Field theory, relying on the concept of continuous space and time while
confronted with the quantum physical nature of observable quantities,
still has some fundamental challenges to face. One such challenge is to
understand the emergence of complexity in the behavior of interacting
elementary fields, including among other things nontrivial phase
structures of elementary matter at high energy density or an atypical
emergence of statistical properties, e.g., when an apparent temperature
is proportional to a constant acceleration in a homogeneous
gravitational field.
Most modern textbooks on thermal field theory are mainly concerned with
how the field theory formalism should be used if a finite temperature is
given. In contrast, this short primer explores how the phenomenon of
temperature emerges physically for elementary fields - inquiring about
the underlying kinetic field theory and the way energy fluctuations and
other noise should be handled - and it investigates whether and how this
harmonizes with traditional field theory concepts like spectral
evolution, the Keldysh formalism, and phase transitions.