String Rearrangement of Gauge Theories
Feynman diagram expressions in ordinary field theories can be written in a string-like manner. The methods and the advantages for doing so are briefly discussed.
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arXiv subjects
C. S. Lam
Publications and source records attributed to C. S. Lam.
String Organization of Field Theories: Duality and Gauge Invariance
String theories should reduce to ordinary four-dimensional field theories at low energies. Yet the formulation of the two are so different that such a connection, if it exists, is not immediately obvious. With the Schwinger proper-time representation, and the spinor helicity technique, it has been shown that field theories can indeed be written in a string-like manner, thus resulting in simplifications in practical calculations, and providing novel insights into gauge and gravitational theories. This paper continues the study of string organization of field theories by focusing on the question of local duality. It is shown that a single expression for the sum of many diagrams can indeed be written for QED, thereby simulating the duality property in strings. The relation between a single diagram and the dual sum is somewhat analogous to the relation between a old- fashioned perturbation diagram and a Feynman diagram. Dual expressions are particularly significant for gauge theories because they are gauge invariant while expressions for single diagrams are not.
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String-Organized Field Theory
A low energy string theory should reduce to an ordinary quantum field theory, but in reality the structures of the two are so different as to make the equivalence obscure. The string formalism is more symmetrical between the spacetime and the internal degrees of freedom, thus resulting in considerable simplification in practical calculations and novel insights in theoretical understandings. We review here how tree or multiloop field-theoretical diagrams can be organized in a string-like manner to take advantage of this computational and conceptual simplicity.
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From Multiloop Spinor Helicity Technique to String Reorganization
The success of the spinor helicity technique for tree processes is reviewed. To apply it to multiloop diagrams one is naturally led to the Schwinger proper-time representation, whose properties are discussed. This representation also serves as a useful link between field theories and string theories.
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Cluster Production in Quark-Hadron Phase Transition
The problem of cluster formation and growth in first-order quark-hadron phase transition in heavy-ion collisions is considered. Behaving as Brownian particles, the clusters carry out random walks and can encounter one another, leading to coalescence and breakup. A simulation of the process in cellular automaton suggests the possibility of a scaling distribution in the cluster sizes. The experimental determination of the cluster-size distribution is urged as a means to find a clear signature of phase transition.
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Spinor Helicity Technique and String Reorganization for Multiloop Diagrams
Methods to apply the spinor helicity technique and string reorganization to multiloop amplitudes using the Feynman- and Schwinger-parameter representations are reviewed and expanded.
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Multiloop String-Like Formulas for QED
Multiloop gauge-theory amplitudes written in the Feynman-parameter representation are poised to take advantage of two important developments of the last decade: the spinor-helicity technique and the superstring reorganization. The former has been considered in a previous article; the latter will be elaborated in this paper. We show here how to write multiloop string-like formulas in the Feynman-parameter representation for any process in QED, including those involving other non-electromagnetic interactions. The general connection between the Feynman-parameter approach and the superstring/first-quantized approach is discussed. In the special case of a one-loop multi-photon amplitude, these formulas reduce to the ones obtained by the superstring and the first quantized methods. The string-like formulas exhibits a simple gauge structure which makes the Ward-Takahashi identity apparent, and enables the integration-by-parts technique of Bern and Kosower to be applied, so that gauge-invariant parts can be extracted diagram-by-diagram with the seagull vertex neglected.
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Navigating Around the Algebraic Jungle of QCD: Efficient Evaluation of Loop Helicity Amplitudes
A method is developed whereby spinor helicity techniques can be used to simplify the calculation of loop amplitudes. This is achieved by using the Feynman-parameter representation where the offending off-shell loop momenta do not appear. Background Feynman gauge also helps to simplify the calculations. This method is applicable to any Feynman diagram with any number of loops as long as the external masses can be ignored, and it is at least as efficient as the string technique in the special circumstances when the latter can be used. In order to minimize the very considerable algebra encountered in non-abelian gauge theories, graphical methods are developed for most of the calculations. This enables the large number of terms encountered to be organized visually in the Feynman diagram without the necessity of having to write down any of them algebraically. A one-loop four-gluon amplitude in a particular helicity configuration is computed explicity to illustrate the method.
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Can a Lattice String Have a Vanishing Cosmological Constant?
We prove that a class of one-loop partition functions found by Dienes, giving rise to a vanishing cosmological constant to one-loop, cannot be realized by a consistent lattice string. The construction of non-supersymmetric string with a vanishing cosmological constant therefore remains as elusive as ever. We also discuss a new test that any one-loop partition function for a lattice string must satisfy.
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