Separating integrals

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I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.










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  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31














up vote
1
down vote

favorite












I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.










share|cite|improve this question























  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31












up vote
1
down vote

favorite









up vote
1
down vote

favorite











I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.










share|cite|improve this question















I went across the following equality:



enter image description here



May I ask why does the first line equate to the second line? What is the proof behind that?



Note: $H$ are linear operators. $T$ means that the linear operators are ordered such that operators with lower value of $t$ as their argument are placed on the right.







integration






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share|cite|improve this question













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share|cite|improve this question








edited Sep 2 at 8:37

























asked Sep 2 at 8:34









Taylor Tiger

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1168











  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31
















  • What is T? $$
    – Sobi
    Sep 2 at 8:36











  • @Sobi I will add this definition to the question
    – Taylor Tiger
    Sep 2 at 8:36






  • 1




    There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
    – GEdgar
    Sep 2 at 12:31















What is T? $$
– Sobi
Sep 2 at 8:36





What is T? $$
– Sobi
Sep 2 at 8:36













@Sobi I will add this definition to the question
– Taylor Tiger
Sep 2 at 8:36




@Sobi I will add this definition to the question
– Taylor Tiger
Sep 2 at 8:36




1




1




There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
– GEdgar
Sep 2 at 12:31




There are $n!$ different arrangements of the arguments. See if you can work out what happens in the $n=2$ term.
– GEdgar
Sep 2 at 12:31















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