ترغب بنشر مسار تعليمي؟ اضغط هنا

Notes on The Feynman Checkerboard Problem

210   0   0.0 ( 0 )
 نشر من قبل Keith Earle
 تاريخ النشر 2010
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Keith A. Earle




اسأل ChatGPT حول البحث

The Feynman checkerboard problem is an interesting path integral approach to the Dirac equation in `1+1 dimensions. I compare two approaches reported in the literature and show how they may be reconciled. Some physical insights may be gleaned from this approach.



قيم البحث

اقرأ أيضاً

116 - W. Ichinose , T. Aoki 2019
The Cauchy problem is studied for the self-adjoint and non-self-adjoint Schroedinger equations. We first prove the existence and uniqueness of solutions in the weighted Sobolev spaces. Secondly we prove that if potentials are depending continuously a nd differentiably on a parameter, so are the solutions, respectively. The non-self-adjoint Schroedinger equations that we study are those used in the theory of continuous quantum measurements. The results on the existence and uniqueness of solutions in the weighted Sobolev spaces will play a crucial role in the proof for the convergence of the Feynman path integrals in the theories of quantum mechanics and continuous quantum measurements.
100 - Bertrand Eynard 2018
This is an introduction to the geometry of compact Riemann surfaces, largely following the books Farkas-Kra, Fay, Mumford Tata lectures. 1) Defining Riemann surfaces with atlases of charts, and as locus of solutions of algebraic equations. 2) Space o f meromorphic functions and forms, we classify them with the Newton polygon. 3) Abel map, the Jacobian and Theta functions. 4) The Riemann--Roch theorem that computes the dimension of spaces of functions and forms with given orders of poles and zeros. 5) The moduli space of Riemann surfaces, with its combinatorial representation as Strebel graphs, and also with the uniformization theorem that maps Riemann surfaces to hyperbolic surfaces. 6) An application of Riemann surfaces to integrable systems, more precisely finding sections of an eigenvector bundle over a Riemann surface, which is known as the algebraic reconstruction method in integrable systems, and we mention how it is related to Baker-Akhiezer functions and Tau functions.
238 - Shamgar Gurevich 2009
In these notes we discuss the self-reducibility property of the Weil representation. We explain how to use this property to obtain sharp estimates of certain higher-dimensional exponential sums which originate from the theory of quantum chaos. As a r esult, we obtain the Hecke quantum unique ergodicity theorem for generic linear symplectomorphism $A$ of the torus $T^{2N}=R^{2N}/Z^{2N}.
In this paper, we correct an inaccurate result of previous works on the Feynman propagator in position space of a free Dirac field in (3+1)-dimensional spacetime, and we derive the generalized analytic formulas of both the scalar Feynman propagator a nd the spinor Feynman propagator in position space in arbitrary (D+1)-dimensional spacetime, and we further find a recurrence relation among the spinor Feynman propagator in (D+1)-dimensional spacetime and the scalar Feynman propagators in (D+1)-, (D-1)- and (D+3)-dimensional spacetimes.
The fundamental solution of the Schrodinger equation for a free particle is a distribution. This distribution can be approximated by a sequence of smooth functions. It is defined for each one of these functions, a complex measure on the space of path s. For certain test functions, the limit of the integrals of a test function with respect to the complex measures, exists. We define the Feynman integral of one such function by this limit.
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