Canonical quantization of constrained systems and coadjoint orbits of Diff(S sup 1 )

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1988

OSTI ID:7160635

Scherer, W M

It is shown that Dirac's treatment of constrained Hamiltonian systems and Schwinger's action principle quantization lead to identical commutations relations. An explicit relation between the Lagrange multipliers in the action principle approach and the additional terms in the Dirac bracket is derived. The equivalence of the two methods is demonstrated in the case of the non-linear sigma model. Dirac's method is extended to superspace and this extension is applied to the chiral superfield. The Dirac brackets of the massive interacting chiral superfluid are derived and shown to give the correct commutation relations for the component fields. The Hamiltonian of the theory is given and the Hamiltonian equations of motion are computed. They agree with the component field results. An infinite sequence of differential operators which are covariant under the coadjoint action of Diff(S{sup 1}) and analogues to Hill's operator is constructed. They map conformal fields of negative integer and half-integer weight to their dual space. Some properties of these operators are derived and possible applications are discussed. The Korteweg-de Vries equation is formulated as a coadjoint orbit of Diff(S{sup 1}).

• Research Organization: Rochester Univ., NY (USA)
• OSTI ID: 7160635
• Country of Publication: United States
• Language: English

Related Subjects

657000* -- Theoretical & Mathematical Physics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
99 GENERAL AND MISCELLANEOUS
990200 -- Mathematics & Computers
CALCULATION METHODS
DATA
DIFFERENTIAL EQUATIONS
DIRAC OPERATORS
EQUATIONS
HAMILTONIANS
HILL EQUATION
INFORMATION
LAGRANGE EQUATIONS
MATHEMATICAL OPERATORS
NUMERICAL DATA
PARTIAL DIFFERENTIAL EQUATIONS
QUANTIZATION
QUANTUM OPERATORS
THEORETICAL DATA