Die Methode der Funktionale in der Quantenfeldtheorie

Novožilov, J. V.; Tulub, A. V.

doi:10.1002/prop.19580060105

Cited by 11 publications

(2 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Refs. [12,13].) Investigation of properties of normal and anti-normal symbols of the evolution operator enabled Berezin to derive sophisticated theorems about spectra of Hamiltonian operators [1,15] for the Euclidean phase space.…”

Section: Historical Backgroundmentioning

confidence: 99%

Berezin quantization and unitary representations of Lie groups

Bar-Moshe¹,

Marinov

1996

Topics in Statistical and Theoretical Physics

View full text Add to dashboard Cite

In 1974, Berezin proposed a quantum theory for dynamical systems having a Kähler manifold as their phase space. The system states were represented by holomorphic functions on the manifold. For any homogeneous Kähler manifold, the Lie algebra of its group of motions may be represented either by holomorphic differential operators ("quantum theory"), or by functions on the manifold with Poisson brackets, generated by the Kähler structure ("classical theory"). The Kähler potentials and the corresponding Lie algebras are constructed now explicitly for all unitary representations of any compact simple Lie group. The quantum dynamics can be represented in terms of a phase-space path integral, and the action principle appears in the semi-classical approximation.

show abstract

Section: Historical Backgroundmentioning

confidence: 99%

Berezin quantization and unitary representations of Lie groups

Bar-Moshe¹,

Marinov

1996

Topics in Statistical and Theoretical Physics

View full text Add to dashboard Cite

show abstract

“…Of course, we have omitted here all detail necessary assumptions concerning spaces X and Y . I n the special case when functional space X is identical with the Hilbert space I2 of the quadratically integrable functions of y and if we assume the functional INGARDEN and KOSSAKOWSKI 1965 b, on functional integration methods cf.SYMANZIK 1954, especially Appendix, GELFAND and YAGLOM 1956, NOVOZILOV and TULUB 1958. By formula (2.27) the problem of expressing P [XI by W ,(y,, .…”

mentioning

confidence: 99%