acta physica slovaca

Acta Physica Slovaca 57, No.3, 407-564 (2007) (157 pages)

Light front field theory: An advanced primer

Ľubomír Martinovič

   Institute of Physics, Slovak Academy of Sciences
   Dúbravská cesta 9, 845 11 Bratislava, Slovakia

Full text: ::pdf :: (received 06 June 2007, accepted 20 June 2007)

Abstract: We 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.

PACS: 11.10.Ef, 11.15.Tf, 11.25.DB
Keywords: Light front field theory, Discretized light cone quantization, Relaticistic two-dimensional models, Spontaneuous symmetry breaking, Quantum solitons, Hamitlonian methods, Light front perturbartion theories

About authors:
RNDr. Ľ. Martinovič, CSc. graduated in general and theoretical physics at the Comenius University in Bratislava (1980). He got PhD. degree at Institute of Physics, Slovak Academy of Sciences in 1986 with the thesis entitled Analytic model of the electromagnetic structure of the pion and its application to other physical problems in the els of theory of elementary particles. Since 1987 he was a postdoctoral researcher in Joint Institute for Nuclear Research in Dubna in USSR and got permanent position at the Institute of Physics, Slovak Academy of Sciences in Bratislava in 1991. As a postoctoral fellow, he collaborated at the Max-Planck-Institut fur Kernphysik in Heidelberg (Germany) for 15 months in group of Prof. H.-C. Pauli, work on discretized light cone quantization with a scholarship of the Max-Planck-Gesellschaft, experienced long-term visits at the Iowa State University, Ames in Iowa in USA (1996 2006) as well as collaborative visits of the Laboratoire de Physique Theorique et Astroparticules, Montpellier University in France under collaboration with Prof. P. Grange. He published 34 publications and worked in the phenomenology of electromagnetic structure of hadrons and in the eld of QCD sum rules. Since 1990, he has been studying several aspects of the light front eld theory, mainly using the quantization in a nite volume (DLCQ) and focusing on nonperturbative issues such as vacuum structure, spontaneous symmetry breaking, quantum solitons and structure of low-dimensional models. Since 1992, he delivered talks at several light-front workshops and conferences (Heidelberg, Telluride, Zurich-Villigen, Regensburg, Schladming, Zakopane, Ames, Lutsen, Adelaide, Trento, Los Alamos, Durham, Amsterdam, Cairns, Minneapolis) and at a number of universities and institutes abroad (Iowa State University (Ames), ICTP Trieste, Ohio State U. (Columbus), U. of Connecticut (Storrs), Charles University Prague, SLAC Stanford, University of Florida (Gainsville), Weizmann Institute (Rehovot), Bern University, Montpellier U., U. of Kentucky (Lexington), North Carolina State U. (Rayleigh), Nagoya U., KEK Tsukuba, Hiroshima U., CERN Geneva.) He supervised one PhD student and three diploma students. He is a member of the organizing committee of a few international conferences Hadron Structure (1996, 2000) and an editor of the proceedings of this conference in 1991 and 1996. Delivered a series of invited lectures at the International School on Light-Front Quantization at the Iowa State University, Ames, Iowa, April 1996 He is also a memeber of the Slovak Physical Society, has a fellowship of the Max-Planck Gesellschaft for 15 months, MPIK Heidelberg, 1992-1993 and NATO fellowship by French NATO national scientic committee for 10 months, Montpellier University, starting summer 2004. Dr. Martinovič is an investigator of National Science Foundation grant with Prof. J. P. Vary, Iowa State University, Ames, Iowa for 3 years and of 3 national VEGA grants as well as the grant of APVV (Slovak Research and Development Agency).

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