Chiral Boson Theory on the Light-Front

The {\it front form} framework for describing the quantized theory of chiral boson is discussed. It avoids the conflict with the requirement of the principle of microcausality as is found in the conventional equal- time treatment. The discussion of the Floreanini-Jackiw model and its modified version for describing the chiral boson becomes very transparent on the light-front.Comment: 9 pages, plain Late

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

Some basic topics in the light-front (LF) quantization of relativistic field theory are reviewed. It is argued that the LF quantization is equally appropriate as the conventional one and that they lead, assuming the micro- causality 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. In the context of the Dyson-Wick pertur- bation 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 $x^{pm}=0$ constitute characteristic surfaces of the hyper- bolic partial differential equation is found irrelevant in the quantized theory.Comment: 50 pages, plain Latex, Invited article for "Saga of Field Theory: From Points to Strings", Eds., A.N. Mitra et al., Indian National Science Academy-INSA, Indi

Light-Front QCD in Light-Cone Gauge

The light-front (LF) quantization of QCD in light-cone (l.c.) gauge is discussed. The Dirac method is employed to construct the LF Hamiltonian and theory quantized canonically. The Dyson-Wick perturbation theory expansion based on LF-time ordering is constructed. The framework incorporates in it simultaneously the Lorentz gauge condition as an operator equation as well. The propagator of the dynamical $\psi_+$ part of the free fermionic propagator is shown to be causal while the gauge field propagator is found to be transverse. The interaction Hamiltonian is re-expressed in the form closely resembling the one in covariant theory, except for additional instantaneous interactions, which can be treated systematically. Some explicit computations in QCD are given.Comment: Presented at VII Hadron Physics 2000, Caraguatatuba, Sao Paulo, Brazil, 10-15 April 200

Light-front Quantized Chiral Schwinger Model and its Vacuum Structure

The bosonized Chiral Schwinger model (CSM) is quantized on the light-front (LF). The physical Hilbert space of CSM is obtained directly once the constraints on the LF phase space are eliminated. The discussion of the degenerate vacua and the absence in the CSM of the $\theta$-vacua, as found in the Schwinger model (SM), becomes straightforward. The differences in the structures of the the mass excitations and the vacua in these gauge theories are displayed transparently. The procedure followed is the one used successfully in the previous works for describing the spontaneous symmetry breaking (SSB) and the SM on the LF. The physical contents following from the LF quantized theory agree with those known in the conventional treatment. The LF hyperplane is argued to be equally appropriate as the conventional equal-time one for the canonical quantization. Some comments on the irrelevance, in quantized field theory, of the fact that the hyperplanes $x^{\pm}=0$ constitute characteristic surfaces of hyperbolic partial differential equation are also made.Comment: 12 pages, plain Late