It is argued that the effective action theory may be regarded as a phenomenological theory describing a certain class of measurements irrespective of the nature of fundamental quantum objects. The effective action in quantum field theory is discussed in detail and used as a guide. A connection between the effective field and observables is established. The approach is applied to the gravitational collapse problem. A procedure for building a basis of non-local gravitational invariants is described and a result for the vacuum radiation in a spherically symmetric in-state is presented. A conclusion about breakdown of measurements at the Planck scale is revised.

https://iopscience.iop.org/article/10.1088/0264-9381/9/4/008/pdf

Effective action in quantum gravity

Hamiltonian form of the path integral for theories with a gauge freedom

Covariant theory of asymptotic symmetries, conservation laws and central charges

This article gives a pedagogical review of recent work in which the Einstein-Hilbert gravitational action is obtained as a symmetry-breaking effect in quantum field theory. Particular emphasis is placed on the case of renormalizable field theories with dynamical scale-invariance breaking, in which the induced gravitational effective action is finite and calculable. A functional integral formulation is used throughout, and a detailed analysis is given of the role of dimensional regularization in extracting finite answers from formally quadratically divergent integrals. Expressions are derived for the induced gravitational constant, for the induced cosmological constant, and for quantized matter theories on a background manifold, and a strategy is outlined for computing the induced constants in the case of an SU(n) gauge theory. By use of the background field method, the formalism is extended to the case in which the metric is also quantized, yielding a derivation of the semiclassical Einstein equations as an approximation to quantum gravity, as well as general formulas for the induced (or renormalized) gravitational and cosmological constants.

Einstein Gravity as a Symmetry Breaking Effect in Quantum Field Theory

This article is devoted to the perturbative renormalization of the abelian Higgs-Kibble model, within the class of renormalizable gauges which are odd under charge conjugation. The Bogoliubov Parasiuk Hepp-Zimmermann renormalization scheme is used throughout, including the renormalized action principle proved by Lowenstein and Lam. The whole study is based on the fulfillment to all orders of perturbation theory of the Slavnov identities which express the invariance of the Lagrangian under a supergauge type family of non-linear transformations involving the Faddeev-Popov ghosts. Direct combinatorial proofs are given of the gauge independence and unitarity of the physicalS operator. Their simplicity relies both on a systematic use of the Slavnov identities as well as suitable normalization conditions which allow to perform all mass renormalizations, including those pertaining to the ghosts, so that the theory can be given a setting within a fixed Fock space. Some simple gauge independent local operators are constructed.

/pdf/renormalization-of-the-abelian-higgs-kibble-model-14fr0vp7oj.pdf

Renormalization of the Abelian Higgs-Kibble Model

Operational quantization of dynamical systems subject to second class constraints

An investigation is carried out of some formal aspects of the operatorial method developed earlier for generalized canonical quantization of dynamical systems subject to constraints. Within the generalized Hamiltonian approach the master equation is obtained for the effective action, as well as an equation that expresses an analog of the basic postulate of covariant quantization. The generating of the operator gauge algebra of the most general form is considered both in the canonical and the Wick realization of the ghost sector with various most common types of the normal orderings used. The explicit form of the corresponding structural relations is also obtained. The phenomenon of quantum deformation of the structural relations is studied on general ground. It is shown, for instance, that the central extension of the Virasoro algebra for a string in the critical dimension appears naturally as an effect of quantum deformation of the involution relations corresponding to the Wick normal form. The local analysis is performed of the existence problem of solutions to generating equations of the operator gauge algebra. It is shown that the solution of quantum equations for the symbols of the gauge algebra generating operators can be locally constructed as formal series in powers of the Planck constant, provided that the corresponding classical solution exists and is locally Abelized (th Relations de base de l'approche operationnelle. Equation principale pour l'action effective. Solution pour le hamiltonien unitarisant, fermion de jauge, independance de jauge. Generation de l'algebre de jauge. Developpements ordonnes normaux des equations generatrices en puissances des operateurs du secteur fantome. Probleme d'existence operatoriel pour les equations generatrices de l'algebre de jauge vu comme un probleme de quantification. Retour aux operateurs. Superalgebre dynamique des systemes de jauge. Deformation quantique dans les relations d'involution

/pdf/operatorial-quantization-of-dynamical-systems-subject-to-4pdkyue1z2.pdf

Operatorial quantization of dynamical systems subject to constraints. A further study of the construction

These two volumes contain 64 essays on quantum field theory and quantum statistical physics specially commissioned in honour of the sixtieth birthday of Efim Fradkin. Over the years Professor Fradkin has continuously figured among the leaders of this very dynamic science, and the star-studded list of authors of this collection reflects the respect in which he is held. More than 90 theoretical physicists from 16 countries have united their efforts to emphasise his many important contributions and create a portrait of the present-day theory. As wide-ranging as have been Fradkin's studies, this book forms an encyclopaedia of modern high-energy theoretical physics. It contains essays which trace the peculiar, even grotesque, paths followed by theoretical physics over the past forty years and it also contains essays which put forward completely new ideas such as field theory of Galois fields. It contains comprehensive reviews and it also contains illuminating research papers. These are essays expounding general methods of field theory such as quantisation of dynamical systems, the effective action approach, the method of conformal field theory and there are also essays containing current work on quantum gravity, supersymmmetry and superstrings. In addition some essays deal with applications of field theory methods to other areas of physics such as polymer blends and amorphous systems in solid state physics. These volumes will be of great interest to researchers, postgraduate students and all those interested in the modern status of quantum field thoery and statistical physics, as well as the paths of their newest development.

Quantum field theory and quantum statistics : essays in honour of the 60th birthday of E.S. Fradkin

We establish the general structure of the BRST-invariant algebra of constraints in its commutator and antibracket forms via the formulation of algebra-generating equations in a supplementally extended phase space. New ghost-type variables behave as fields and antifields with respect to quantum antibrackets. The explicit form of the BRST-invariant gauge algebra is given in detail for rank-one theories with a Weyl- and a Wick-ordered ghost sector. We construct a fixed-gauge unitarizing Hamiltonian and show that the formalism is physically equivalent to the standard BRST–BFV approach.

BRST-Invariant Algebra of Constraints in Terms of Commutators and Quantum Antibrackets

/pdf/brst-invariantnaia-algebra-sviazei-v-terminakh-kommutatorov-76at9otfhy.pdf

БРСТ-инвариантная алгебра связей в терминах коммутаторов и квантовых антискобок@@@BRST-Invariant Algebra of Constraints in Terms of Commutators and Quantum Antibrackets

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