Transcript Document

Hamiltonian Light Front Field Theory:
Recent Progress and Tantalizing Prospects
James P. Vary
Iowa State University
Light Cone 2011
Dallas, Texas
May 23 - 27, 2011
Abstract
Fundamental theories, such as Quantum Chromodynamics (QCD) and Quantum Electrodynamics (QED)
promise great predictive power spanning phenomena on all scales from the microscopic to cosmic scales.
However, new non-perturbative tools are required to build bridges from one scale to the next. I will outline
recent theoretical and computational progress to build these bridges and provide illustrative results
for Hamiltonian Light Front Field Theory. One key area is our development of basis function approaches
that cast the theory as a Hamiltonian matrix problem while preserving a maximal set of symmetries [1].
Regulating the theory with an external field that can be removed to obtain the continuum limit offers
additional advantages as we showed recently in an application to the anomalous magnetic moment
of the electron [2]. Recent progress capitalizes on algorithm and computer developments for setting up
and solving very large sparse matrix eigenvalue problems. Matrices with dimensions of 10 billion basis
states are now solved routinely in leadership-class computers for their low-lying eigenstates
and eigenfunctions.
This work was supported in part by US DOE Grant DE-FG02-87ER40371
[1] J. P. Vary, H. Honkanen, Jun Li, P. Maris, S. J. Brodsky, A. Harindranath, G. F. de Teramond,
P. Sternberg, E. G. Ng, C. Yang, “Hamiltonian light-front field theory in a basis function approach”,
Phys. Rev. C 81, 035205 (2010); arXiv nucl-th 0905.1411
[2] H. Honkanen, P. Maris, J. P. Vary and S. J. Brodsky, “Electron in a transverse harmonic cavity”,
Phys. Rev. Lett. 106, 061603 (2011); arXiv: 1008.0068
Ab initio nuclear physics - hierarchy of fundamental questions
 Can hadron structures and their interactions be derived from QCD?
 Can nuclei provide precision tests of the fundamental laws of nature?
 What controls nuclear saturation - 3-nucleon interactions?
 How does the nuclear shell model emerge from the underlying theory?
 What are the properties of nuclei with extreme neutron/proton ratios?
Jaguar
Franklin/Hopper
Blue Gene/p
Atlas
Bridging the nuclear physics scales
QCD
Nuclear
Structure
Applications in astrophysics,
defense, energy, and medicine
- D. Dean, JUSTIPEN Meeting, February 2009
http://extremecomputing.labworks.org/nuclearphysics/report.stm
Effective Nucleon Interaction
(Chiral Perturbation Theory)
Chiral perturbation theory (χPT) allows for controlled power series expansion
 Q 
Expansion parameter
: 
 
 , Q  momentum transfer,
  
   1 GeV,  - symmetry breaking scale
Within χPT 2-NNN Low Energy Constants (LEC)

are related to the NN-interaction LECs {ci}.
CD
CE
Terms suggested within the
Chiral Perturbation Theory
R. Machleidt, D. R. Entem, nucl-th/0503025
Further renormalization is necessary
since momentum transfers still too high,
reaching ~ 0.6 GeV/c
No Core Shell Model
A large sparse matrix eigenvalue problem
H  Trel  VNN  V3N  
H i  E i i

i   Ani n
n 0
Diagonalize m H n
•
•
•
•

Adopt realistic NN (and NNN) interaction(s) & renormalize as needed - retain induced
many-body interactions: Chiral EFT interactions and JISP16
Adopt the 3-D Harmonic Oscillator (HO) for the single-nucleon basis states,  , ,…
nuclear Hamiltonian, H or renormalized Heff, in basis space of HO
Evaluate the
(Slater) determinants (manages the bookkeepping of anti-symmetrization)
Diagonalize this sparse many-body H in its “m-scheme” basis where [ =(n,l,j,mj,z)]
n  [a  a ]n 0
n  1,2,...,1010 or more!
•
Evaluate observables and compare with experiment

Comments
• Straightforward
 but computationally demanding => new algorithms/computers
• Requires convergence assessments and extrapolation tools
• Achievable for nuclei up to A=16 (40) today with largest computers available
NOTE: No known limitations in principle on choice of
 Hamiltonian
 Basis space
 Renormalization scheme
(CD= -0.2)
Note additional predicted states!
Shown as dashed lines
P. Maris, P. Navratil, J. P. Vary, to be published
“Anomalous Long Lifetime of Carbon-14”
Objectives
 Solve the puzzle of the long but
useful lifetime of 14C
 Determine the microscopic origin
of the suppressed β-decay rate
Impact
 Establishes a major role for strong 3-nucleon forces in nuclei
 Verifies accuracy of ab initio microscopic nuclear theory
 Provides foundation for guiding DOE-supported experiments
3-nucleon forces suppress critical component
 Dimension of matrix solved
for 8 lowest states ~ 1x109
 Solution takes ~ 6 hours on
215,000 cores on Cray XT5
Jaguar at ORNL
 “Scaling of ab initio nuclear
physics calculations on
multicore computer
architectures," P. Maris, M.
Sosonkina, J. P. Vary, E. G.
Ng and C. Yang, 2010
net decay rate Intern. Conf. on Computer
Is very small Science, Procedia
Computer Science 1, 97
(2010)
Descriptive Science
Predictive Science
“Proton-Dripping Fluorine-14”
Objectives
 Apply ab initio microscopic
nuclear theory’s predictive
power to major test case
Impact
 Deliver robust predictions important for improved energy sources
 Provide important guidance for DOE-supported experiments
 Compare with new experiment to improve theory of strong interactions
P. Maris, A. Shirokov and J.P. Vary,
Phys. Rev. C 81 (2010) 021301(R)
Experiment confirms
our published
predictions!
V.Z. Goldberg et al.,
Phys. Lett. B 692, 307 (2010)
 Dimension of matrix solved
for 14 lowest states ~ 2x109
 Solution takes ~ 2.5 hours
on 30,000 cores (Cray XT4
Jaguar at ORNL)
 “Scaling of ab-initio nuclear
physics calculations on
multicore computer
architectures," P. Maris, M.
Sosonkina, J. P. Vary, E. G.
Ng and C. Yang, 2010
Intern. Conf. on Computer
Science, Procedia
Computer Science 1, 97
(2010)
Recent noteworthy accomplishments of the
ab initio no core shell model (NCSM)
and no core full configuration (NCFC)
 Described the anomaly of the nearly vanishing quadrupole moment of 6Li
 Established need for NNN potentials to explain neutrino -12C cross sections
 Explained quenching of Gamow-Teller transitions (beta-decays) in light nuclei
 Obtained successful description of A=10-13 nuclei with chiral NN+NNN potentials
 Explained ground state spin of 10B by including chiral NNN potentials
 Developed/applied methods to extract phase shifts (J-matrix, external trap)
 Successful prediction of low-lying 14F spectrum (resonances) before experiment
 Explained the mystery of the anomalous long lifetime of
14C,
useful for archeology
Light cone coordinates and generators


M  P P0  P P1  (P  P )(P0  P1)  P P  KE
2
0
1
Equal time
“Instant Form”
x0
H=P0
x1
P1
0
1
Some perspectives on Hamiltonian applications to LFQ
1+1 dimensional theories
DLCQ initiated many applications (Review: Brodsky, Pauli, Pinsky)
Spontaneous symmetry breaking (Chakrabarti, Martinovic, Harindranath,…)
Critical phenomena - e.g. kink condensation (Chakrabarti, …)
Zero modes, boundary conditions, regulators, …(Bassetto, McCartor,…)
QCD SU(3) color singlet structures (Hornbostel)
2+1 dimensional theories
QCD - Bloch and SRG Heff treatments (Chakrabarti, Harindranath)
3+1 dimensional theories
QED - LF wave equations (Hiller, Chabysheva, Brodsky, …)
QCD - Transverse lattice (Dalley, van de Sande, Chakrabarti,….)
SRG approach (Wilson, Glazek, Perry, … )
DIS - Q2 evolution (Zhang, Harindranath,…)
“Near” LFQ (Franke, Prokhvatilov, Paston, Pirner, Naus, Lenz, Moniz, .…)
Consistent quantization (D. Kulshreshtha, U. Kulshreshtha,…)
Renormalization/Reg’n (Ji, Bakker, Karmanov, Mathiot, Smirnov, Grange’, …)
DVCS (Brodsky, Mukherjee, Chakrabarti, …)
BLFQ (this talk)
QED - BLFQ approach (Zhao poster at this meeting)
Discretized Light Cone Quantization (c1985)
Basis Light Front Quantization*
 x    f x a  f * x a 

where a  satisfy usual (anti-) commutation rules.
Furthermore,f  x  are arbit rary except for conditions
:
Orthonormal:
Complete:
 f x f x d x  
 f x f x'   x  x'
*
'
3
'
*
3

=> Wide range of choices for f a x and our initial choice is

f x  Ne
ik  x 
n,m (, )  Ne
ik  x 

f n,m ()  m ( )
*J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath, G.F. de Teramond,
P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010). ArXiv:0905:1411
Set of transverse 2D HO modes for n=0
m=0
m=1
m=3
m=2
m=4
J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath,
G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010).
Steps to implement BLFQ
• Enumerate Fock-space basis subject to symmetry constraints
• Evaluate/renormalize/store H in that basis
• Diagonalize (Lanczos)
• Iterate previous two steps for sector-dep. renormalization
• Evaluate observables using eigenvectors (LF amplitudes)
• Repeat previous 4 steps for new regulator(s)
• Extrapolate to infinite matrix limit – remove all regulators
• Compare with experiment or predict new experimental results
Above now achieved for QED test case – electron in a trap
H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky,
Phys. Rev. Lett. 106, 061603 (2011)
Improvements: trap independence, (m,e) renormalization, . . .
X. Zhao, P. Maris, J.P. Vary, S.J. Brodsky, poster at this meeting
Symmetries & Constraints
 bi  B
i
 (m i  s i )  J z
i
 ki  K
i
 2ni  | m i | 1  N max
Finite basis regulators
i
Global Color Singlets (QCD)
Light Front Gauge
Optional - Fock space cutoffs
Hamiltonian for “cavity mode” QCD in the chiral limit
Why interesting - cavity modes of AdS/QCD
H  H 0  H int
Massless partons in a 2D harmonic trap solved in basis functions
commensurate with the trap :

2M 0  1
 2ni  | m i | 1
H 0  2M 0 PC 
K i xi
with  defining the confining scale as well as the basis function scale.
Initially, we study this toy model of harmonically trapped partons in the
chiral limit on the light front. Note Kx i  k i and BC' s will be specified.
Non-interacting QED cavity mode with zero net charge
Photon distribution functions
Labels: Nmax = Kmax ~ Q
“Weak” coupling:
Equal weight to low-lying states
“Strong” coupling:
Equal weight to all states
J.P. Vary, H. Honkanen, J. Li, P. Maris, S.J. Brodsky, A. Harindranath,
G.F. de Teramond, P. Sternberg, E.G. Ng and C. Yang, PRC 81, 035205 (2010).
ArXiv:0905:1411
Comment based on Stan Glazek’s, Craig Roberts’
and Stan Brodsky’s presentations
Operator SRG (Glazek) appears to be a natural route
to obtain the effective (Q-dependent) qluon mass invoked
for the Dyson-Schwinger approach (Roberts)
If the “gluon condensate” indeed exists only within the
hadron and is representable by the gluon mean field,
as is consistent with LFQ approach,
then the mean field of the glue could be defined (derived?)
at a given Nmax ~ K ~ Q. We would then increase
the number of gluons until convergence is reached at
that scale Q.
That is, we adopt the scale Q as defining the border
between dynamical gluons and high momentum gluons
that define the gluon mean field.
For such calculations we initially retain one parameter
for the strength of the SRG mean field interaction Vmf
between pairs of constituent quarks and gluons.
Elementary vertices in LF gauge
QED & QCD
QCD
Initial application to QED*
**
*H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky, Phys. Rev. Lett. 106, 061603 (2011);
X. Zhao, H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky, poster at this meeting
** T. Heinzl, A. Ilderton and H. Marklund, Phys. Lett. B692, 250(2010); arXiv:1002.4018
Initial QED problem
Electron in a transverse
harmonic trap*
Invariant M2 spectra
*H. Honkanen, P. Maris, J.P. Vary, S.J. Brodsky,
Phys. Rev. Lett. 106, 061603 (2011);
X. Zhao, P. Maris, J.P. Vary, S.J. Brodsky,
poster at this meeting
Extended and Improved QED Calculations
Xingbo Zhao, Heli Honkanen, Pieter Maris,
James P. Vary and Stanley J. Brodsky – Poster Session
1.Corrects some implementation errors
2.Implements sector-dependent renormalization
of mass and charge
3.Decouples trap frequency from basis frequency
to improve convergence
4.Preliminary results lead to a puzzle in the electron
anomalous magnetic moment => Spurious CM motion?
5. Working now on alternative setup with external
field removed completely to verify Schwinger moment
Stay tuned for the paper!
g-2 for Electron in Harmonic Trap
• δμ=(g-2)/2 vs. basis ω (at Ω=0.5MeV):
Convergence
reached at large ω
or Nmax
δμ should be independent of the choice of basis in the limit of Nmax->∞
• δμ=(g-2)/2 vs. trap potential Ω:
?
• Each point is the extrapolated result at Nmax->∞
• δμ decreases with the strength of trap potential
• Extrapolated value at Ω=0 larger than the result
from perturbation theory
• Contribution from center-of-mass motion in
truncated HO basis?
• Remove center-of-mass KE from Hamiltonian!
38
Additional recent progress
Derivation of all HQCD vertices in momentum
representation and HO basis spaces
(Harindranath, Honkanen, Zhao, Wiecki, Li)
Comprehensive notes under development (All)
Jun Li’s color singlet code transferred to Wiecki and is
undergoing verification tests.
Programming of additional QCD vertices under development
(Zhao, Wiecki, Li)
Commencing initial applications to quarkonia
Applications of LF amplitudes to experiment - DVCS
S.J. Brodsky, D. Chakrabarti, A. Harindranath, A. Mukherjee, and J.P. Vary,
Phys. Letts B641, 440 (2006); Phys. Rev. D75, 14003 (2007)
Hadron
Optics!
Key to graphs
x Bjorken variable
 invariant longitudinal
impact parameter
 invariant conjugate
longitudinal momentum
M++ Helicity non-flip DVCS amplitude
FS Fourier Spectrum
F2 DIS structure function
Applications of LF AdS/CFT amplitudes to experiment - DVCS
S.J. Brodsky, D. Chakrabarti, A. Harindranath, A. Mukherjee, and J.P. Vary,
Phys. Letts B641, 440 (2006); Phys. Rev. D75, 14003 (2007)
Observation
Ab initio approaches maximize predictive power
& represent a theoretical and computational physics challenge
Key issue
How to achieve the full physics potential of ab initio theory
Conclusions
We have entered an era of first principles, high precision,
many-body and quantum field theory for strongly interacting systems
Linking hadronic physics and the cosmos
through the Standard Model (and beyond) is well underway
and LFQ could play a leading role
Collaborators on BLFQ
Avaroth Harindranath, Saha Institute, Kolkota
Dipankar Chakarbarti, IIT, Kanpur
Asmita Mukherjee, IIT, Mumbai
Stan Brodsky, SLAC
Guy de Teramond, Costa Rica
Usha Kulshreshtha, Daya Kulshreshtha, University of Delhi
Xingbo Zhao, Pieter Maris, Jun Li, Paul Wiecki, Young Li
Heli Honkanen, University of Jyvaskyla
Esmond Ng, Chou Yang, Metin Aktulga, Philip Sternberg, Lawrence Berkeley Laboratory
Thank You!