Mark Burgess
In contemporary field theory, the word classical is reserved for an analytical framework in which the local equations of motion provide a complete description of the evolution of the fields. Classical field theory is a differential expression of change in functions of space and time, which summarizes the state of a physical system entirely in terms of smooth fields. The differential (holonomic) structure of field theory, derived from the action principle, implies that field theories are microscopically reversible by design: differential changes experience no significant obstacles in a system and may be trivially undone. Yet, when summed macroscopically, in the context of an environment, such individually reversible changes lead to the well known irreversible behaviours of thermodynamics: the reversal of paths through an environmental landscape would require the full history of the route taken. Classical field theory thus forms a basis for both the microscopic and the macroscopic. When applied to quantum mechanics, the classical framework is sometimes called the first quantization . The first quantization may be considered the first stage of a more complete theory, which goes on to deal with the issues of many–particle symmetries and interacting fields. Quantum mechanics is classical field theory with additional assumptions about measurement. The term quantum mechanics is used as a name for the specific theory of the Schrödinger equation, which one learns about in undergraduate studies, but it is also sometimes used for any fundamental description of physics, which employs the measurement axioms of Schrödinger quantum mechanics, i.e. where change is expressed in terms of fields and groups.
Cambridge University Press eBooks•Apr 4, 2002•0 citations