Fundamental Phase Space Formula for the Similitude Group
Document Type
Conference Proceeding
Publication Date
3-7-2024
Abstract
In this work, the statement and proof of a fundamental formula in the phase space representation of quantum systems will be carried out for the similitude group, Sim(2). This formula takes the form ∫ a(Y)P(Y)d(Y) = {A}, where Y is the phase space variable and {A} is a linear operator on Hilbert space representing a quantum dynamical observable. {A} is the quantum expected value of the observable in a state of the system. The focus on the similitude group is due to current interest in signal analysis, localization operators and pseudo-differential operators. The fundamental formula states that this may be computed in a classical manner, as an integral against a probability distribution. The formula is intimately related to the quantization-dequantization problem a(Y) ↔ A which assigns a quantum operator to the classical phase space function a(Y).
Recommended Citation
Laarni B. Natividad, Job A. Nable; Fundamental phase space formula for the similitude group. AIP Conf. Proc. 7 March 2024; 2895 (1): 080007. https://doi.org/10.1063/5.0192115
