Note and Comment

Courts--Jurisdiction of Circuit Court--Enjoining Writ of Error; Criminal Law--Arraignment--Waiver; Damages--Personal Injuries--Expense of Nursing; Deeds--Boundaries--Navigable Waters; Deeds--Variance Between Granting Clause and Habendum--Construction; Eminent Domain--Use of Urban Street Car Lines by Interurban Cars; Evidence--Admissibility of Statement of One Partner to a Commercial Agency as to Asset and Liabilities; Evidence--Admission of a Carbon Copy of a Contract as a Duplicate Original; Federal Courts--jurisdiction--Action Against State Officers; Foreign Corporations--Liability to be Sued; Homicide--Self-Defense--Provoking Difficulty; Insurance--Certificate Silent as to Suicide; Joint Stock Associations--have they at Common law Powers and Privileges of a Corporation not Possessed by Individuals or Partnerships?; Municipal corporations--Protecting Against Fraud by Ordinance--Sale of Jewelry by Auctioneers; Parent and Child--Obligation of Father to Support After Divorce; Public Officers--Resignation--Necessity of Acceptance; Sales--good Will--Solicitation of Old Customers--Professional and Trading Partnerships; Trial--Appeal to Prejudice in Argument; Wills--Construction--Testamentary Trusts--Gifts to Trustee; Wills--distinguished from Deeds--Future Interes

The Quantized O(1,2)/O(2)×Z2O(1,2)/O(2)\times Z_2 Sigma Model Has No Continuum Limit in Four Dimensions. I. Theoretical Framework

The nonlinear sigma model for which the field takes its values in the coset space $O(1,2)/O(2)\times Z_2$ is similar to quantum gravity in being perturbatively nonrenormalizable and having a noncompact curved configuration space. It is therefore a good model for testing nonperturbative methods that may be useful in quantum gravity, especially methods based on lattice field theory. In this paper we develop the theoretical framework necessary for recognizing and studying a consistent nonperturbative quantum field theory of the $O(1,2)/O(2)\times Z_2$ model. We describe the action, the geometry of the configuration space, the conserved Noether currents, and the current algebra, and we construct a version of the Ward-Slavnov identity that makes it easy to switch from a given field to a nonlinearly related one. Renormalization of the model is defined via the effective action and via current algebra. The two definitions are shown to be equivalent. In a companion paper we develop a lattice formulation of the theory that is particularly well suited to the sigma model, and we report the results of Monte Carlo simulations of this lattice model. These simulations indicate that as the lattice cutoff is removed the theory becomes that of a pair of massless free fields. Because the geometry and symmetries of these fields differ from those of the original model we conclude that a continuum limit of the $O(1,2)/O(2)\times Z_2$ model which preserves these properties does not exist.Comment: 25 pages, no figure

Self force on static charges in Schwarzschild spacetime

We study the self forces acting on static scalar and electric test charges in the spacetime of a Schwarzschild black hole. The analysis is based on a direct, local calculation of the self forces via mode decomposition, and on two independent regularization procedures: A spatially-extended particle model method, and on a mode-sum regularization prescription. In all cases we find excellent agreement with the known exact results.Comment: 21 pages, 9 Encapsulated PostScript figures, submitted to Class. Quantum Gra

The Quantized O(1,2)/O(2)×Z2O(1,2)/O(2)\times Z_2 Sigma Model Has No Continuum Limit in Four Dimensions. II. Lattice Simulation

A lattice formulation of the $O(1,2)/O(2)\times Z_2$ sigma model is developed, based on the continuum theory presented in the preceding paper. Special attention is given to choosing a lattice action (the ``geodesic'' action) that is appropriate for fields having noncompact curved configuration spaces. A consistent continuum limit of the model exists only if the renormalized scale constant $\beta_R$ vanishes for some value of the bare scale constant~$\beta$. The geodesic action has a special form that allows direct access to the small-$\beta$ limit. In this limit half of the degrees of freedom can be integrated out exactly. The remaining degrees of freedom are those of a compact model having a $\beta$-independent action which is noteworthy in being unbounded from below yet yielding integrable averages. Both the exact action and the $\beta$-independent action are used to obtain $\beta_R$ from Monte Carlo computations of field-field averages (2-point functions) and current-current averages. Many consistency cross-checks are performed. It is found that there is no value of $\beta$ for which $\beta_R$ vanishes. This means that as the lattice cutoff is removed the theory becomes that of a pair of massless free fields. Because these fields have neither the geometry nor the symmetries of the original model we conclude that the $O(1,2)/O(2)\times Z_2$ model has no continuum limit.Comment: 32 pages, 7 postscript figures, UTREL 92-0

Super-Hubble de Sitter Fluctuations and the Dynamical RG

Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of perturbation theory at late times. We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms. In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if a dynamical mass is generated. We compare this improved infrared behavior with large-N expansions when applicable.Comment: 33 pages, 4 figure

Note and Comment

Courts--Jurisdiction of Circuit Court--Enjoining Writ of Error; Criminal Law--Arraignment--Waiver; Damages--Personal Injuries--Expense of Nursing; Deeds--Boundaries--Navigable Waters; Deeds--Variance Between Granting Clause and Habendum--Construction; Eminent Domain--Use of Urban Street Car Lines by Interurban Cars; Evidence--Admissibility of Statement of One Partner to a Commercial Agency as to Asset and Liabilities; Evidence--Admission of a Carbon Copy of a Contract as a Duplicate Original; Federal Courts--jurisdiction--Action Against State Officers; Foreign Corporations--Liability to be Sued; Homicide--Self-Defense--Provoking Difficulty; Insurance--Certificate Silent as to Suicide; Joint Stock Associations--have they at Common law Powers and Privileges of a Corporation not Possessed by Individuals or Partnerships?; Municipal corporations--Protecting Against Fraud by Ordinance--Sale of Jewelry by Auctioneers; Parent and Child--Obligation of Father to Support After Divorce; Public Officers--Resignation--Necessity of Acceptance; Sales--good Will--Solicitation of Old Customers--Professional and Trading Partnerships; Trial--Appeal to Prejudice in Argument; Wills--Construction--Testamentary Trusts--Gifts to Trustee; Wills--distinguished from Deeds--Future Interes