Does heat kernel factorize on product spaces?
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yes heat kernel factorise on product spaces
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I have a doubt regarding whether the trace of the vector heat kernel on a product space factorizes into the corresponding heat kernel traces on each manifold in the product space. I know this holds for the spin-0 as well as spin-1/2 cases, but I am not sure about the spin-1 case. Can somebody please help me out in this regard?
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