Variational calculation of the spectrum of two-dimensionalφ4theory in light-front field theory

Light front field theory: An advanced PrimerWe present an elementary introduction to quantum field theory formulated in terms of Dirac's light front variables. In addition to general principles and methods, a few more specific topics and approaches based on the author's work will be discussed. Most of the discussion deals with massive two-dimensional models formulated in a finite spatial volume starting with a detailed comparison between quantization of massive free fields in the usual field theory and the light front (LF) quantization. We discuss basic properties such as relativistic invariance and causality. After the LF treatment of the soluble Federbush model, a LF approach to spontaneous symmetry breaking is explained and a simple gauge theory - the massive Schwinger model in various gauges is studied. A LF version of bosonization and the massive Thirring model are also discussed. A special chapter is devoted to the method of discretized light cone quantization and its application to calculations of the properties of quantum solitons. The problem of LF zero modes is illustrated with the example of the two-dimensional Yukawa model. Hamiltonian perturbation theory in the LF formulation is derived and applied to a few simple processes to demonstrate its advantages. As a byproduct, it is shown that the LF theory cannot be obtained as a "light-like" limit of the usual field theory quantized on an initial space-like surface. A simple LF formulation of the Higgs mechanism is then given. Since our intention was to provide a treatment of the light front quantization accessible to postgradual students, an effort was made to discuss most of the topics pedagogically and a number of technical details and derivations are contained in the appendices.

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Deuteron binding energies and form factors from light-front Hamiltonian field theory

Physical Review C ◽

10.1103/physrevc.66.034002 ◽

2002 ◽

Vol 66 (3) ◽

Cited By ~ 12

Author(s):

Jason R. Cooke ◽

Gerald A. Miller

Keyword(s):

Field Theory ◽

Form Factors ◽

Binding Energies ◽

Light Front

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Light-front nuclear physics: Mean field theory for finite nuclei

Physical Review C ◽

10.1103/physrevc.60.055211 ◽

1999 ◽

Vol 60 (5) ◽

Cited By ~ 11

Author(s):

P. G. Blunden ◽

M. Burkardt ◽

G. A. Miller

Keyword(s):

Field Theory ◽

Nuclear Physics ◽

Mean Field Theory ◽

Mean Field ◽

Light Front ◽

Finite Nuclei

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Variational Solution of the Gross–Neveu Model: Finite N and Renormalization

International Journal of Modern Physics A ◽

10.1142/s0217751x97001730 ◽

1997 ◽

Vol 12 (19) ◽

pp. 3307-3334 ◽

Cited By ~ 32

Author(s):

C. Arvanitis ◽

F. Geniet ◽

M. Iacomi ◽

J.-L. Kneur ◽

A. Neveu

Keyword(s):

Field Theory ◽

Renormalization Group ◽

General Framework ◽

Free Field ◽

Variational Calculation ◽

Final Point ◽

Variational Calculations ◽

Perturbative Renormalization ◽

Good Agreement ◽

Gross Neveu Model

We show how to perform systematically improvable variational calculations in the O(2N) Gross–Neveu model for generic N, in such a way that all infinities usually plaguing such calculations are accounted for in a way compatible with the perturbative renormalization group. The final point is a general framework for the calculation of nonperturbative quantities like condensates, masses, etc., in an asymptotically free field theory. For the Gross–Neveu model, the numerical results obtained from a "two-loop" variational calculation are in a very good agreement with exact quantities down to low values of N.

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