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Register a new userConic Constrained Particle Quantization within the DB, FJBW and BRST Approaches
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We consider a second degree algebraic curve describing a general conic constraint imposed on the motion of a massive spinless particle. The problem is trivial at classical level but becomes involved and interesting in its quantum counterpart with subtleties in its symplectic structure and symmetries. The model is used here to investigate quantization issues related to the Hamiltonian constraint structure, Dirac brackets, gauge symmetry and BRST transformations. We pursue the complete constraint analysis in phase space and perform the Faddeev-Jackiw symplectic quantization following the Barcelos-Wotzasek iteration program to unravel the fine tuned and more relevant aspects of the constraint structure. A comparison with the longer usual Dirac-Bergmann algorithm, still more well established in the literature, is also presented. While in the standard DB approach there are four second class constraints, in the FJBW they reduce to two. By using the symplectic potential obtained in the last step of the FJBW iteration process we construct a gauge invariant model exhibiting explicitly its BRST symmetry. Our results reproduce and neatly generalize the known BRST symmetry of the rigid rotor showing that it constitutes a particular case of a broader class of theories.
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We present the BRST cohomologies of a class of constraint (super) Lie algebras as detour complexes. By giving physical interpretations to the components of detour complexes as gauge invariances, Bianchi identities and equations of motion we obtain a large class of new gauge theories. The pivotal new machinery is a treatment of the ghost Hilbert space designed to manifest the detour structure. Along with general results, we give details for three of these theories which correspond to gauge invariant spinning particle models of totally symmetric, antisymmetric and Kahler antisymmetric forms. In particular, we give details of our recent announcement of a (p,q)-form Kahler electromagnetism. We also discuss how our results generalize to other special geometries.
We discuss the BRST quantization of General Relativity (GR) with a cosmological constant in the unimodular gauge. We show how to gauge fix the transverse part of the diffeomorphism and then further to fulfill the unimodular gauge. This process requires the introduction of an additional pair of BRST doublets which decouple from the physical sector together with the other three pairs of BRST doublets for the transverse diffeomorphism. We show that the physical spectrum is the same as GR in the usual covariant gauge fixing. We then suggest to define the quantum theory of Unimodular Gravity (UG) by making Fourier transform of GR in the unimodular gauge with respect to the cosmological constant and slightly generalizing it. This suggests that the quantum theory of UG may describe the same theory as GR but the spacetime volume is fixed. We also discuss problems left in this formulation of UG.
We present a local setup for the recently introduced BRST-invariant formulation of Yang-Mills theories for linear covariant gauges that takes into account the existence of gauge copies `a la Gribov and Zwanziger. Through the convenient use of auxiliary fields, including one of the Stueckelberg type, it is shown that both the action and the associated nilpotent BRST operator can be put in local form. Direct consequences of this fully local and BRST-symmetric framework are drawn from its Ward identities: (i) an exact prediction for the longitudinal part of the gluon propagator in linear covariant gauges that is compatible with recent lattice results and (ii) a proof of the gauge-parameter independence of all correlation functions of local BRST-invariant operators.
A constrained BRST-BV Lagrangian formulation for totally symmetric massless HS fields in a $d$-dimensional Minkowski space is extended to a non-minimal constrained BRST-BV Lagrangian formulation by using a non-minimal BRST operator $Q_{c|mathrm{tot}}$ with non-minimal Hamiltonian BFV oscillators $overline{C}, overline{mathcal{P}}, lambda, pi$, as well as antighost and Nakanishi-Lautrup tensor fields, in order to introduce an admissible self-consistent gauge condition. The gauge-fixing procedure involves an operator gauge-fixing BRST-BFV Fermion $Psi_H$ as a kernel of the gauge-fixing BRST-BV Fermion functional $Psi$, manifesting the concept of BFV-BV duality. A Fock-space quantum action with non-minimal BRST-extended off-shell constraints is constructed as a shift of the total generalized field-antifield vector by a variational derivative of the gauge-fixing Fermion $Psi$ in a total BRST-BV action $S^{Psi}_{0|s} = int d eta_0 langle chi^{Psi{} 0}_{mathrm{tot}|c} big| Q_{c|mathrm{tot}}big| chi^{Psi{} 0}_{mathrm{tot}|c}rangle$. We use a gauge condition which depends on two gauge parameters, thereby extending the case of $R_xi$-gauges. For triplet and duplet formulations we explored the representations with only traceless field-antifield and source variables. For the generating functionals of Greens functions, BRST symmetry transformations are suggested and Ward identities are obtained.
Background: Models based on using perturbative polarization corrections and mean-field blocking approximation give conflicting results for masses of odd nuclei. Purpose: Systematically investigate the polarization and mean-field models, implemented within self-consistent approaches that use identical interactions and model spaces, so as to find reasons for the conflicts between them. Methods: For density-dependent interactions and with pairing correlations included, we derive and study links between the mean-field and polarization results obtained for energies of odd nuclei. We also identify and discuss differences between the polarization-correction and full particle-vibration-coupling (PVC) models. Numerical calculations are performed for the mean-field ground-state properties of deformed odd nuclei and then compared to the polarization corrections determined by using the approach that conserves spherical symmetry. Results: We have identified and numerically evaluated self-interaction (SI) energies that are at the origin of different results obtained within the mean-field and polarization-correction approaches. Conclusions: Mean-field energies of odd nuclei are polluted by the SI energies, and this makes them different from those obtained by using polarization-correction methods. A comparison of both approaches allows for the identification and determination of the SI terms, which then can be calculated and removed from the mean-field results, giving the self-interaction-free energies. The simplest deformed mean-field approach that does not break parity symmetry is unable to reproduce full PVC effects.
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