论文标题
半空间上的无质量费米斯：2+1维的奇怪案例
Massless Fermions on a half-space: The curious case of 2+1-dimensions
论文作者
论文摘要
详细讨论了2+1个尺寸的无质量dirac fermion的边界条件，详细讨论了空间为半平面。有人认为，使汉密尔顿遗产的线性边界条件通常打破$ c $ $ p $，$ t $ symmetries以及洛伦兹和保形对称性。我们表明，基本上有一种特殊情况，其中一种fermion具有$ cpt $，以及边界的完整繁殖性和保形对称性。我们表明，随着费米昂的加倍，有第二个特殊情况尊重$ CPT $，但仍然违反了Lorentz和Sonformal Symmetry。第二种特殊情况本质上是狄拉克运算符具有零模式边缘状态的独特边界条件。我们讨论边缘状态如何导致尺度，相位和翻译对称性的异国情调表示，以及施加对称要求的方式如何导致系统的边缘铁磁性。我们证明，异国情调的铁磁表示确实是由系统的基接地状态携带的，这是由一类相互作用的汉密尔顿人扰动的，其中包括非偏见的库仑相互作用。
Boundary conditions for a massless Dirac fermion in 2+1 dimensions where the space is a half-plane are discussed in detail. It is argued that linear boundary conditions that leave the Hamiltonian Hermitian generically break $C$ $P$ and $T$ symmetries as well as Lorentz and conformal symmetry. We show that there is essentially one special case where a single species of fermion has $CPT$ and the full Poincare and conformal symmetry of the boundary. We show that, with doubled fermions, there is a second special case which respects $CPT$ but still violates Lorentz and conformal symmetry. This second special case is essentially the unique boundary condition where the Dirac operator has fermion zero mode edge states. We discuss how the edge states lead to exotic representations of scale, phase and translation symmetries and how imposing a symmetry requirement leads to edge ferromagnetism of the system. We prove that the exotic ferromagnetic representations are indeed carried by the ground states of the system perturbed by a class of interaction Hamiltonians which includes the non-relativistic Coulomb interaction.
