Construction of consistent interactions in higher derivative Yang-Mills gauge theory with matter fields
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We show the consistent interactions in the generalized electrodynamics gauge theory with higher derivative matter fields by means of the order reduction method. We deduce the BRST deformations in the reduced Lagrangian and using the equations of motion of the auxiliary fields in the antighost number zero part in the resulting deformed action, we are able to obtain the consistent coupling terms added into the original Lagrangian density which are compatible with the deformation master equations. We emphasize that the order of deformations is truncated at four and the corresponding higher-order deformations are equal to zero precisely. Moreover, the local Abelian gauge symmetry turns out to be non-Abelian after the deformation procedure.Keywords:
BRST quantization
We study the general structure of field theories with the unfree gauge symmetry where the gauge parameters are restricted by differential equations. The examples of unfree gauge symmetries include volume preserving diffeomorphisms in the unimodular gravity and various higher spin field theories with transverse gauge symmetries. All the known examples of the models with unfree gauge symmetry share one common feature. They admit local quantities which vanish on shell, though they are not linear combinations of Lagrangian equations and their derivatives. We term these quantities as mass shell completion functions. In the case of usual gauge symmetry with unconstrained gauge parameters, the irreducible gauge algebra involves the two basic constituents: the action functional and gauge symmetry generators. For the case of unfree gauge symmetry, we identify two more basic constituents: operators of gauge parameter constraints and completion functions. These two extra constituents are involved in the algebra of unfree gauge symmetry on equal footing with action and gauge symmetry generators. Proceeding from the algebra, we adjust the Faddeev-Popov (FP) path integral quantization scheme to the case of unfree gauge symmetry. The modified FP action involves the operators of the constraints imposed on the gauge parameters, while the corresponding BRST transformation involves the completion functions. The BRST symmetry ensures gauge independence of the path integral. We provide two examples which admit the alternative unconstrained parametrization of gauge symmetry and demonstrate that they lead to the equivalent FP path integral.
BRST quantization
Quantum gauge theory
Gauge covariant derivative
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We show that any BRST invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the antifield formalism, then the effective action possesses a local background gauge invariance. The presence of antifields (BRST sources) is necessary. As an example we analyze chiral $W_3$ gravity.
BRST quantization
Quantum gauge theory
Mixed anomaly
Background field method
Gauge covariant derivative
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We provide a gauge covariant formalism of the canonically quantized theory of spin-3/2 Rarita-Schwinger gauge field. The theory admits a quantum gauge transformation by which we can shift the gauge fixing parameter. The quantum gauge transformation does not change the BRST charge. Thus, the physical Hilbert space is trivially independent of the gauge fixing parameter.
BRST quantization
Gauge covariant derivative
Quantum gauge theory
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Abstract Chapter 11 is the first of four chapters that discuss various issues connected with the Standard Model of fundamental interactions at the microscopic scale. It discusses the important notion of gauge invariance, first Abelian and then non–Abelian, the basic geometric structure that generates interactions. It relates it to the concept of parallel transport. Due to gauge invariance, not all components of the gauge field are dynamical and gauge fixing is required (with the problem of Gribov copies in non–Abelian theories). The quantization of non–Abelian gauge theories is briefly discussed, with the introduction of Faddeev–Popov ghost fields and the appearance of BRST symmetry.
BRST quantization
Quantum gauge theory
Faddeev–Popov ghost
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We propose a generalisation of the Faddeev-Popov trick for Yang-Mills fields in the Landau gauge. The gauge-fixing is achieved as a genuine change of variables. In particular the Jacobian that appears is the modulus of the standard Faddeev-Popov determinant. We give a path integral representation of this in terms of auxiliary bosonic and Grassman fields extended beyond the usual set for standard Landau gauge BRST. The gauge-fixing Lagrangian density appearing in this context is local and enjoys a new extended BRST and anti-BRST symmetry though the gauge-fixing Lagrangian density in this case is not BRST exact.
BRST quantization
Quantum gauge theory
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An inhomogeneous gauge transformation law for non-Abelian two-forms in B ^ F type theories is proposed and corresponding invariant actions are discussed. The auxiliary one-form, required for maintaining vector gauge symmetry in some of these theories, transforms like a gauge field, and hence cannot be set to zero by a gauge choice. It can be set equal to the usual gauge field by a gauge choice, leading to gauge equivalences between different types of theories, those with the auxiliary field and those without. A new type of symmetry also appears in some of these theories, one which depends on local functions but cannot be generated by local constraints. The corresponding conserved currents and BRST charges are parametrized by the space of flat connections.
BRST quantization
Quantum gauge theory
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BRST quantization
Quantum gauge theory
Yang–Mills theory
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A simplified mathematical approach is presented and used to find a suitable free-field Lagrangian to complete previous work on constructing a gauge theory of CPT transformations. The new Lagrangian is a slight but important modification of the previous candidate. The new version satisfies an additional requirement which had been overlooked and not satisfied by the previous candidate.
Field theory (psychology)
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BRST quantization
Quantum gauge theory
Yang–Mills theory
Formalism (music)
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Non-Abelian gauge theories with composite fields are examined in the background field method. Generating functionals of Green's functions for a Yang--Mills theory with composite and background fields are introduced, including the generating functional of vertex Green's functions (effective action). The corresponding Ward identities are obtained, and the issue of gauge dependence is investigated. A gauge variation of the effective action is found in terms of a nilpotent operator depending on the composite and background fields. On-shell independence from the choice of gauge fixing for the effective action is established. In the study of the Ward identities and gauge dependence, finite field-dependent BRST transformations with a background field are introduced and utilized on a systematic basis. On the one hand, this involves the consideration of (modified) Ward identities with a field-dependent anticommuting parameter, also depending on a non-trivial background.On the other hand, the issue of gauge dependence is studied with reference to a finite variation of the gauge Fermion. The concept of a joint introduction of composite and background fields to non-Abelian gauge theories is exemplified by the Gribov--Zwanziger theory, including the case of a local BRST-invariant horizon, and by the Volovich--Katanaev model of two-dimensional gravity with dynamical torsion.
BRST quantization
Quantum gauge theory
Background field method
Lattice gauge theory
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