Critical coupling for two-dimensional ϕ4 theory in discretized light-cone quantization

James P Vary,Mamoon Sharaf,Dipankar Chakrabarti,Avaroth Harindranath,Shreeram Jawadekar,Mengyao Huang

doi:10.1103/physrevd.105.016020

James P Vary, Mamoon Sharaf + Show 4 more

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https://doi.org/10.1103/physrevd.105.016020

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Abstract

We solve for the critical coupling in the symmetric phase of two-dimensional ${\ensuremath{\phi}}^{4}$ field theory using discretized light-cone quantization. We adopt periodic boundary conditions, neglect the zero mode, and obtain a critical coupling consistent with the critical coupling reported using conformal truncation in light-front quantization. We find a 17% difference from the critical coupling reported with light-front quantization in a symmetric polynomial basis.

Highlights

It is well known that most of our intuition about spectra and wave functions in quantum mechanics come from solving Hamiltonians and a variety of methods exist for this purpose
Center (NERSC) [34], with the many fermion dynamics (MFD) code adapted to bosons [17,18,19,35]
The main result of the present work is that Discretized light-cone quantization (DLCQ) is capable of producing the critical coupling for the vanishing mass gap in two-dimensional φ4 theory, with accuracy competitive with other methods

Summary

Introduction

It is well known that most of our intuition about spectra and wave functions in quantum mechanics come from solving Hamiltonians and a variety of methods exist for this purpose. One would like to make use of the intuition developed and experience gained in solving nonrelativistic systems to devise methods to solve systems governed by relativistic quantum field theories. Hamiltonian methods were rarely developed for this purpose. There are major stumbling blocks to this path caused by the presence of infinitely many degrees of freedom and the mandatory need for renormalization. Noteworthy is the severe divergence caused by vacuum processes which are addressed analytically in the perturbative framework. One has to learn how to handle them or at least how to side step them in the nonperturbative Hamiltonian framework

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Conclusion