Hamiltonian Light-Front Ffield Theory in a Basis Function Approach Page: 4 of 32
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
For example, one can now obtain the low-lying solutions for A = 14 systems with matrices
of dimension one to three billion on 8000 to 50000 processors within a few hours of wall-
clock time. Since the techniques are evolving rapidly [11] and the computers are growing
dramatically, much larger matrices are within reach.
In a NCSM or NCFC application, one adopts a 3-D harmonic oscillator for all the par-
ticles in the nucleus (with harmonic oscillator energy Q), treats the neutrons and protons
independently, and generates a many-fermion basis space that includes the lowest oscillator
configurations as well as all those generated by allowing up to Nma, oscillator quanta of ex-
citations. The single-particle states are formed by coupling the orbital angular momentum
to the spin forming the total angular momentum j and total angular momentum projection
mi. The many-fermion basis consists of states where particles occupy the allowed orbits
subject to the additional constraint that the total angular momentum projection MA is a
pre-selected value. This is referred to as the rn-scheme basis and, in a single run, one ob-
tains eigenstates with total angular momentum J > M,. For the NCSM one also selects a
renormalization scheme linked to the many-body basis space truncation while in the NCFC
the renormalization is either absent or of a type that retains the infinite matrix problem. In
the NCFC case [6], one extrapolates to the continuum limit as we now illustrate.
We show in Fig. 1 results for the ground state of '2C as a function of Nmax obtained
with a realistic NN interaction, JISP16 [12]. The smooth curves portray fits that achieve the
desired independence of Nma, and Q so as to yield the extrapolated ground state energy. Our
assessed uncertainty in the extrapolant is about 2 MeV and there is rather good agreement
with experiment within that uncertainty. The largest cases presented in Fig. 1 correspond to
Nmax = 8, where the matrix reaches a basis dimension near 600 million. Nmax = 10 produces
a matrix near 8 billion whose lowest eigenvalues will be obtained in the near future.
III. CHOICE OF REPRESENTATION FOR LIGHT FRONT HAMILTONIANS
It has long been known that light-front Hamiltonian quantum field theory has similarities
with non-relativistic quantum many-body theory. We further exploit this connection, in
what we will term a "Basis Light Front Quantized (BLFQ)" approach, by adopting a light-
front single-particle basis space consisting of the 2-D harmonic oscillator for the transverse
modes (radial coordinate p and polar angle 0) and a discretized momentum space basis for
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Vary, J.P.; Honkanen, H.; Li, Jun; Maris, P.; Brodsky, S.J.; Harindranath, A. et al. Hamiltonian Light-Front Ffield Theory in a Basis Function Approach, article, May 15, 2009; United States. (https://digital.library.unt.edu/ark:/67531/metadc932957/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.