THIS PAGE IS OBSOLETE as of Dec 2 2005

Predrag Cvitanovic´
- quantum field theory publications

	worth a read (better still: or )
	gone to bats
	the dog chewed the paper
	SPIRES citation search

Turbulent field theory

Program whose goal is a non-perturbative theory of turbulent dynamics of classical, stochastic and quantum fields. Turbulent field theory is developed in two directions:
1) explorations of the feasibility of describing weak turbulence in terms of spatiotemporally recurrent patterns, and
2) new perturbation theory methods for computing corrections about nontrivial saddles of path integrals.

Read the sketch paper first, click through the trace formulas papers next.

Perturbative QED

One big calculation, the answer

$\begin{displaymath} {1 \over 2} (g-2) = {1 \over 2} {\alpha \over \pi} - 0.3284... ...ght)^2 + (1.183 \pm 0.011) \left({\alpha \over \pi}\right)^3. \end{displaymath}$

and why did I do this? The electron magnetic moment is the most precise prediction of quantum field theory, and its most precise experimental test. It is also the simplest physical quantity on which to test ideas about the convergence of QED perturbation theory.

	Predrag Cvitanovic´ and Toichiro Kinoshita Feynman-Dyson rules in parametric space Phys. Rev. D10, 3478 (1974) [ SPIRES citations ]
	A (hopefully) pedagogical overview of the Schwinger and Feynman parametric representation of Feynman integrals, should be useful for any QFT perturbative calculation. Some new results, for example the theorem derived in the appendix.
	Predrag Cvitanovic´ and Toichiro Kinoshita New approach to the separation of ultraviolet and infrared divergences of Feynman-parametric integrals Phys. Rev. D10, 3991 (1974) [ SPIRES citations ]
	A new method for dealing with Feynman diagram infrared divergences is introduced. The main result are the very ellegant and compact formulas (3.40) and (5.14) which extract the finite part from any general mass-shell Feynman diagram, removing both ultraviolet and infrared parts of the diagram and all of its counterterms. What remains after the projection is a pointwise-convergent integrand, well suited to numerical integrations.
	Predrag Cvitanovic´ and Toichiro Kinoshita Sixth-order radiative corrections to the electron magnetic moment Phys. Rev. Lett. 29, 1534 (1972)
	At the time perhaps the most demanding numerical computation in theoretical physics, it remained QED's most precise prediction for a number of years. A step in T. Kinoshita's heroic undertaking, but nothing you would want to read today.
	Predrag Cvitanovic´ and Toichiro Kinoshita Sixth order magnetic moment of the electron Phys. Rev. D10, 4007 (1974) [ SPIRES citations ]
	Most of this you can safely skip, unless you happen to be evaluating (g-2) to 3-loop level. However, the new formula (6.22) for the electron magnetic moment, Sect. VI, might be of interest: (g-2) is evaluated from a derivative of the 2-point electron self-energy, rather than a 3-point electron-photon vertex, with fewer Feynman graphs: (1) it enabled us to calculate the electron magnetic moment by two wholy independent methods.
	Predrag Cvitanovic´ Computer generation of integrands for Feynman parametric integrals Cornell preprint CLNS-234 (June, 1973) and Proc. 3rd Coll. on Advanced Comp. Meth. in Theoretical Physics (Marseille, 1973)
	One of the ur-algebraic symbol manipulation programs

Finiteness of gauge field theories

For me the conceptually most striking lesson of these long QED calculations were the amazing cancellations induced by gauge invariance. The desire to understand and exploit gauge invariance more effectively has motivated much of my subsequent research. The most interesting results of this effort were the mass-shell QCD Ward identities and the construction of the QCD gauge sets. This work also motivated the formulation of planar field theory.

Other papers in this series are those on the QCD mass-shell infrared singularities and the diagram counting, both attempts to formulate gauge-invariant models computable to high orders, in order to investigate the nature of gauge-invariance induced cancellations.

Predrag Cvitanovic´
Asymptotic estimates and gauge invariance
Nucl. Phys. B127, 176 (1977) [ SPIRES citations ]

On basis of very skimpy numerical evidence, I conjecture that the gauge invariance induced cancellations are so dramatic that the growth rate of high order perturbation theory corrections to mass-shell gauge-invariant quantities is slower than Dyson's asymptotic series n! estimate. In the case of QED vertex corrections, the smallest gauge invariant set contributing to (m+m'+k)th order consists of m photon "strands" attached to the incoming electron, m' photon "strands" attached to the outgoing electron, and k photon "strands" crossing the external photon vertex. Ignoring sets with electron loops and assuming that each gauge set gives a finite contribution leads to a guess that perturbation series for the electron magnetic moment sums up to approximately

$\begin{displaymath} {1 \over 2} (g-2) = {1 \over 2} {\alpha \over \pi} { 1 \ov... ...ha \over \pi}\right)^2 \right)^2 } + \mbox{\lq\lq corrections''}. \end{displaymath}$

The story behind the conjecture.

Planar field theory

The method that I have used to develop the planar field theory is somewhat different from what is in most field theory textbooks; consulting my Field Theory textbook might make this derivation more accessible.

	Predrag Cvitanovic´ Planar perturbation expansion Phys. Lett. 99B, 49 (1981) [ SPIRES citations ]

	Predrag Cvitanovic´ The planar sector of field theories (with P.G. Lauwers and P.N. Scharbach), Nucl. Phys. B203, 385 (1982) [ SPIRES citations ]
	Though the formalism is rather different, essentially the same theory was rederived in 1994 by M.A. Douglas, D.J. Gross, R. Gopakumar, D.V. Voiculescu and others.

Perturbative QCD

	Predrag Cvitanovic´ Yang-Mills theory of the mass-shell Phys. Rev. Lett. 37, 1528 (1976) [ SPIRES citations ]
	Mass-shell amplitudes for both QED and QCD are defined via dimensional regularization, and shown to to be gauge invariant trough a cancellation between UL and IR singularities. Prior to this article, IR and UR were regularized by different methods which, when applied to QCD, violated gauge invariance.
	Predrag Cvitanovic´ Infra-red structure of Yang-Mills theories Phys. Lett. 65B, 272 (1976) [ SPIRES citations ]

	Predrag Cvitanovic´ Quantum Chromodynamics on the mass-shell Nucl. Phys. B130, 114 (1977) [ SPIRES citations ]

	Predrag Cvitanovic´, B. Lautrup and R.B. Pearson The number and weights of Feynman diagrams Phys. Rev. D18, 1939 (1978) [ SPIRES citations ]

	Predrag Cvitanovic´, P.G. Lauwers and P.N. Scharbach Gauge invariance structure of Quantum Chromodynamics Nucl. Phys. B186, 165 (1981) [ SPIRES citations ]

Phenomoenology, miscelaneous

	Predrag Cvitanovic´ Wide-angle behavior of a double-scattering diagram Phys. Rev. D10, 338 (1974)
	Predrag Cvitanovic´, R.J. Gonsales and D.E. Neville Color charge algebras in Adler's Chromodynamics Phys. Rev. D18, 3881 (1978)
	Predrag Cvitanovic´, P. Hoyer and K. Konishi Partons and branching Phys. Lett. 85B 413 (1979)
	Predrag Cvitanovic´ and R. Horsley Exact solutions of the Altarelli-Parisi equations Nucl. Phys. B173, 229 (1980)
	Predrag Cvitanovic´, P. Hoyer and K. Zalewski Parton evolution as a branching process Nucl. Phys. B176, 429 (1980)

Aug 7 2005 - Predrag.Cvitanovic[at]physics.gatech.edu

THIS PAGE IS OBSOLETE as of Dec 2 2005

Predrag Cvitanovic´ - quantum field theory publications

Predrag Cvitanovic´
- quantum field theory publications