ترغب بنشر مسار تعليمي؟ اضغط هنا

Huygens principle for the generalized Dirac operator in curved spacetime

126   0   0.0 ( 0 )
 نشر من قبل Karen Yagdjian
 تاريخ النشر 2020
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Karen Yagdjian




اسأل ChatGPT حول البحث

In this article we give sufficient conditions for the generalized Dirac operator to obey the incomplete Huygens principle, as well as necessary and sufficient conditions to obey the Huygens principle by the Dirac operator in the curved spacetime of the Friedmann-Lema^itre-Robertson-Walker models of cosmology.



قيم البحث

اقرأ أيضاً

265 - Monika Winklmeier 2008
The operator associated to the angular part of the Dirac equation in the Kerr-Newman background metric is a block operator matrix with bounded diagonal and unbounded off-diagonal entries. The aim of this paper is to establish a variational principle for block operator matrices of this type and to derive thereof upper and lower bounds for the angular operator mentioned above. In the last section, these analytic bounds are compared to numerical values from the literature.
We present the fundamental solutions for the spin-1/2 fields propagating in the spacetimes with power type expansion/contraction and the fundamental solution of the Cauchy problem for the Dirac equation. The derivation of these fundamental solutions is based on formulas for the solutions to the generalized Euler-Poisson-Darboux equation, which are obtained by the integral transform approach.
83 - Karen Yagdjian 2020
The equation of the spin-$frac{1}{2}$ particles in the Friedmann-Lema^itre-Robertson-Walker spacetime is investigated. The retarded and advanced fundamental solutions to the Dirac operator and generalized Dirac operator as well as the fundamental sol utions to the Cauchy problem are written in explicit form via the fundamental solution of the wave equation in the Minkowski spacetime.
We consider a Dirac operator with a dislocation potential on the real line. The dislocation potential is a fixed periodic potential on the negative half-line and the same potential but shifted by real parameter $t$ on the positive half-line. Its spec trum has an absolutely continuous part (the union of bands separated by gaps) plus at most two eigenvalues in each non-empty gap. Its resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface. We prove that it has only two simple poles on each open gap: on the first sheet (an eigenvalue) or on the second sheet (a resonance). These poles are called states and there are no other poles. We prove: 1) each state is a continuous function of $t$, and we obtain its local asymptotic; 2) for each $t$ states in the gap are distinct; 3) in general, a state is non-monotone function of $t$ but it can be monotone for specific potentials; 4) we construct examples of operators, which have: a) one eigenvalue and one resonance in any finite number of gaps; b) two eigenvalues or two resonances in any finite number of gaps; c) two static virtual states in one gap.
We present a variational approach which shows that the wave functions belonging to quantum systems in different potential landscapes, are pairwise linked to each other through a generalized continuity equation. This equation contains a source term pr oportional to the potential difference. In case the potential landscapes are related by a linear symmetry transformation in a finite domain of the embedding space, the derived continuity equation leads to generalized currents which are divergence free within this spatial domain. In a single spatial dimension these generalized currents are invariant. In contrast to the standard continuity equation, originating from the abelian $U(1)$-phase symmetry of the standard Lagrangian, the generalized continuity equations derived here, are based on a non-abelian $SU(2)$-transformation of a Super-Lagrangian. Our approach not only provides a rigorous theoretical framework to study quantum mechanical systems in potential landscapes possessing local symmetries, but it also reveals a general duality between quantum states corresponding to different Schr{o}dinger problems.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا