Massive Yang-Mills Theory Research Articles

A gauge invariant action for (2 + 1)-dimensional topologically massive Yang-Mills theory

Under homotopically non-trivial gauge transformations, U n , with winding number n, the action, I, for topologically massive Yang-Mills theory changes by 2 πn: I → I + 2 πn. Equivalently, Gauss' law requires the physical states Ψ phs[ A] to change by a phase under time-independent gauge transformations: A U = U + AU + U + ∂U, Ψ phs[ A U ] = exp[− iα( A, U)] Ψ phs[ A]. By a unitary transformation, Ψ′[ A] = e iW[ A] Ψ[ A], we remove this phase (the Gauss law condition becomes the usual Ψ′ phs[ A U ] = Ψ′ phs[ A]) and find a new action, I′, which is manifestly gauge invariant, but is spatially non-local and not manifestly Lorentz invariant. W[ A] is proportional to the one-loop chiral fermion effective action, − i ln det( ∂ + A) in two dimensions. In the primed system, analysis of the wavefunctional Ψ′ phs[ A] near points in gauge function space where the two-dimensional chiral determinant, det( ∂ + A), vanishes leads to quantization of the mass parameter μ. We use our results to comment upon the connection between the (2 n + 1)-dimensional non-perturbative anomaly and anomalies in one higher and one lower dimension.

Classical solutions to topologically massive Yang-Mills theory

Classical solutions to (2 + 1)-dimensional Yang-Mills theory in the presence of the Chern-Simons invariant are considered. The SO(3)-invariant solutions to the Euclidean field equations are complex, whereas the equations in Minkowski space-time possess real SO(2, 1)-invariant solutions. The field equations for time independent axially symmetric vector potentials are derived and some solutions are obtained. The behavior of general Euclidean spacetime solutions is discussed. It is also shown that, because of the gauge dependence of the Chern-Simons invariant, the reduced field equations cannot be uniquely obtained from the reduced action. Applications of the results to the infrared structure of finite temperature QCD are discussed; in particular, it is argued that the Chern-Simons invariant cannot be consistently incorporated as a gauge-invariant magnetic mass term in a three-dimensional effective long distance theory at high temperatures.

Minimal structure of the one-loop divergencies of the massive Yang-Mills theory

The one-loop divergencies of a locally invariant nonpolynomial scalar theory (which is equivalent to the pure massive YM theory by a gauge transformation) are calculated for some simple gauges and general, compact gauge groups. It is shown that the structure of the corresponding counterterms can be absorbed down to only one nonrenormalizable structure by nonmultiplicative redefinition of the gauge fields plus the usual multiplicative renormalization. The origin of this divergence can be traced back to the scalar sector of the model.

N = 2, three-dimensional massless and topologically massive supersymmetric Yang-Mills theory

The actions for the N = 2 supersymmetric massless and topological massive three-dimensional non-abelian gauge theory are given. The basic potential is a real superscalar field defined on the natural complex superspace induced by the N = 2 extended supersymmetry in the real Grassmann sector.

On a relation between massive Yang-Mills theories and dual string models

The relations between mass terms in Yang-Mills theories, projective representations of the group of gauge transformations, boundary conditions on vector potentials and Schwinger terms in local charge algebra commutation relations are discussed. The commutation relations (with Schwinger terms) are similar to the current algebra commutation relations of the SU(N) extended dual string model.

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields B μν subject to the gauge transformation δB μν = ϖ μ ξ ν − ϖ ν ξ μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.

Hamiltonian of the massive Yang-Mills theory

The Schr\"odinger equation for a Yang-Mills massive field is written by using a physically useful formulation of the Kemmer-Duffin-Petiau equation due to Sakata and Taketani. It is shown that the linear terms correspond to the usual spin-1 equation. An interaction between the spin and the Yang-Mills field is obtained, even in the absence of the electromagnetic field.

The unitarity problem and the zero-mass limit for a model of massive Yang-Mills theory

The unitarity problem and the zero-mass limit for a model of massive Yang-Mills theory

Structure and renormalizability of massive Yang-Mills field theories

We observe that the theory of the Yang-Mills field with bare mass is included in the framework of spontaneously broken gauge theories, except that the Higgs field is realized nonlinearly. With the nonlinear symmetry associated with the Higgs field taken into account, the $\mathrm{SU}(N)$ massive Yang-Mills theory and the associated ${\mathrm{SU}(N)}_{L}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(N)}_{R}$ nonlinear $\ensuremath{\sigma}$ model are shown to be renormalizable and asymptotically free theories in two dimensions.

Renormalization of two-dimensional massive Yang-Mills theory and non-renormalizability of its four-dimensional version

The renormalizability of two-dimensional massive Yang-Mills theory is shown. In renormalizable gauges, the Yang-Mills field with a bare mass is described by a Lagrangian which is non-polynomial in some field variables, and correspondingly an infinite number of renormalization counter-terms are needed. The theory looks non-renormalizable by power-counting, but nevertheless with the aid of the Ward-Takahashi identities it turns out to be multiplicatively renormalizable. A brief discussion is given of the short-distance behavior of this massive theory. In contrast with the two-dimensional case, four-dimensional massive Yang-Mills theory is found to be non-renormalizable even at the one-loop level; it is shown by direct calculation that non-renormalizable divergences appear in some physical S-matrix elements.

Symmetry and exact dyon solutions for classical Yang–Mills field equations

We show that the generalized electromagnetic field tensor F̄μν and the magnetic and electric charges in non-Abelian gauge theories have little to do with the Higgs scalars and/or the dynamics of the Lagrangian. They are consequences of a symmetry in the theory. We present several exact static dyon solutions to the nonlinear classical field equations in both massless and massive Yang–Mills theories, which possess both electric and magnetic charges. The implications of F̄μν are also discussed.

Path integral quantization of field theories with second-class constraints

Faddeev's Hamiltonian path integral method for singular Lagrangians is generalized to the case when second-class constraints appear in the theory. The general formalism is then applied to several problems: quantization of the massive Yang-Mills field theory, light-cone quantization of the self-interacting scalar field theory, and quantization of a local field theory of magnetic monopoles.

The unitarity problem and the zero-mass limit for a model of massive yang-mills theory

In a previous paper we proposed a Lagrangian model for a massive Yang-Mills field. This model exhibits invariance under the Slavnov transformations proposed by Becchi, Rouet and Stora. This invariance implies the Slavnov-Taylor identities. Here we study the problem of unitarity and gauge invariance. For a massless field one can prove physical unitarity and gauge invariance at the formal level,i.e. by ignoring infra-red problems. Form≠0 theS-matrix is not unitary and gauge invariant, when restricted to the physical subspace. We show how these properties are restored in the limit of zero mass.

Quantization of the massive Yang-Mills field in arbitrary gauges

A general gauge formulation of the massive Yang-Mills theory is presented with emphasis on the fact that the massive Yang-Mills field is, like the massless counterpart, also a non-Abelian gauge field.

Rearrangement of Feynman rules and renormalizability of massive vector fields

A general procedure is presented for recasting a set of Feynman rules of vector field theories into another set by use of functional integration techniques. This procedure, when applied to the neutral vector meson coupled to a conserved current, allows us to recast conventional Feynman rules into the ones of arbitrary (even non-linear) gauges, and reveals the fact that this theory is manifestly renormalizable in any covariant (nonlinear) gauges. Likewise, the massive Yang-Mills theory can be converted into the one with a generalized Feynman gauge-like constraint, and it is then shown that the massive Yang-Mills field is not renormalizable.

Scattering of gauge bosons in sixth order and nonrenormalizability of massive Yang-Mills theories

We consider the unitarity relation in order ${g}^{6}$ for the canonically quantized massive Yang-Mills theory. The three-particle intermediate-state contribution to the absorptive part of ${T}_{22}=T({W}_{a}+{W}_{b}\ensuremath{\rightarrow}{W}_{c}+{W}_{d})$ is reexpressed in terms of the absorptive parts of Feynman diagrams constructed using only "soft" propagators $\frac{\ensuremath{-}{g}_{\ensuremath{\mu}\ensuremath{\nu}}}{({k}^{2}\ensuremath{-}{m}^{2})}$ and $\frac{1}{({k}^{2}\ensuremath{-}{m}^{2})}$. The vertices which appear in this decomposition of Abs ${T}_{22}$ are the usual ones which occur in order ${g}^{4}$, together with two new vertices of dimension five which couple a $W$ to three ghost particles; these vertices are similar to those found by Veltman in his study of radiative corrections to the $W$ propagator. It is shown that, as a consequence, the Feynman rules proposed recently by Hsu and Sudarshan for a quantized massive Yang-Mills theory do not yield a unitary $S$ matrix. Our result is in harmony with Boulware's formal argument that such theories are not renormalizable.

A compensating functional method in the massive Yang-Mills theory

In the massive and massless Yang-Mills theories the generating functional (the S-matrix) independence of the gauge parameter is provided on the mass shell without introducing an extra degree of freedom (gauge group integration).

Regge-Pole Content of Chiral and Gauge Field Theories

The high-energy limits of the 4-pion and 6-pion tree-approximation amplitudes in the nonlinear chiral-invariant Lagrangian and of the $\ensuremath{\rho}\ensuremath{-}\ensuremath{\rho}$ scattering amplitude in massive Yang-Mills theory are investigated in order to see whether Reggeization of elementary particles occurs. We find that the 4- and 6-pion amplitudes are dominated asymptotically by exchange of Regge poles with quantum numbers of the $\ensuremath{\rho}$ and ${A}_{1}$ mesons, respectively. These trajectories are regarded as "ancestors," because $\ensuremath{\rho}$ and ${A}_{1}$ particles are not present in the initial Lagrangian. The $\ensuremath{\rho}\ensuremath{-}\ensuremath{\rho}$ scattering amplitude is dominated by the exchange of quantum numbers of the $\ensuremath{\rho}$ meson, but there are two trajectories present, so that Reggeization does not occur. Nevertheless, in all amplitudes computed there is a striking regularity in the dominance of high-energy limits by the exchange of quantum numbers of the $\ensuremath{\rho}$ and ${A}_{1}$ mesons.

Divergences of Massive Yang-Mills Theories: Higher Groups

The analysis of our previous paper is extended to massive Yang-Mills theories based on semisimple groups other than SO(3). The multiplet of vector mesons may have arbitrary Yukawa couplings to fermions. We show that the naive degree of divergence of any Feynman amplitude is no worse than for the same theory without the meson self-couplings; the worst divergences are like ${(g\ensuremath{\Lambda})}^{2n}$.

Divergences of Massive Yang-Mills Theories

In an earlier paper, we suggested a model of weak interactions where the divergences of higher-order amplitudes are properly ordered. In this paper, we show that the introduction of Yang-Mills self-couplings preserves this ordering. We show, in particular, that the worst divergences of Feynman amplitudes are like ${({g}^{2}{\ensuremath{\Lambda}}^{2})}^{n}$, despite the fact that individual Feynman diagrams diverge like ${({g}^{2}{\ensuremath{\Lambda}}^{4})}^{n}$.