Unifying the theory of Integration within normal-, Weyl- and antinormal-ordering of operators and the s--ordered operator expansion formula of density operators

New approach for deriving operator identities by alternately using normally, antinormally, and Weyl ordered integration

Dirac's ket-bra formalism is the "language" of quantum mechanics and quantum field theory. In Refs.(Fan et al, Ann. Phys. 321 (2006) 480; 323 (2008) 500) we have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra projectors. In this work by alternately using the technique of integration within normal, antinormal, and Weyl ordering of operators we not only derive some new operator ordering identities, but also deduce some useful integration formulas regarding to Laguerre and Hermite polynomials. This opens a new route of deriving mathematical integration formulas by virtu…

Coherent State Path Integrals in the Weyl Representation

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in \cite{Klau85}, which involve the normal or the antinormal ordering of the Hamiltonian. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. We show that the semiclassical limit of the coherent state propagator in Weyl representation is involves classical trajectories that are independent on the coherent stat…

乘积Weyl-Heisenberg协变MUBs与魔力最大值

Product Weyl--Heisenberg covariant mutually unbiased bases and extremal non-stabilizerness

研究乘积Hilbert空间中的离散结构，通过协变于乘积群的构造，提出魔力概念并证明其最大值对应于生成MUBs的fiducial态，尤其在素数幂维度中构造了此类态。

A general approach to quantum mechanics as a statistical theory

Since the very early days of quantum theory there have been numerous attempts to interpret quantum mechanics as a statistical theory. This is equivalent to describing quantum states and ensembles together with their dynamics entirely in terms of phase-space distributions. Finite dimensional systems have historically been an issue. In recent works [Phys. Rev. Lett. 117, 180401 and Phys. Rev. A 96, 022117] we presented a framework for representing any quantum state as a complete continuous Wigner function. Here we extend this work to its partner function -- the Weyl function. In doing so we comp…