In previous work on the quantum mechanics of an atom freely falling in a general curved background spacetime, the metric was taken to be sufficiently slowly varying on time scales relevant to atomic transitions that time derivatives of the metric in the vicinity of the atom could be neglected. However, when the time-dependence of the metric cannot be neglected, it was shown that the Hamiltonian used there was not Hermitian with respect to the conserved scalar product. This Hamiltonian was obtained directly from the Dirac equation in curved spacetime. This raises the paradox of how it is possible for this Hamiltonian to be non-hermitian. Here, we show that this non-hermiticity results from a time dependence of the position eigenstates that enter into the Schrodinger wave function, and we write the expression for the Hamiltonian that is Hermitian for a general metric when the time-dependence of the metric is not neglected.
Chongqing University（重庆大学）；Universidad de Guanajuato（瓜纳华托大学）；Secretaría de Ciencia, de Humanidades, Tecnología e Innovación（科学、人文、技术与创新秘书处）；Dual CP Institute of High Energy Physics（双CP高能物理研究所）
Bosonization in curved spacetime maps massive Thirring model (self-interacting Dirac fermions) to a generalized sine-Gordon model, both living in $1+1$-dimensional curved spacetime. Applying this duality we have shown that the Thirring model fermion, in non-relativistic limit, gets identified with the soliton of non-linear Scrodinger model with Kerr form of non-linearity. We discuss one particular optical soliton in the latter model and relate it with the Thirring model fermion.
In this work, we have obtained the solutions of the (1 + 1) dimensional Dirac equation on a gravitational background within the generalized uncertainty principle. We have shown that how minimal length parameters effect the Dirac particle in a spacetime described by conformally flat metric. Also, supersymmetric quantum mechanics is used both to factorize the Dirac Hamiltonians and obtain new metric functions. Finally, it is observed that the energy dependent potentials may be extended to the energy dependent metric functions.
A mathematical formulation for particle states and electronic properties of a curved graphene sheet is provided, exploiting a massless Dirac spectrum description for charge carriers living in a curved bidimensional background. In particular, we study how the new description affects the characteristics of the sample, writing an appropriate conductivity Kubo formula for the modified background. Finally, we provide a theoretical analysis for the particular case of a cylindrical graphene sample.
We discuss a new realization of $\mathcal{N}$-extended quantum-mechanical supersymmetry (QM SUSY) with central charges hidden in the four-dimensional (4D) mass spectrum of higher dimensional Dirac action with curved extra dimensions. We show that this $\mathcal{N}$-extended QM SUSY results from symmetries in extra dimensions, and the supermultiplets in this supersymmetry algebra correspond to the Bogomol'nyi--Prasad--Sommerfield states. Furthermore, we examine the model of the $S^2$ extra dimension with a magnetic monopole background and confirm that the $\mathcal{N}$-extended QM SUSY explains…
Undistorted monolayer graphene has energy bands which cross at protected Dirac points. It elastically deforms and much research has assumed the Dirac description persists, now in a curved space and coupled to a gauge field related to lattice strain. We show this is incorrect by using a real space gradient expansion to study how the Dirac equation derives from the tight binding model. Generic spatially varying hopping functions give rise to large magnetic fields which spoil the truncation in derivatives. In the perturbative regime, the only consistent truncation to Dirac is one with nontrivial …
We present a semiclassical analysis for Dirac fields on an arbitrary spacetime background and in the presence of a fixed electromagnetic field. Our approach is based on a Wentzel-Kramers-Brillouin approximation, and the results are analyzed at leading and next-to-leading order in the small expansion parameter $\hbar$. Taking into account the spin-orbit coupling between the internal and external degrees of freedom of wave packets, we derive effective ray equations with spin-dependent terms. These equations describe the gravitational spin Hall effect of localized Dirac wave packets. We treat bot…
A chiral alternative to the vierbein field in general relativity was considered by 't Hooft in an attempt to facilitate the construction of a quantum theory of gravity. These objects $ f^a{}_{μν}$ behave like the "cube root" of the metric tensor. We try to construct specific representations of these tensors in terms of Dirac $γ$ matrices in Euclidean and Minkowski space, and promote these to curved space through Newman-Penrose formalism. We conjecture that these are new objects with physical significance and are the analog of Killing-Yano tensors. As an application, we try to construct non-Abe…
The Yukawa model in curved spacetime is considered. We consider a complex scalar field coupled to a $U(1)$ gauge field and also interacting with Dirac fields with a general Yukawa coupling. The local momentum space method is used to obtain the one-loop effective action and we adopt the gauge condition independent background field method introduced by Vilkovisky and DeWitt. The pole parts of the one-loop effective action that depend on the background scalar field, that we do not assume to be constant, are found and used to calculate the counterterms and to determine the relevant renormalization…
In spinor formalism, since any massless free-field spinor with spin higher than $1/2$ can be constructed with spin-1/2 spinors (Dirac-Weyl spinors) and scalars, we introduce a map between Weyl fields and Dirac-Weyl fields. We determine the corresponding Dirac-Weyl spinors in a given empty spacetime. Regarding them as basic units, other higher spin massless free-field spinors are then identified. Along this way, we find some hidden fundamental features related to these fields. In particular, for non-twisting vacuum Petrov type N solutions, we show that all higher spin massless free-field spinor…
We provide an updated study of some electronic properties of graphene nanoscrolls, exploiting a related curved space Dirac equation for the charge carriers. To this end, we consider an explicit parametrization in cylindrical coordinates, together with analytical solutions for the pseudoparticle modes living on the two--dimensional background. These results are then used to obtain a compact expression for the sample optical conductivity, deriving from a Kubo formula adapted to the 1+2 dimensional curved space. The latter formulation is then adopted to perform some simulations for a cylindrical …
Deformed Heisenberg algebra and its Hilbert space representations
African Institute for Mathematical Sciences (AIMS)（非洲数学科学研究所）；Universite Thomas Sankara（托马斯·桑卡拉大学）；Université Felix Houphouët Boigny-Abidjan（费利克斯·乌弗埃-博瓦尼大学）
