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Bulletin of the Military University of Technology

Anti-Wick symbol for an operator

Jan A. Rempała

Published Jan 1, 2003• 0 citations
OpenAlex

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We consider the covariant and contravariant symbols of operators that are a generalization of the Wick and anti-Wick symbols introduced earlier. With the help of these symbols we investigate the spectral characteristics of operators, and construct a method of successive approximations to calculate the exponential of an operator. In an application to anti-Wick symbols this method provides a basis of one of the variants of the Feynman functional integral along trajectories in phase space.

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This article is concerned with compositions in the context of three standard quantizations in the framework of Fock spaces, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states also known as a Wick product and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for issues on time dynamics (see [ 29 , 13 ]). Anti-Wick quantization and Segal–Bargmann transforms are implied here for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick and Weyl symbols of the composition of two operators, we obtain an absolutely converging series and for the Weyl symbol, the remainder terms up to any orders of the expansion are controlled, still in the Fock space framework.

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Composition of states and observables in Fock spaces

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This article is concerned with compositions in the context of three standard quantizations in the Fock space framework, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for time dynamics issues. Anti-Wick quantization and Segal Bargmann transforms are implied there for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick symbol of the composition of two operators, we obtain an absolutely converging series, and for the Weyl symbol, the remainder term of the asymptotic expansion is absolutely converging, still in the Fock spaces framework.

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Quadratic Operators

Pure and applied physics•Jan 1, 1966•0 citations
This article is concerned with compositions in the context of three standard quantizations in the framework of Fock spaces, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states also known as a Wick product and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for issues on time dynamics (see [ 29 , 13 ]). Anti-Wick quantization and Segal–Bargmann transforms are implied here for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick and Weyl symbols of the composition of two operators, we obtain an absolutely converging series and for the Weyl symbol, the remainder terms up to any orders of the expansion are controlled, still in the Fock space framework.
This article is concerned with compositions in the context of three standard quantizations in the Fock space framework, namely, anti-Wick, Wick and Weyl quantizations. The first one is a composition of states and is closely related to the standard scattering identification operator encountered in Quantum Electrodynamics for time dynamics issues. Anti-Wick quantization and Segal Bargmann transforms are implied there for that purpose. The other compositions are for observables (operators in some specific classes) for the Wick and Weyl symbols. For the Wick symbol of the composition of two operators, we obtain an absolutely converging series, and for the Weyl symbol, the remainder term of the asymptotic expansion is absolutely converging, still in the Fock spaces framework.