Gauge Fixing Constraints Research Articles

The quantum-optics Hamiltonian in the Multipolar gauge

This article deals with the fundamental problem of light-matter interaction in the quantum theory. Although it is described through the vector potential in quantum electrodynamics, it is believed by some that a hamiltonian involving only the electric and the magnetic fields is preferable. In the literature this hamiltonian is known as the Power-Zienau-Woolley hamiltonian. We question its validity and show that it is not equivalent to the minimal-coupling hamiltonian. In this article, we show that these two hamiltonians are not connected through a gauge transformation. We find that the gauge is not fixed in the Power-Zienau-Woolley hamiltonian. The interaction term is written in one gauge whereas the rest of the hamiltonian is written in another gauge. The Power-Zienau-Woolley hamiltonian and the minimal-coupling one are related through a unitary transformation that does not fulfill the gauge fixing constraints. Consequently, they predict different physical results. In this letter, we provide the correct quantum theory in the multipolar gauge with a hamiltonian involving only the physical fields.

Gauge symmetry breaking in gravity and auxiliary effective action

In the context of the covariant symmetry breaking in gravity, we study the quantum aspect of Chamseddine–Mukhanov model by making use of path integral method. Utilizing one of the gauge fixing constraints, we remove the specific ghost degree of freedom. In continuation, we define an auxiliary effective action. Introducing an auxiliary field, we will have a new dynamic field in addition to the fundamental field.

CONSTRAINT STRUCTURE AND QUANTIZATION OF A NON-ABELIAN GAUGE THEORY BY MEANS OF DIRAC BRACKETS

An SO(3) non-Abelian gauge theory is introduced. The Hamiltonian density is determined and the constraint structure of the model is derived. The first-class constraints are obtained and gauge-fixing constraints are introduced into the model. Finally, using the constraints, the Dirac brackets can be determined and a canonical quantization is found using Dirac's procedure.

A CHIRAL SCHWINGER MODEL, ITS CONSTRAINT STRUCTURE AND APPLICATIONS TO ITS QUANTIZATION

The Jackiw–Rajaraman version of the chiral Schwinger model is studied as a function of the renormalization parameter. The constraints are obtained and they are used to carry out canonical quantization of the model by means of Dirac brackets. By introducing an additional scalar field, it is shown that the model can be made gauge invariant. The gauge invariant model is quantized by establishing a pair of gauge fixing constraints in order that the method of Dirac can be used.

Self-annihilation of the neutralino dark matter into two photons or aZand a photon in the minimal supersymmetric standard model

We revisit the one-loop calculation of the annihilation of a pair of the lightest neutralinos into a pair of photons, a pair of gluons and also a Z photon final state. For the latter we have identified a new contribution that may not always be negligible. For all three processes we have conducted a tuned comparison with previous calculations for some characteristic scenarios. The approach to the very heavy higgsino and wino is studied and we argue how the full one-loop calculation should be matched into a more complete treatment that was presented recently for these extreme regimes. We also give a short description of the code that we exploited for the automatic calculation of one-loop cross sections in the MSSM that could apply both for observables at the colliders and for astrophysics or relic density calculations. In particular the automatic treatment of zero Gram determinants which appear in the latter applications is outlined. We also point out how generalised non-linear gauge fixing constraints can be exploited.

Integrable models as constrained topological gauge theory

Integrable models in 1+1 dimensions are related to the hierarchy of gauge fixing constraints for BF topological gauge theory. The gauge equivalent systems for Zweibein fields are described by a pair of time reserved nonlinear equations as in termo-field theory. For the related Lax pair the spectral parameter must appear as a constant valued spin connection associated with Abelian gauge symmetry. Dissipative structures with integrable dynamics in the gauge theory of gravity are discussed as well as the 2+1 dimensional extension to the Chern-Simons theory.

Integrable Hierarchy from Topological Gauge Theory

By the recursion operator of nonlinear Schrödinger hierarchy, integrable models in 1+1 dimensions are related to the hierarchy of U(1) invariant gauge fixing constraints for the BF gauge theory. The loop algebra structure for the related linear problem with the spectral parameter as a constant valued, zero-strength gauge degree of freedom is derived.

PLUGGING THE GAUGE-FIXING INTO THE LAGRANGIAN

A complete analysis of the consequences of introducing a set of holonomic gauge-fixing constraints (to fix the dynamics) into a singular Lagrangian is performed. It is shown that in general the dynamical system originating from the reduced Lagrangian erases all the information regarding the first class constraints of the original theory, but retains the second class ones. It is proved that even though the reduced Lagrangian can be singular, it never possesses any gauge freedom. As an application, the example of n·A=0 gauges in electromagnetism is treated in full detail.

Slave fermions, slave bosons, and semions from bosonization of the two-dimensional t-J model.

We extend Abelian and non-Abelian bosonization formulas found in a previous paper, in combination with coherent-state methods, to present a systematic derivation of the slave-fermion, slave-boson, and semion representations of the two-dimensional t-J model in path-integral form. The slave-fermion and slave-boson representations are shown to arise from two different gauge fixing constraints introduced in the path-integral representation of the bosonized t-J model. For each representation we discuss the approximations leading to a mean-field theory. In the mean-field theory based on the semion representation, the holons are shown to be ``Dirac semions.''

Gauge fixings, evolution generators and world-line conditions in relativistic classical mechanics with constraints

After a review of the main models for classical relativisticN-particle systems based upon Dirac’s theory of constraints, a detailed study of their Hamiltonian formulation is made. The choice of the arbitrary functions and of the gauge-fixing constraints and the associated realizations of the reduced phase-space and of the observables by means of Dirac brackets are examined in detail. The restrictions on the gauge fixings to obtain compatibility between the evolution in the reduced phase space, generated by the total energy of the system, and the one in the constraint hypersurface, generated by the Dirac Hamiltonian, are found. It is also demonstrated that these restrictions are nothing else than the world-line conditions,i.e. gauge transformations are needed to ensure the objective existence of the world-lines and manifest covariance is broken. This is due to the property of the Dirac brackets of preserving the gauge fixings in every frame of reference. Predictive mechanics and the Currie-Hill world-line conditions are not in contradiction with the previous results: avoiding the Dirac-bracket mechanism, they save the manifest covariance but at the price of using accelerations which are complicated functions of the original potentials depending upon the whole history of the system.

Supersymmetric quantization of linearized supergravity

We give a manifestly supersymmetric quantization scheme for linearized supergravity, motivated by the desire to develop a background field method for the full non-linear theory. Supersymmetric gauge-fixing constraints are constructed and the corresponding ghost action is discussed. It is found that the Faddeev-Popov action itself possesses invariances, requiring “secondary” gauge fixing, which in turn leads to “secondary” ghost fields, the latter having normal statistics. The gauge-fixing constraints are used to construct gauge-fixing terms in the action, with a total of four gauge-fixing parameters. The superpropagators are found and may be greatly simplified by certain choices of these parameters.