Continuous-Representation Theory. II. Generalized Relation between Quantum and Classical Dynamics
An application to the study of dynamics of the typical overcomplete, nonindependent sets of unit vectors that characterize continuous-representation theory is discussed. It is shown in particular that the conventional, classical hamiltonian dynamical formalism arises from an analysis of quartum dynamics restricted to an overcomplete, nonindependent set of vectors that lie in oneto- one correspondence with, and are labeled by, points in phase space. A generalized classical mechanics is then defined by the extremal of the quantum- mechanical action functional with respect to a restricted set of unit vectors whose c-number labels become the dynamical variables. This kind of classical formalism is discussed in some generality, and is applied not only to simple single-particle problems, but also to finite-spin degrees of freedom and to fermion field oscillators. These latter cases are examples of an important class of problems called exact, for which a study of the classical dynamics alone is sufficient to infer the correct quantum dynamics.
- Research Organization:
- Bell Telephone Labs., Murray Hill, N.J.
- Sponsoring Organization:
- USDOE
- NSA Number:
- NSA-17-032763
- OSTI ID:
- 4659723
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 8 Vol. 4; ISSN JMAPAQ; ISSN 0022-2488
- Publisher:
- American Institute of Physics (AIP)
- Country of Publication:
- Country unknown/Code not available
- Language:
- English
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