Spacetime algebra and electron physics

Unification of versions of photon quantum mechanics through Clifford spacetime algebra

The Clifford spacetime algebraic description of Maxwell's equations is reviewed and shown to give a unified picture of recently published versions of photon quantum mechanics. Photon wave equations and a conserved four-current are derived from the complexified standard Lagrangian. The equations of motion and scalar product are found to be in good agreement with those obtained from Fourier transformation of momentum space wave function and scalar product [Phys. Rev. A 102, 042201 (2020)].

Algebraic approach and coherent states for a relativistic quantum particle in cosmic string spacetime

We study a relativistic quantum particle in cosmic string spacetime in the presence of a uniform magnetic field and a Coulomb-type scalar potential. It is shown that the radial part of this problem possesses the $su(1,1)$ symmetry. We obtain the energy spectrum and eigenfunctions of this problem by using two algebraic methods: the Schrödinger factorization and the tilting transformation. Finally, we give the explicit form of the relativistic coherent states for this problem.

The Density Operators of Qubit Systems in the Multiparticle Spacetime Algebra

We provide a method to write down the density operator for any pure state of multi-qubit systems in the multiparticle spacetime algebra (MSTA) introduced by Doran, Gull, and Lasenby. Using the MSTA formulation, we analyze several aspects of quantum mechanics in a geometrical way including the Bell inequality and the dynamics of two coupled qubits. Lastly, we provide a natural way to construct the local unitary invariants in the MSTA. Using these invariants, we analyze the space of the two-qubit and three-qubit pure states with local and non-local degrees of freedom separated.

时空代数中布洛赫球的非厄米推广

Non-Hermitian Generalization of Bloch Sphere in Spacetime Algebra

该研究利用时空代数建立了非厄米两能级量子系统的布洛赫球几何推广，将态空间扩展为未来光锥，分类了哈密顿量动力学类型并研究了PT对称量子力学的异常点拓扑特征。

Comments on "Dirac theory in spacetime algebra"

In contrast to formulations of the Dirac theory by Hestenes and by the current author, the formulation recently presented by W. P. Joyce [J. Phys. A: Math. Gen. 34 (2001) 1991--2005] is equivalent to the usual Dirac equation only in the case of vanishing mass. For nonzero mass, solutions to Joyce's equation can be solutions either of the Dirac equation in the Hestenes form or of the same equation with the sign of the mass reversed, and in general they are mixtures of the two possibilities. Because of this relationship, Joyce obtains twice as many linearly independent plane-wave solutions for a…

自旋和赝自旋对称性下弯曲时空中修正狄拉克振子的代数方法与相干态

Algebraic Approach and Coherent States for the Modified Dirac Oscillator in Curved Spacetime with Spin and Pseudospin Symmetries

该研究采用代数方法精确求解弯曲时空中带自旋与赝自旋对称性的修正狄拉克振子，通过薛定谔因式分解法证明其SU(1; 1)对称性，得到波函数与能谱，并算出两类极限下的径向相干态及时间演化。