Braid group action on theq-Weyl algebra

We provide a braid group action on theq-deformed Weyl algebraW _q (n). The restriction of this action to the representations ofU _q (A _n–1 ) andU _q (C _n ) inW _q (n) is seen to agree with the braid group action introduced by Lusztig on these quantum algebras.Supported in part by the National Sciences and Engineering Research Council (NSERC) of Canada.     

The effective action of W 3-gravity

A new method for integrating anomalous Ward identities and finding the effective action is proposed. Two-dimensional supergravity and W ₃-gravity are used as examples to demonstrate its potential. An operator is introduced that associates each physical quantity with a Ward identity, i.e., a quantity that is transformed without anomalous terms and can be nullified in a consistent manner. A covariant form of the action for matter fields interacting with a gravitational and W ₃-gravitational background is proposed. Zh. éksp. Teor. Fiz. 111, 1537–1553 (May 1997)     

Vilkovisky-de Witt effective action in quantum field theory in curved spacetime

The potentialities of the application of the Vilkovisky-de Witt effective action in quantum field theory in curved spacetime are discussed. A number of examples is given, in which this effective action eliminates problems related to the standard effective action.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 107–110, April, 1990.The author thanks I. L. Buchbinder for discussion of the work.     

Noncommutative geometric spaces with boundary: Spectral action

We study spectral action for Riemannian manifolds with boundary, and then generalize this to noncommutative spaces which are products of a Riemannian manifold times a finite space. We determine the boundary conditions consistent with the hermiticity of the Dirac operator. We then define spectral triples of noncommutative spaces with boundary. In particular we evaluate the spectral action corresponding to the noncommutative space of the standard model and show that the Einstein–Hilbert action gets modified by the addition of the extrinsic curvature terms with the right sign and coefficient necessary for consistency of the Hamiltonian. We also include effects due to the addition of a dilaton field.     

Anatomy of one-loop effective action in non-commutative scalar field theories

The one-loop effective action of non-commutative scalar field theory with cubic self-interaction is studied. Utilizing the worldline formulation, both the planar and non-planar parts of the effective action are computed explicitly. We find complete agreement of the result with the Seiberg–Witten limit of a string worldsheet computation and with the standard Feynman diagrammatics. We prove that, in the low-energy and large non-commutativity limit, the non-planar part of the effective action is simplified enormously and is resummable into a quadratic action of scalar open Wilson line operators. Received: 22 July 2001 / Revised version: 19 October 2001 / Published online: 7 December 2001     

Breaking of permutation symmetry and diagonal group action: Nielsen model and the standard model as low-energy limit

We point out that, on the basis of a theorem by L. Michel, every model based on the symmetryG ... G has a generic low-energy limit the breaking to diagonal action, i.e., toG. This applies in particular to the proposal by Nielsen to consider such a model withG the standard model group.     

The induced action ofW 3 gravity

We obtain the induced action [h, b] for chiralW ₃ gravity in thec± limit from the induced action of a gaugedSl(3,R) Wess-Zumino-Witten model by imposing constraints on the currents of the latter. In the process we find a closed gauge algebra for the gauge sector ofW ₃ gravity in which the currentsT andW become auxiliary fields. An explicit realization ofT andW in terms of the gauge fields is given. In terms of new fieldsr ands, which are a generalization of Polyakov'sf variable for ordinary gravity, the complete induced action [h, b; c±] becomes local.Work supported in part by NSF grant No. PHYS 89-08495Address after September 1, 1991: Physics Department, U.C. Berkeley, Berkeley, CA 94720, USA     

Multiloop calculations of effective action for local composite operators

Effective action for local composite operators is described for both the standard loop expansion formulation and an improved two-particle irreducible formulation. Rules for calculating multiloop contributions to the effective action are given in both formulations and are exemplified in the Gross-Neveu model in the large-N limit. Calculation of the exact effective action in the Gross-Neveu model is considerably simplified in the improved formulation. Results obtained from the conventional auxiliary field method, like dynamical symmetry breaking, non-classical solitions, etc., can all be obtained in the present formulation by dealing with the composite operators directly without introducing auxiliary fields. The present method can be applied to models in which the auxiliary field method is difficult to implement.     

Nonlocal action in the induction motor

It is pointed out that local field-contact action depends entirely on field-energy momentum transfer to matter, orvice versa. Contact with stationary electromagnetic energy does not produce forces. With this in mind, the paper examines the electrodynamic operation of the common induction motor and concludes that the motor is not, and could not be, driven by local field-contact action.     

On the new definition of off-shell effective action

We analyze the recently proposed definition of the off-shell, gauge-invariant, gauge-independent, effective action $\text{Γ}$, utilizing an invariant metric on the field space. It is shown how to establish correspondence between $\text{Γ}$ and the standard effective action, calculated in some particular (Landau-type) gauge. Several examples are explicitly discussed, including Yang-Mills theory, the effective potential in scalar QED, and one-loop quantum gravity. Generalization to the case of super-invariant theories (e.g. super-Yang-Mills and supergravity) is also presented.     

Effective action in multidimensional (Super)gravities

In the present paper we have obtained unique effective action ford=5 gravity on the backgroundM ₄×s ₁, whereM ₄ is the Minkowski space,S ₁ is a one-sphere. The effective action is calculated forN=1d=11 supergravity on the backgroundR _n xT _11–n whereR _n is then-dimensional curved space, T_d is thed-dimensional torus. A mechanism of inducing the Einstein gravity with zero--term is proposed.We thank A. O. Barvinsky, E. S. Fradkin, I. V. Tyutin and A. A. Tseytlin for helpful discussions. We are grateful to L. G. Fonova for technical assistance.     

Unique effective action in Kaluza-Klein quantum theories and spontaneous compactification

The one-loop unique effective action by Vilkovisky in the d = 5 Einstein gravity and R²-gravity on the space M₄×S₁ is calculated, where M₄ is the Minkowski space and S₁ is a one-dimensional sphere. Also, the one-loop unique effective action for d-dimensional Einstein gravity on M₄×T_d−4 is calculated. The results of the calculation of the standard effective action are compared with those in the same theories.     

The effective gauge field action of a system of non-relativistic electrons

We consider a system of free, non-relativistic electrons at zero temperature and positive density, coupled to an arbitrary, external electromagnetic vector potential,A. By integrating out the electron degrees of freedom we obtain the effective action forA. We show that, in the scaling limit, this effective action is quadratic inA and can be viewed as an integral over the Fermi sphere of effective actions of (1+1)-dimensional, chiral schwinger models. We use this result to elucidate Luther-Haldane bosonization of systems of non-relativistic electrons. We also study systems of weakly coupled interacting electrons for which the BCS channel is turned off. Using the quadratic dependence of the effective action onA, we show that, in the scaling limit, the RPA yields the dominant contribution.     

Study of optical shuttering action in supramolecular hydrogen bonded nematogens

Supramolecular hydrogen bonded mesogens are formed between p-n-undecyloxy benzoic acid (11BAO) and p-n-alkyl benzoic acids (nBA, where n?=?2–8). The isolated mesogens are characterized by distinct techniques in order to appreciate the optical, thermal, electrical, and dielectric properties. The optical tilt angle measurement is studied for all the members of this homologous series and is found to concur with the mean field theory predicted value. An interesting factor to notice is the observation of optical shuttering action in nematic phase of the entire series which privilege these materials to be used as light modulators. Dielectric measurements were carried out and the dispersion curves were discussed in terms of relaxation frequency and activation energies.     

Effective action for the Yukawa2 quantum field theory

Using a rigorous version of the renormalization group we construct the effective action for theY ₂ model. The construction starts with integrating out the bosonic field which eliminates the large fields problem. Studying the soobtained purely fermionic theory proceeds by a series of convergent perturbation expansions. We show that the continuum limit of the effective action exists and its perturbation expansion is Borel summable.     

Semileptonic decays of charmed mesons in the effective action of QCD

Within the framework of phenomenological Lagrangians we construct the effective action of QCD relevant for the study of semileptonic decays of charmed mesons. Hence we evaluate the form factors of at leading order in the 1/N _C expansion and, by demanding their QCD-ruled asymptotic behavior, we constrain the couplings of the Lagrangian. The features of the model-independent parameterization of form factors are provided, and their relevance for the analysis of experimental data are pointed out. Received: 28 October 2002 / Published online: 24 January 2003     

Quantum action principle in curved space

Schwinger's action principle is formulated for the quantum system which corresponds to the classical system described by the LagrangianL _c( , x)=(M/2)g_ij(x) ^{i j}–v(x). It is sufficient for the purpose of deriving the laws of quantum mechanics to consider onlyc-number variations of coordinates and time. The Euler-Lagrange equation, the canonical commutation relations, and the canonical equations of motion are derived from this principle in a consistent manner. Further, it is shown that an arbitrary point transformation leaves the forms of the fundamental equations invariant. The judicious choice of the quantal Lagrangian is essential in our formulation. A quantum mechanical analog of Noether's theorem, which relates the invariance of the quantal action with a conservation law, is established. The ambiguities in the quantal Lagrangian are also discussed and it is pointed out that the requirement of invariance is not sufficient to determine uniquely the quantal Lagrangian and the Hamiltonian.     

On higher derivative corrections of tachyon action

We have examined the momentum expansion of the disk level S-matrix element of two tachyons and two gauge fields to find, up to on-shell ambiguity, the couplings of these fields in the world volume theory of N coincident non-BPS D-branes to all order of α^′. Using the proposal that the action of D-brane–anti-D-brane is given by the projection of the action of two non-BPS D-branes with (−1)^F_L, we find the corresponding couplings in the world volume theory of the brane–anti-brane system. Using these infinite tower of couplings, we then calculate the massless pole of the scattering amplitude of one RR field, two tachyons and one gauge field in the brane–anti-brane theory. We find that the massless pole of the field theory amplitude is exactly equal to the massless pole of the disk level S-matrix element of one RR, two tachyons and one gauge field to all order of α^′. We have also found the couplings of four tachyons to all order of α^′ by examining the S-matrix element of four tachyons.     

A geometrical property of action in gravitation theory

It is shown that in regard to the special spacial foliation associated with the gas of a standard clock, the action of gravitation theory is proportional to the time parameter, while the coefficient of proportionality is equal to the energy of the gravitational field and other fields in the reference system formed by the gas of the standard clock.St. Petersburg State Technical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 81–84, November, 1993.     

An action principle for the motion of particles

An action principle is set up for the motion of charged matter in the presence of the Einstein gravitational field. It can be applied to the motion of an extended particle and avoids the difficulties of a point particle arising from the singularities in the field.