Nonperturbative Analysis of Field Theories Quantized on the Light Cone
Quantum field theories are used to describe interactions between fundamental particles. In determining the properties of the bound states that these particles can form, the use of light-cone coordinates, with t+z/c playing the role of time, can be advantageous. The state of the system can then be expanded in a basis of momentum eigenstates, with wave functions as the coefficients in the expansion. The wave functions satisfy a coupled system of integral equations that almost always require numerical techniques for their solution. Within the integrals there are infinities that must be regulated in some way in order to properly define the given theory.
In this project, two methods are considered: Pauli–Villars regularization, which requires the introduction of unphysical massive particles, and supersymmetry. These methods have been applied to various field theories, in particular Yukawa theory, quantum electrodynamics (QED), super Yang-Mills (SYM) theory, and phi4 theory, and continue to be explored, with the ultimate goal of applying them to quantum chromodynamics (QCD), the theory of the strong interactions that determine the properties of mesons and baryons. Recent progress has been in the development of the light-front coupled-cluster method, which applies the mathematics of the nonrelativistic coupled-cluster method to the light-front Hamiltonian problem in a way that avoids truncations in particle number. This allows calculations to avoid difficulties with uncanceled divergences in the integral equations. Applications to QED and phi4 theory are underway. For QED, a new quantization has been constructed to permit nonperturbative calculations in an arbitrary covariant gauge, which has already yielded a direct check on the gauge independence of a calculation of the electron's anomalous magnetic moment. In phi4 theory, zero-momentum modes have been incorporated in the LFCC method to represent symmetry-breaking effects. Future work will also include convergence of light-front holographic models with the LFCC method.
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