Quenched QED in the chiral limit. [QED (quantum electrodynamics)]

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1993

OSTI ID:7073088

Vandermark, S W

The main goal in this project has been to understand, through analytical methods, whether there could be a continuum limit for QED. This possibility is motivated by recent lattice simulations on quenched QED which apparently exhibit a chiral phase transition at strong coupling in the chiral limit. Another goal is to develop a novel perturbation expansion which may also be usefully applied to other theories. The author begins with the general expression for the chiral order parameter, ([bar [psi]][psi]), in the quenched limit of euclidean QED, where the number of fermion flavors goes to zero, using the path integral formulation. A cutoff scale, [Lambda], is introduced into the photon propagator and a new expansion, the [open quotes]wormhole expansion,[close quotes] in powers of [Lambda][sup 2]/m[sup 2], where m is the fermion mass, is derived. Graphical rules for the wormhole expansion of [l angle][bar [psi]][psi][r angle] are described in detail. The author then devises algorithms to generate recursively the graphs at each successive order and to perform the loop momentum integral and [gamma] matrix trace involved in the evaluation of each graph. These algorithms are implemented in Mathmatica and the [l angle][bar [psi]][psi][r angle] expansion is carried out to order ([Lambda][sup 2]/[sub m][sup 2])[sup 6]. The author employs pade techniques to extrapolate this expansion to the chiral limit ([Lambda][sup 2]/m[sup 2] [yields] [infinity]) and looks for a singularity at strong coupling to signal a phase transition. Indications have been found that there may be a phase transition but apparently there are not enough terms in the wormhole expansion to attain stability in our pade analysis. The author therefore cannot conclude that there is a chiral phase transition, although the results are consistent with the existence of one.

• Research Organization: Princeton Univ., NJ (United States)
• OSTI ID: 7073088
• Country of Publication: United States
• Language: English

Related Subjects

662220* -- Quantum Electrodynamics-- (1992-)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
CHIRAL SYMMETRY
ELECTRODYNAMICS
FIELD THEORIES
PERTURBATION THEORY
PHASE TRANSFORMATIONS
QUANTUM ELECTRODYNAMICS
QUANTUM FIELD THEORY
SERIES EXPANSION
SINGULARITY
SYMMETRY