Publication details
Batalin-Vilkovisky Quantization and Generalizations
| Authors | |
|---|---|
| Year of publication | 1997 |
| Type | Monograph |
| MU Faculty or unit | |
| Citation | |
| Description | Gauge theories play an important role in modern physics. Whenever a gauge symmetry is present, one should provide for a manifestly gauge independent formalism. It turns out that the BRST symmetry plays a prominent part in providing the gauge independence. The importance of gauge independence in the Hamiltonian Batalin-Fradkin-Fradkina-Vilkovisky formalism and in the Lagrangian Batalin-Vilkovisky formalism is stressed. Parallels are drawn between the various theories. // A Hamiltonian path integral that takes into account quantum ordering effects arising in the operator formalism, should be written with the help of the star-multiplication or the Moyal bracket. It is generally believed, that this leads to higher order quantum corrections in the corresponding Lagrangian path integral. A higher order Lagrangian path integral based on a nilpotent higher order odd Laplacian is proposed. A new gauge independence mechanism that adapts to the higher order formalism, and that by-passes the problem of constructing a BRST transformation of the path integral in the higher order case, is developed. // The new gauge mechanism is closely related to the cohomology of the odd Laplacian operator. Various cohomology aspects of the odd Laplacian are investigated. Whereas for instance the role of the ghost-cohomology properties of the BFV-BRST charge has been emphasized by several authors, the cohomology of the odd Laplacian is in general not well known. |