Structure and renormalizability of massive Yang-Mills field theories

Bardeen, William A.; Shizuya, K.

doi:10.1103/physrevd.18.1969

Cited by 35 publications

(45 citation statements)

References 52 publications

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“…of the Higgs phase alone without the residual Higgs field, so that also its quantum fluctuations would be absent. Instead these fluctuations are the main left quantum effect in the limit m H → ∞, which is known to produce [24], in the non-Abelian case, a gauge theory coupled to a nonlinear σ-model, equivalent [22] to a massive Yang-Mills theory. Indeed, in absence of fermions, the Lagrangian density (1) can be rewritten in terms…”

Section: The Final Canonical Basis Of Dirac's Observables Ismentioning

confidence: 99%

Dirac's Observables for the Higgs Model II: The Non-Abelian SU(2) Case

Lusanna

Valtancoli

1997

Int. J. Mod. Phys. A

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We search a canonical basis of Dirac's observables for the classical nonAbelian Higgs model with fermions in the case of a trivial SU(2) principal bundle with a complex doublet of Higgs fields and with the fermions in a given representation of SU(2). Since each one of the three Gauss law first class constraints can be solved either in the corresponding longitudinal electric field or in the corresponding Higgs momentum, we get a priori eight disjoint phases of solutions of the model. The only two phases with SU(2) covariance are 1 the SU(2) phase with massless SU(2) fields and the Higgs phase with massive SU(2) fields. The Dirac observables and the reduced physical (local) Hamiltonian and (nonlocal) Lagrangian of the Higgs phase are evaluated: the main result is the nonanalyticity in the SU(2) coupling constant, or equivalently in the sum of the residual Higgs field and of the mass of the SU(2) fields. Some comments on the function spaces needed for the gauge fields are made.

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Section: The Final Canonical Basis Of Dirac's Observables Ismentioning

confidence: 99%

Dirac's Observables for the Higgs Model II: The Non-Abelian SU(2) Case

Lusanna

Valtancoli

1997

Int. J. Mod. Phys. A

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“…By this way of constructing spontaneous symmetry breaking one can avoid the introduction of physical Higgs-bosons: there are as many scalars as massive gauge bosons. The simplest model of this type for electroweak interaction is the SU(2) L × U(1) Ygauged nonlinear σ-model [5], which is just the limit of the SM for infinite Higgs mass. This model contains additional local ("hidden") symmetries [9], which can be made apparent by increasing the number of unphysical scalar degrees of free-dom and introducing the gauge bosons connected to the hidden symmetry groups [3,4].…”

Section: The Bess Modelmentioning

confidence: 99%

“…In difference to renormalizable models, at each loop-order new couplings are induced, which do not have the tree-level structure and cannot be removed by ordinary counterterms (that have the structure of the original Lagrangian). These quantum induced interactions have necessarily to be taken into account if the model is taken seriously [5]. For gauge-boson selfinteractions they have been completely calculated to one-loop level [6].…”

Section: Introductionmentioning

confidence: 99%

Bounds on BESS model parameters from vector-boson production ine + e ? collisions

Bonisch¹,

Grosse-Knetter

Kögerler

1993

Z. Phys. C - Particles and Fields

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The BESS model is the Higgs-less alternative to the standard model of electroweak interaction, based on nonlinearly realized spontaneous symmetry breaking. Since it is nonrenormalizable, new couplings (not existing in the SM) are induced at each loop order. On the basis of the one loop induced vector-boson self-couplings we study the two-and three-vectorboson-production processes in e + e − collisions at √ s = 500GeV, the expected energy of the next e + e − linear collider (NLC). Assuming that NLC results will agree with the SM predictions within given accuracy we identify the bounds for the free parameters of the BESS model.

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“…This model is renormalizable, in contrast to the same model in higher dimensions [1]. Renormalizability is proven by noticing that the Massive Yang-Mills action is equivalent to a gauged principal chiral sigma model (PCSM), which is asymptotically free.…”

Section: Introductionmentioning

confidence: 99%

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

Cubero

2015

Proceedings of the 32nd International Symposium on Lattice Field Theory — PoS(LATTICE2014)

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Massive Yang-Mills theory is known to be renormalizable in 1+1 dimensions. The gluon mass is introduced by coupling the gauge field to an SU(N) principal chiral nonlinear sigma model. The proof of renormalizability relies on the asymptotic freedom of the sigma model. However, renormalization forces the gluon mass to infinity. The continuum theory is in a confined phase rather than a Higgs phase. The physical excitations of the system are hadron-like bound states of sigma model particles. We calculate the massive spectrum of meson-like bound states analytically, using the exact S-matrix of the sigma model. The baryon-like spectrum can be found in principle by solving a quantum mechanical N-body problem. We remark on the evidence for the confined phase found for SU(2) in recent lattice simulations by Gongyo and Zwanziger. Their simulations show evidence for a Higgs-like phase which seems to disappear with increasing volume, finding agreement with our analysis in the continuum.

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Structure and renormalizability of massive Yang-Mills field theories

Cited by 35 publications

References 52 publications

Dirac's Observables for the Higgs Model II: The Non-Abelian SU(2) Case

Dirac's Observables for the Higgs Model II: The Non-Abelian SU(2) Case

Bounds on BESS model parameters from vector-boson production ine + e ? collisions

The Hadronic Spectrum and Confined Phase in (1+1)-Dimensional Massive Yang-Mills Theory

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