Nondiagonal Values of the Heat Kernel for Scalars in a Constant Electromagnetic Field

High-temperature expansion of the grand thermodynamic potential for scalar particles in crossed electromagnetic fields

“…It should be noted that despite the fact that H 0 is quadratic in momentum [x, [x, [x, H 0 ]]] = 0. This is the reason why the naive expression for the heat kernel in external homogeneous electromagnetic fields [5,16] is not applicable in our case. Time evolution operator takes an especially simple form in the interaction picture (Dyson series)…”

“…Hereinafter both types will be denoted by ζ k (ν). For the field configuration at issue the problem is complicated by the fact that the expression for the heat kernel (exponent on the right-hand side of (2)) derived in [5] (see also [16]) is not appropriable. The standard definition of the vacuum state in a stationary field can be used only when the work of the electromagnetic field is smaller than the energy required to create a particle-antiparticle pair from the vacuum, ∆A 0 < 2mc 2 , see [6] (the situation with strong enough electric fields is considered in, e.g., [7]).…”