Symmetric space scalar field theory

Some quantum field theories, such as the chiral SU(2) ? SU(2) theory, can have a dynamics invariant under a group $\text{G}$ that is realized on a vacuum which is invariant only under a subgroup $\text{H}$ of $\text{G}$. These theories may be defined by scalar fields which are coordinates for the coset manifold $\text{G}$/$\text{H}$. They are thus non-polynomial theories on a symmetric space, with the group motions in this space described by a set of Killing vectors. We show how the Lagrange function may be constructed entirely from the Killing vectors. In particular, all physical quantities may be expressed in terms of the currents formed out of the Killing vectors. The current correlation functions do not exhibit the spurious wave function renormalizations which are encountered if ordinary Green's functions are computed. We illustrate the general method by calculating one-loop counter terms in a completely invariant fashion. An Appendix describes in simple terms the general theory of symmetric spaces, which should prove useful in other contexts.     

Classification of conformal steckel spaces in the vaidia problem

The classification of isotropic conformal Steckel spaces satisfying a system of Einstein equations in which the right-hand side is the energy—momentum tensor of an isotropic ideal liquid is considered. The complete solution of the problem is found for the case of a conformal Steckel space admitting of one isotropic Killing vector field and two Killing tensor fields, when these objects form a complete set. Tomsk State University. Tomsk State Pedagogical University. Institute of High-Power Electronics, Siberian Branch, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 48–53, August, 1996.     

Anti-self-dual Conformal Structures with Null Killing Vectors from Projective Structures

Using twistor methods, we explicitly construct all local forms of four–dimensional real analytic neutral signature anti–self–dual conformal structures (M, [g]) with a null conformal Killing vector. We show that M is foliated by anti-self-dual null surfaces, and the two-dimensional leaf space inherits a natural projective structure. The twistor space of this projective structure is the quotient of the twistor space of (M, [g]) by the group action induced by the conformal Killing vector. We obtain a local classification which branches according to whether or not the conformal Killing vector is hyper-surface orthogonal in (M, [g]). We give examples of conformal classes which contain Ricci–flat metrics on compact complex surfaces and discuss other conformal classes with no Ricci–flat metrics. Dedicated to the memory of Jerzy Plebański     

The Carter constant and Petrov classification of the Vaidya–Einstein–Kerr spacetime

The existence of the Carter constant in the Vaidya–Einstein–Kerr (VEK) spacetime and its relation to the Petrov type is investigated. This spacetime is an example of a black hole in an asymptotically non-flat background. We construct the Carter constant and obtain the Killing tensor in the VEK spacetime. The Newman–Penrose formalism is employed to obtain the spin coefficients. We present a complete (Petrov) classification of the VEK spacetime and the special case of the non-rotating Vaidya–Einstein–Schwarzschild spacetime. We demonstrate explicitly that both spacetimes are of type-D.     

Conformal Killing Vectors in LRS Bianchi Type V Spacetimes

In this note, we investigate conformal Killing vectors (CKVs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Subject to some integrability conditions, CKVs up to implicit functions of (t,x) are obtained. Solving these integrability conditions in some particular cases, the CKVs are completely determined, obtaining a classification of LRS Bianchi type V spacetimes. The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.     

Basic gravitational currents and Killing–Yano forms

It has been shown that for each Killing–Yano (KY)-form accepted by an n-dimensional (pseudo)Riemannian manifold of arbitrary signature, two different gravitational currents can be defined. Conservation of the currents are explicitly proved by showing co-exactness of the one and co-closedness of the other. Some general geometrical facts implied by these conservation laws are also elucidated. In particular, the conservation of the one-form currents implies that the scalar curvature of the manifold is a flow invariant for all of its Killing vector fields. It also directly follows that, while all KY-forms and their Hodge duals on a constant curvature manifold are the eigenforms of the Laplace–Beltrami operator, for an Einstein manifold this is certain only for KY 1-forms, (n − 1)-forms and their Hodge duals.     

A note on a family of type {3, 1} vacuum solutions with twist

A four-parameter family of vacuum solutions of Petrov type {3, 1} possessing nonvanishing twist, which was obtained separately by A. Held and I. Robinson, is investigated. Various techniques that were reviewed in an earlier paper are employed for interpreting the coordinates. In addition, the functionally form invariant solutions of a functionally related metric are obtained, thereby enabling the Killing structure of the family to be fully analyzed.     

Factorized Combinations of Virasoro Characters

We investigate linear combinations of characters for minimal Virasoro models which are representable as a product of several basic blocks. Our analysis is based on consideration of asymptotic behaviour of the characters in the quasi-classical limit. In particular, we introduce a notion of the secondary effective central charge. We find all possible cases for which factorization occurs on the base of the Gau?-Jacobi or the Watson identities. Exploiting these results, we establish various types of identities between different characters. In particular, we present several identities generalizing the Rogers–Ramanujan identities. Applications to quasi-particle representations, modular invariant partition functions, super-conformal theories and conformal models with boundaries are briefly discussed.     

Hawking Radiation via Tunnelling from Black Holes by Using Eddington–Finkelstein Coordinates

In this paper, by using well-known Eddington–Finkelstein coordinates instead of Painlevè coordinates, we study the tunnelling effect of the black holes once again. As examples of the static and stationary black holes, we calculate the tunnelling rates of Schwarzschild and Kerr black holes. In addition, the result obtained by adopting Eddington–Finkelstein coordinates is in agreement with the Parikh’s and Zhang’s recent work which adopts the Painlevè coordinates. At last, we discuss carefully the condition that the coordinates system in which we study the tunnelling process should satisfy. In our opinion, the terms of the tunnelling effect are not as strict as ones in Parikh’s paper and could be softened properly. PACS: 04.70.Dy     

Elimination the centre-of-mass motion in the nuclear shell-model with isospin

An efficient procedure for large-scale calculations of the two-particle translational invariant coefficients of fractional parentage (CESO’s) for several j-shells with isospin is presented. The approach is based on a simple enumeration scheme for antisymmetric many-particle states and efficient algorithms for calculation of the coefficients of fractional parentage for a single j-shell and several j-shells with isospin. The CESO’s may be obtained by diagonalizing the centre-of-mass Hamiltonian in the basis set of antisymmetric A-particle oscillator functions with singled out dependence on intrinsic coordinates of two last particles and choosing the subspace of its eigenvectors corresponding to the minimal eigenvalue equal to 3/2. An arbitrary number of oscillator quanta can be involved. The characteristics of the introduced CESO’s basis are investigated.     

Natural Energy Bounds in Quantum Thermodynamics

Given a stationary state for a noncommutative flow, we study a boundedness condition, depending on a parameter β>0, which is weaker than the KMS equilibrium condition at inverse temperature β. This condition is equivalent to a holomorphic property closely related to the one recently considered by Ruelle and D'Antoni–Zsido and shared by a natural class of non-equilibrium steady states. Our holomorphic property is stronger than Ruelle's one and thus selects a restricted class of non-equilibrium steady states. We also introduce the complete boundedness condition and show this notion to be equivalent to the Pusz–Woronowicz complete passivity property, hence to the KMS condition. In Quantum Field Theory, the β-boundedness condition can be interpreted as the property that localized state vectors have energy density levels increasing β-subexponentially, a property which is similar in the form and weaker in the spirit than the modular compactness-nuclearity condition. In particular, for a Poincaré covariant net of C^*-algebras on Minkowski spacetime, the β-boundedness property,β≥ 2π, for the boosts is shown to be equivalent to the Bisognano–Wichmann property. The Hawking temperature is thus minimal for a thermodynamical system in the background of a Rindler black hole within the class of β-holomorphic states. More generally, concerning the Killing evolution associated with a class of stationary quantum black holes, we characterize KMS thermal equilibrium states at Hawking temperature in terms of the boundedness property and the existence of a translation symmetry on the horizon. Received: 2 October 2000 / Accepted: 5 December 2000     

Comment on ‘Stationary perfect fluid solutions with differential rotation’

We vindicate our results in Mars and Senovilla (Phys Rev D 54, 6166–6180, 1996), which have been recently put in doubt or misunderstood in García and Ulloa (Gen Rel Grav 39, 1639–1650, 2007). In particular, we maintain that there indeed exist axially symmetric differentially rotating perfect-fluid solutions satisfying all energy conditions within the family of solutions presented in Senovilla (Class Quant Grav 9, L167–L169, 1992). We remark that the existence of an axis of symmetry can never be “re-interpreted” as the existence of a Killing horizon, and vice versa. We prove that such horizons are simply impossible for the perfect fluids within the family, and that regular axes of symmetry (or curvature singularities) are the only possibilities. Other inaccuracies or misunderstandings appeared in García and Ulloa (Gen Rel Grav 39, 1639–1650, 2007) are clarified.     

Supersymmetric chiral normal coordinates

The (anti-) chiral Killing vectors of the supersymmetric Kähler manifold associated with the nonlinear realization of a global symmetry are used to define (anti-) chiral normal coordinates. This in turn leads to a background superfield expansion of the super-Kähler potential that is manifestly gauge invariant and supersymmetric. The chiral normal coordinates are further employed to construct a background superfield expansion for a locally gauge invariant supersymmetric action.     

Exact solutions of the generalized Lane–Emden equations of the first and second kind

In this paper we discuss the integrability of the generalized Lane–Emden equations of the first and second kinds. We carry out their Noether symmetry classification. Various cases for the arbitrary functions in the equations are obtained for which the equations have Noether point symmetries. First integrals of such cases are obtained and also reduction to quadrature of the corresponding Lane–Emden equations are presented. New cases are found.     

Tunneling Effect and Hawking Radiation from a Gibbon–Maeda Black Hole by Using Eddington–Finkelstein Coordinates

In this paper, by using well-known Eddington–Finkelstein coordinates instead of Painlevè coordinates, we study the tunneling effect of black holes. As examples of special static black holes, we calculate the tunneling rates of Gibbon–Maeda black holes. The result obtained by adopting Eddington–Finkelstein coordinates is in agreement with the Parikh’s standard result, Γ∼exp (−2Im S), which adopts the Painlevè coordinates. In addition, we discuss carefully the condition that the coordinates system in which we study the tunneling process should satisfy. In our opinion, the terms of the tunneling effect are not as strict as ones in Parikh’s paper and could be softened properly.     

Spin–gravity coupling and gravity-induced quantum phases

External gravitational fields induce phase factors in the wave functions of particles. The phases are exact to first order in the background gravitational field, are manifestly covariant and gauge invariant and provide a useful tool for the study of spin–gravity coupling and of the optics of particles in gravitational or inertial fields. We discuss the role that spin–gravity coupling plays in particular problems.     

Killing spinors for the bosonic string and Kaluza–Klein theory with scalar potentials

The paper consists mainly of two parts. In the first part, we obtain well-defined Killing spinor equations for the low-energy effective action of the bosonic string with the conformal anomaly term. We show that the conformal anomaly term is the only scalar potential that one can add into the action that is consistent with the Killing spinor equations. In the second part, we demonstrate that Kaluza–Klein theory can be gauged so that the Killing spinors are charged under the Kaluza–Klein vector. This gauging process generates a scalar potential with a maximum that gives rise to an AdS spacetime. We also construct solutions of these theories.     

A theoretical model for the collective motion of proteins by means of principal component analysis

A coarse grained model in the frame work of principal component analysis is presented. We used a bath of harmonic oscillators approach, based on classical mechanics, to derive the generalized Langevin equations of motion for the collective coordinates. The dynamics of the protein collective coordinates derived from molecular dynamics simulations have been studied for the Bovine Pancreatic Trypsin Inhibitor. We analyzed the stability of the method by studying structural fluctuations of the C _a atoms obtained from a 20 ns molecular dynamics simulation. Subsequently, the dynamics of the collective coordinates of protein were characterized by calculating the dynamical friction coefficient and diffusion coefficients along with time-dependent correlation functions of collective coordinates. A dual diffusion behavior was observed with a fast relaxation time of short diffusion regime 0.2–0.4 ps and slow relaxation time of long diffusion about 1–2 ps. In addition, we observed a power law decay of dynamical friction coefficient with exponent for the first five collective coordinates varying from −0.746 to −0.938 for the real part and from −0.528 to −0.665 for its magnitude. It was found that only the first ten collective coordinates are responsible for configuration transitions occurring on time scale longer than 50 ps.     

Metrics of Homogeneous Spaces Admitting (3.1)-Type Complete Sets

A classification has been obtained for spaces which admit complete sets of motion integrals of the (3.1)-type and are spatially homogeneous. The metrics and Killing vectors have been found in explicit form for all types of these spaces. A classification by Bianchi is given for the spaces obtained.