Integration of Maurer-Cartan form
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Let $G$ be a Lie group with Lie algebra $g$. As it is well known the Maurer-Cartan form $ω:TGrightarrow g$ transports any vector $Xin T_{x}G$ to the start $l_{x^{-1}*}(X)in g$, $l_{x^{-1}}$ denoting the left translation. Let $σ:[0,1]rightarrow G$ a smooth path on $G$. It there a way to define path integration on $G$ such that $int_{σ}{ω}=σ(1)σ(0)^{-1}$?
integration lie-groups
asked Nov 18 at 8:13
Allotrios
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Let $G$ be a Lie group with Lie algebra $g$. As it is well known the Maurer-Cartan form $ω:TGrightarrow g$ transports any vector $Xin T_{x}G$ to the start $l_{x^{-1}*}(X)in g$, $l_{x^{-1}}$ denoting the left translation. Let $σ:[0,1]rightarrow G$ a smooth path on $G$. It there a way to define path integration on $G$ such that $int_{σ}{ω}=σ(1)σ(0)^{-1}$?
integration lie-groups
asked Nov 18 at 8:13
Allotrios
736
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Let $G$ be a Lie group with Lie algebra $g$. As it is well known the Maurer-Cartan form $ω:TGrightarrow g$ transports any vector $Xin T_{x}G$ to the start $l_{x^{-1}*}(X)in g$, $l_{x^{-1}}$ denoting the left translation. Let $σ:[0,1]rightarrow G$ a smooth path on $G$. It there a way to define path integration on $G$ such that $int_{σ}{ω}=σ(1)σ(0)^{-1}$?
integration lie-groups
asked Nov 18 at 8:13
Allotrios
736
Let $G$ be a Lie group with Lie algebra $g$. As it is well known the Maurer-Cartan form $ω:TGrightarrow g$ transports any vector $Xin T_{x}G$ to the start $l_{x^{-1}*}(X)in g$, $l_{x^{-1}}$ denoting the left translation. Let $σ:[0,1]rightarrow G$ a smooth path on $G$. It there a way to define path integration on $G$ such that $int_{σ}{ω}=σ(1)σ(0)^{-1}$?
integration lie-groups
integration lie-groups
asked Nov 18 at 8:13
Allotrios
736
asked Nov 18 at 8:13
Allotrios
736
asked Nov 18 at 8:13
Allotrios
736
asked Nov 18 at 8:13
Allotrios
736
asked Nov 18 at 8:13
Allotrios
736
736
add a comment |
add a comment |
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