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Symmetries under reflecting temperature to negative values
Nordita east wing 132:028 ()
Nordita east wing 132:028
Partition functions' convergence in e.g. statistical mechanics seem
deeply tied to temperature's positivity. Surprisingly, one can
explicitly check that many model partition functions are invariant
under reflecting their temperature-parameter to negative values
(T-reflection). Demanding this invariance selects a unique vacuum
energy of the system. Finite temperatures in relativistic quantum
field theory are introduced through putting the theory on a circle of
radius 1/T; T-reflection seems deeply tied to a redundancy in the
geometry of this so-called thermal circle. It has already revealed
both two-dimensional structures governing four-dimensional physics,
and new aspects of deep theorems in modern mathematics.