g_ wildcard replacement

[mgerlach-phys]

Wildcard replacement that work on general tensors do not work on g_. As can be seen in

symbol x;
index i,j,k1,k2;
t g;

local A = g_(1, i, j); 
local B = g(1, i, j); 

print;
.sort

id g_(?x, k1?, k2?) = g_(?x, k2, k1);
id g(?x, k1?, k2?) = g(?x, k2, k1);

print;
.end

[vermaseren]

g_ is a very special object with its own rules and a completely ‘private’ treatment. It is simultaneously a string of matrices or a sequence of individual matrices. Hence ?a cannot work in it.

Anytime you want to do something nontrivial with gamma matrices, it is best to emulate your own. If you want to use the built in trace algorithms, you convert to g_ at the last moment.

Cheers

Jos

On 7 Nov 2019, at 10:13, mgerlach-phys notifications@github.com wrote:

Wildcard replacement that work on general tensors do not work on g_. As can be seen in

symbol x; index i,j,k1,k2; t g;

local A = g_(1, i, j); local B = g(1, i, j);

print; .sort

id g(?x, k1?, k2?) = g(?x, k2, k1); id g(?x, k1?, k2?) = g(?x, k2, k1);

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[mgerlach-phys]

Dear Jos,

thanks for your reply. In that case it would be a good idea to provide the multi-argument wildcard replacement since, for example,

id g_(i?, k1?, k2?) = g_(i, k2, k1);

works as intended.

Best, Marvin

[vermaseren]

That would be a nice assignment for the second week of the Form workshop coming August. It might be too difficult though, due to ‘backtracking’.

Personally I do not have time for this. At the moment I try to concentrate on completely novel aspects.

Cheers

Jos

On 7 Nov 2019, at 10:51, mgerlach-phys notifications@github.com wrote:

Dear Jos,

thanks for your reply. In that case it would be a good idea to provide the multi-argument wildcard replacement since, for example,

id g(i?, k1?, k2?) = g(i, k2, k1); works as intended.

Best, Marvin

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