Perspectives of Light - Front Quantized Field Theory : Some New Results

A review of some basic topics in the light-front (LF) quantization of relativistic field theory is made. It is argued that the LF quantization is equally appropriate as the conventional one and that they lead, assuming the microcausality principle, to the same physical content. This is confirmed in the studies on the LF of the spontaneous symmetry breaking (SSB), of the degenerate vacua in Schwinger model (SM) and Chiral SM (CSM), of the chiral boson theory, and of the QCD in covariant gauges among others. The discussion on the LF is more economical and more transparent than that found in the conventional equal-time quantized theory. The removal of the constraints on the LF phase space by following the Dirac method, in fact, results in a substantially reduced number of independent dynamical variables. Consequently, the descriptions of the physical Hilbert space and the vacuum structure, for example, become more tractable. In the context of the Dyson-Wick perturbation theory the relevant popagators in the front form theory are causal. The Wick rotation can then be performed to employ the Euclidean space integrals in momentum space. The lack of manifest covariance becomes tractable, and still more so if we employ, as discussed in the text, the Fourier transform of the fermionic field based on a special construction of the LF spinor. The fact that the hyperplanes x± = 0 constitute characteristic surfaces of the hyperbolic partial differential equation is found irrelevant in the quantized theory; it seems sufficient to quantize the theory on one of the charateristic hyperplanes. Research partially supported by the Department of Energy under contract DE-AC03-76SF00515. Invited article for: Saga of Field Theory: From Points to Strings, Ed., A.N. Mitra, Indian National Science Academy-INSA, New Delhi, India. E-mail: (1) [email protected]; (2) [email protected]; (3) [email protected]. On leave of absence from Instituto de F́ısica, UERJUniversidade do Estado de Rio de Janeiro, RJ, Brasil.