Spontaneous symmetry breaking in discretized light-cone field theory

Robertson, David G.

doi:10.1103/physrevd.47.2549

Cited by 65 publications

(67 citation statements)

References 16 publications

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“…There are zero modes, modes with zero longitudinal momentum. In DLCQ these are not dynamical but instead constrained by the spatial average of the Euler-Lagrange field equation [55,68,69]. These zero modes are usually either neglected or excluded by the choice of antiperiodic boundary conditions.…”

Section: Discretized Light-cone Quantizationmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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We examine the current state-of-the-art in nonperturbative calculations done with Hamiltonians constructed in light-front quantization of various field theories. The language of light-front quantization is introduced, and important (numerical) techniques, such as Pauli-Villars regularization, discrete light-cone quantization, basis light-front quantization, the light-front coupled-cluster method, the renormalization group procedure for effective particles, sector-dependent renormalization, and the Lanczos diagonalization method, are surveyed. Specific applications are discussed for quenched scalar Yukawa theory, φ 4 theory, ordinary Yukawa theory, supersymmetric Yang-Mills theory, quantum electrodynamics, and quantum chromodynamics. The content should serve as an introduction to these methods for anyone interested in doing such calculations and as a rallying point for those who wish to solve quantum chromodynamics in terms of wave functions rather than random samplings of Euclidean field configurations.

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Section: Discretized Light-cone Quantizationmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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“…It is generally believed that these modes carry the information on the non-trivial vacuum aspects. This has been shown in particular for φ 4 -theory in d = 1 + 1, where the ZMs are responsible for spontaneous symmetry breaking [18,21,23,24,25]. This article elaborates on the quoted works on φ This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

The vacuum structure of light-frontφ 1+1 4 -theory

Heinzl

Zellermann

Stern

et al. 1996

Z. Phys. C - Particles and Fields

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We discuss the vacuum structure of φ 4 -theory in 1+1 dimensions quantised on the light-front x + = 0. To this end, one has to solve a non-linear, operator-valued constraint equation. It expresses that mode of the field operator having longitudinal light-front momentum equal to zero, as a function of all the other modes in the theory. We analyse whether this zero mode can lead to a non-vanishing vacuum expectation value of the field φ and thus to spontaneous symmetry breaking. In perturbation theory, we get no symmetry breaking. If we solve the constraint, however, non-perturbatively, within a mean-field type Fock ansatz, the situation changes: while the vacuum state itself remains trivial, we find a non-vanishing vacuum expectation value above a critical coupling. Exactly the same result is obtained within a light-front Tamm-Dancoff approximation, if the renormalisation is done in the correct way.

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“…Studies of model field theories have shown that certain aspects of vacuum physics can in fact be reproduced by a careful treatment of the field zero modes. For example, solutions of the zero mode constraint equation in φ 4 1+1 [3] exhibit spontaneous symmetry breaking [4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

(1+1)-dimensional Yang-Mills theory coupled to adjoint fermions on the light front

Pinsky¹

1997

Phys. Rev. D

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We consider SU (2) Yang-Mills theory in 1+1 dimensions coupled to massless adjoint fermions. With all fields in the adjoint representation the gauge group is actually SU (2)/Z 2 , which possesses nontrivial topology. In particular, there are two distinct topological sectors and the physical vacuum state has a structure analogous to a θ vacuum. We show how this feature is realized in light-front quantization, with periodicity conditions in x ± used to regulate the infrared and treating the gauge field zero mode as a dynamical quantity. We find expressions for the degenerate vacuum states and construct the analog of the θ vacuum. We then calculate the bilinear condensate in the model. We argue that the condensate does not affect the spectrum of the theory, although it is related to the string tension that characterizes the potential between fundamental test charges when the dynamical fermions are given a mass. We also argue that this result is fundamentally different from calculations that use periodicity conditions in x 1 as an infrared regulator.

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Spontaneous symmetry breaking in discretized light-cone field theory

Cited by 65 publications

References 16 publications

Nonperturbative light-front Hamiltonian methods

Nonperturbative light-front Hamiltonian methods

The vacuum structure of light-frontφ 1+1 4 -theory

(1+1)-dimensional Yang-Mills theory coupled to adjoint fermions on the light front

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