Alan Bromborsky wrote: > Ondrej Certik wrote: > >> On Thu, Oct 2, 2008 at 2:08 PM, Alan Bromborsky <[EMAIL PROTECTED]> wrote: >> >> >>> Ondrej Certik wrote: >>> >>> >>>> On Thu, Oct 2, 2008 at 2:09 AM, william ratcliff >>>> <[EMAIL PROTECTED]> wrote: >>>> >>>> >>>> >>>>> I'l let you know how it goes. The real application is rather cute. In >>>>> condensed matter, we often measure the elementary excitations of solids. >>>>> In >>>>> simple magnets, these excitations are spin-waves. What I'm trying to do >>>>> is >>>>> make an application so that if you have an insulator and define the >>>>> interactions, you can predict what excitations you will measure (in the >>>>> simple case) to fit against experimental data. If it works, it will make >>>>> exploring different models a lot easier and definetely more fun :> I >>>>> really >>>>> appreciate the work you guys have put into this! >>>>> >>>>> >>>>> >>>> Thanks for the info. This is exactly the kind of thing why I started >>>> sympy couple years ago, so I am glad it's fulfilling the purpose. If >>>> you are interested and the code is not so long, we can put it in the >>>> examples. Having studied theoretical physics, I am interested myself >>>> to play with your code. :) >>>> >>>> Ondrej >>>> >>>> >>>> >>>> >>> You might be interested in the following link >>> >>> http://www.informaworld.com/smpp/content~content=a901881501~db=all~jumptype=rss >>> >>> which references the article "Geometric formulation of correlation in a >>> many-electron system" >>> >>> with abstract >>> >>> "We present a systematic analysis of the introduction of correlation in >>> the many-electron time-dependent problem with an accurate formulation >>> based on geometric algebra notation. This provides a systematic >>> definition of the configuration space, of the external potentials, of >>> the one-electron operators for a many-electron system, and of the >>> electron-electron interaction terms. We arrive both at a formal equation >>> for the total energy and at the equation for the time-evolution of the >>> wavefunction. From this, using the new geometric notation and the >>> indistinguishability and equivalence of the electrons and the fact that >>> we are interested either in the ground state or in states near the >>> ground state, we formulate a variational problem from which a set of >>> tractable equations, which self-consistently define the many-electron >>> wavefunction and density, is obtained. The main emphasis is on the >>> electron-electron correlation." >>> >>> >> Thanks for the tip, indeed, the article is clearly written. Nice >> introduction to the field. >> >> >> >>> I am referencing this since I have added a geometric algebra module to >>> sympy. >>> >>> >> How can the geometric algebra be applied to the electronic structure above? >> >> Ondrej >> >> >> >> > I don't know since I do not have the actual paper available to me, only > the abstract. > > > > > More information. The geometric algebra is just a real clifford algebra of a finite dimensional vector space of signature (p,q). The pauli and dirac algebra's are instances of this except that the geometric algebra allows a simple geometric interpretation of spinors. While my geometric algebra module will allow manipulation of arbitrary symbolic multivectors (elements of the clifford algebra) it would be better for electronic calculations (both symbolic and numerical) to have separate modules for symbolic and numerical calculations with respect to an orthogonal basis. While my module could do both it would probably not be too efficient do to its general nature. Comment on the nature of spinors. In the geometric algebra a pure grade multivector is isomorphic to a antisymmetric tensor while a spinor is a sum of even grade multivectors and thus cannot be represented by tensors. See the sympy wiki section on geometric algebra.
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