Generalized BRST Quantization and Massive Vector Fields

Marnelius, Robert; Sogami, Ikuo S.

doi:10.1142/s0217751x98001530

Cited by 7 publications

(11 citation statements)

References 19 publications

(55 reference statements)

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“…The gluon mass and gauge-fixing term is constructed from a gauge-invariant piece and a gauge-fixing piece, each with couplings to an auxiliary set of PV scalar fields φ ak , in a non-Abelian extension of a Stueckelberg mechanism [36,111,112] …”

Section: Non-abelian Gauge Theoriesmentioning

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: Non-abelian Gauge Theoriesmentioning

confidence: 99%

Nonperturbative light-front Hamiltonian methods

Hiller

2016

Progress in Particle and Nuclear Physics

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“…where the gluon mass µ k is explicit and the scalar is given a mass µ k / √ ζ and inherits the metric r k . This is a non-Abelian extension of a Stueckelberg mechanism [10][11][12].…”

Section: A Pauli-villars Regulated Lagrangianmentioning

confidence: 99%

“…The Higgs mechanism is, of course, one possible approach, but investigations of this invariably found only null combinations of gluon fields to be massless, rather than a massless physical gluon. There is, however, another mechanism for generating masses [10][11][12], by coupling the PV gluons and PV quarks to a PV scalar, with all removed from the spectrum in the infinite-mass limit. The mixing of currents can be overcome by extension of the gauge transformation to include mixing PV fields; the original gauge transformation is obtained when the fields are removed from the spectrum.…”

Section: Introductionmentioning

confidence: 99%

Pauli–Villars Regularization of Non-Abelian Gauge Theories

Hiller

2016

Few-Body Syst

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As an extension of earlier work on QED, we construct a BRST-invariant Lagrangian for SU(N) Yang-Mills theory with fundamental matter, regulated by the inclusion of massive Pauli-Villars (PV) gluons and PV quarks. The underlying gauge symmetry for massless PV gluons is generalized to accommodate the PV-index-changing currents that are required by the regularization. Auxiliary adjoint scalars are used, in a mechanism due to Stueckelberg, to attribute mass to the PV gluons and the PV quarks. The addition of Faddeev-Popov ghosts then establishes a residual BRST symmetry. Although there are drawbacks to the approach, in particular the computational load of a large number of PV fields and a nonlocal interaction of the ghost fields, this formulation could provide a foundation for renormalizable nonperturbative solutions of light-front QCD in an arbitrary covariant gauge.a Based on an invited talk presented at the Lightcone 2015 workshop, Frascati, Italy, September 21-25, 2015.

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“…We have resolved these difficulties. The giving of mass to the PV gluons and the lifting of the PV-quark masses is accomplished by a non-Abelian generalization of Stueckelberg's mechanism [17,18], which associates an auxiliary real scalar with each gluon field, simultaneously giving mass to the gluon and the scalar while also fixing the gauge. The breaking of gauge invariance by the field-mixing interactions is eliminated by generalizing the definition of the gauge transformation to also include field mixing; the original gauge transformation is recovered in the limit that the PV fields are removed, by taking their masses to infinity.…”

mentioning

confidence: 99%

“…To give mass to the PV gluons, we use a non-Abelian extension of the Stueckelberg mechanism [17,18]. Real adjoint scalar fields φ ak are introduced with a gauge transformation of…”

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confidence: 99%

BRST-invariant Pauli-Villars regularization of QCD

Chabysheva¹,

Hiller²

2015

Preprint

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We extend the QCD Lagrangian to include Pauli-Villars (PV) gluons, quarks, and ghosts in such a way as to retain BRST invariance in an arbitrary covariant gauge. The extended Lagrangian can provide a starting point for nonperturbative calculations in QCD, particularly with light-front techniques, and the methods used to construct it may be useful for perturbative calculations in theories where dimensional regularization is not viable. The regularization is arranged by having all interaction terms in the Lagrangian be couplings between null fields, specific combinations of positive and negative-metric PV fields. The construction is done in steps, beginning with a gaugeinvariant Lagrangian with massless PV gluons and degenerate-mass PV quarks. Auxiliary scalars are introduced to give mass to the PV gluons, and break the mass degeneracy of the PV quarks, following a method due to Stueckelberg. Gauge fixing terms for the gluon fields are a part of this construction. The ghost terms are then obtained and shown to provide the BRST invariance. A lack of dependence on the gauge parameter can be checked by the calculation of physical quantities for a range of values of the parameter.

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Generalized BRST Quantization and Massive Vector Fields

Cited by 7 publications

References 19 publications

Nonperturbative light-front Hamiltonian methods

Nonperturbative light-front Hamiltonian methods

Pauli–Villars Regularization of Non-Abelian Gauge Theories

BRST-invariant Pauli-Villars regularization of QCD

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