Quantum field theory  From Encyclopedia of Mathematics Jump to:
navigation, search  The theory of relativistic quantum systems.
The origins of quantum field theory are connected with problems
of the interaction of matter with radiation and with the
attempts to construct a relativistic quantum mechanics (P.A.M.
Dirac (1927), W. Heisenberg, W. Pauli, and others). At
relativistic (that is, high) energies there cannot be a
consistent quantum mechanics of particles, since a relativistic
quantum particle is capable of producing new (similar or
different) particles and of vanishing itself. As a result one
cannot distinguish a definite number of mechanical degrees of
freedom connected with this particle, but one has to talk about
a system with a variable, generally infinite, number of degrees
of freedom. Quantum field theory unifies the description of
fields and particles, which in classical physics appear as two
distinct entities.  The notion of a quantum field plays a
central role in the theory. It is convenient to