Supposing a matrix exponential which is a function of two sets of variables, $e^{F(\{x\},\{y\})}$
What would the meaning of $Tr_x(e^{F(\{x\},\{y\})})$ be?
Terribly sorry if this is a dumb question, but I've been searching everywhere and can't find the answer. It showed up in a paper related to QFT which I was reading.
The $\equiv$ in the equation seems to indicate that equation (2) is meant to be a definition of the "trace". That is, we have (by definition) $$ \operatorname{Tr}_{v_i} e^{\mathbf H(\{v_i\})} = \sum_{v_1,\dots,v_N = \pm 1} e^{-\mathbf H(\{v_i\})} $$