Aharonov–Casher effect in the presence of spin-dependent potential

Missing He–McKellar–Wilkens geometric quantum phase

“…In addition, the radial quantum number has an upper limit that depends on the missing He–McKellar–Wilkens geometric quantum phase. Due to the dependence of the energy levels on the missing He–McKellar–Wilkens geometric phase, there exists an Aharonov–Bohm-type effect for bound states [36,40,50].…”

“…Let us begin with the time-independent Schrödinger–Pauli equation that describes the interaction of the permanent electric dipole moment of a neutral particle with electric and magnetic fields [27,28,33,37–39] (we shall work with ℏ=1 and c=1): Eψ=12mfalse[πfalse^−dbold-italicσ×bold-italicBfalse]2ψ−d2B22mψ−d2mfalse(bold∇⋅bold-italicBfalse)ψ+dbold-italicσ⋅bold-italicEψ. Note that bold-italicσ that appears in equation (2.1) corresponds to the Pauli matrices; in turn, they satisfy the relation false(σiσj+σjσifalse)=2δij. Moreover, the operator πfalse^ is defined as [40] π^k=−ihk∂k−…”

“…Moreover, the operator πfalse^ is defined as [40] π^k=−ihk∂k−12rσ3δφk. The operator πfalse^ defined in equation (2.2) is based on the cylindrical symmetry; therefore, we need to observe that the second term of the right-hand side of equation (2.2) stems from the cylindrical coordinates [40,41]. From the perspective of quantum field theory in curved space–time, the second term of the right-hand side of equation (2.2) corresponds to the spinorial connection [39,40,42,43]. In addition, the parameter hk corresponds to the scale factors of this coordinate system.…”

“…Note that σ that appears in equation (2.1) corresponds to the Pauli matrices; in turn, they satisfy the relation (σ i σ j + σ j σ i ) = 2δ ij . Moreover, the operator π is defined as [40]…”

Dynamics, symmetries, anomaly and vortices in a rotating cosmic string background

“…On the other hand, the (super)conformally invariant systems are the simplest integrable models that can be studied in different geometric backgrounds, and which are essential with their own right due to appearance in various applications in physics. For some recent interesting results see [30][31][32][33] and references therein.…”