classical problem at least one
evolutionary equation or one symmetry should contain a fermion field
or a D_i derivative.
- If N>1 then each of D_1,..,D_N must occur in at least one evolutionary
equation or symmetry.
If entries in tables are empty then the corresponding computations have not been
completed yet.
So far the following cases have been considered:
Overview
weights: --> | 1 | 2 | 3 |
4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 |
N=1, 1 fermion field |
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N=1, 1 fermion field f, weight 1
N=1, 1 fermion field f, weight 2
N=1, 1 fermion field f, weight 3
N=1, 1 fermion field f, weight 4
N=1, 1 fermion field f, weight 5
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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N=1, 1 fermion field f, weight 6
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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N=1, 1 fermion field f, weight 7
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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N=1, 1 fermion field f, weight 8
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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N=1, 1 fermion field f, weight 9
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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N=1, 1 fermion field f, weight 10
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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6 |
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7 |
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8 |
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9 |
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10 |
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11 |
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12 |
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13 |
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N=1, 1 fermion field f, weight 11
weight(s):> |
2 | 3 | 4 | 5 | 6 | 7 | 8 |
9 | 10 | 11 | 12 | 13 | 14 |
weight(t): 1 |
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8 |
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9 |
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10 |
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11 |
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13 |
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This page is maintained by
Thomas Wolf
E-mail: twolf@brocku.ca