scholarly journals EFFECTS OF GAUGING ON SYMPLECTIC STRUCTURE, THE HOPF TERM COUPLED TO THE CP1 MODEL, AND FRACTIONAL SPIN

1999 ◽  
Vol 14 (10) ◽  
pp. 1561-1590 ◽  
Author(s):  
B. CHAKRABORTY ◽  
A. S. MAJUMDAR
Keyword(s):  
Symplectic Structure ◽  
Energy Momentum Tensor ◽  
Time Derivative ◽  
Momentum Tensor ◽  
Total Charge ◽  
Dynamical Structure ◽  
Independent Manner ◽  
Classical Level ◽  
Fractional Spin ◽  
Chern Simons

We couple the Hopf term to the relativistic CP 1 model and carry out the Hamiltonian analysis at the classical level in a gauge-independent manner. The symplectic structure of the model given by the set of Dirac brackets among the phase space variables is found to be the same as that of the pure CP 1 model. This symplectic structure is shown to be inherited from the global SU(2)-invariant S3 model, and undergoes no modification upon gauging the U(1) subgroup, except for the appearance of an additional first class constraint generating U(1) gauge transformation. We then address the question of fractional spin as imparted by the Hopf term at the classical level. For that we construct the expression of angular momentum through both the symmetric energy–momentum tensor and Noether's prescription. The two expressions agree for the model, indicating that no fractional spin is imparted by this term at the classical level in an approach which is different from the earlier analyses carried out in the literature. We next show that the model has to be altered à la Bowick et al., by using an identity (which is not a constraint as it involves a time derivative and thus changes the basic dynamical structure of the model) valid in the radiation gauge in order to yield the fractional spin given in terms of the soliton number. Finally, by making the gauge field of the CP 1 model dynamical by adding the Chern–Simons term, we find that the model ceases to be a CP 1 model, as is the case with its nonrelativistic counterpart. This model is also shown to reveal the existence of "anomalous" spin. This is, however, given in terms of the total charge of the system, rather than any soliton number.

scholarly journals QUANTIZING HIGHER-SPIN STRING THEORIES

1995 ◽  
Vol 10 (14) ◽  
pp. 2123-2142 ◽  
Author(s):  
H. LU ◽  
X.J. WANG ◽  
K.-W. XU ◽  
C.N. POPE ◽  
K. THIELEMANS
Keyword(s):  
String Theory ◽  
Classical Theory ◽  
Energy Momentum Tensor ◽  
Standard Form ◽  
Momentum Tensor ◽  
Minimal Models ◽  
Classical Level ◽  
Higher Spin ◽  
String Theories ◽  
The Way

In this paper, we examine the conditions under which a higher-spin string theory can be quantized. The quantizability is crucially dependent on the way in which the matter currents are realized at the classical level. In particular, we construct classical realizations for the W2,s algebra, which is generated by a primary spin-s current in addition to the energy-momentum tensor, and discuss the quantization for s≤8. From these examples we see that quantum BRST operators can exist even when there is no quantum generalization of the classical W2,s algebra. Moreover, we find that there can be several inequivalent ways of quantizing a given classical theory, leading to different BRST operators with inequivalent cohomologies. We discuss their relation to certain minimal models. We also consider the hierarchical embeddings of string theories proposed recently by Berkovits and Vafa, and show how the already known W strings provide examples of this phenomenon. Attempts to find higher-spin fermionic generalizations lead us to examine whether classical BRST operators for [Formula: see text](n odd) algebras can exist. We find that even though such fermionic algebras close up to null fields, one cannot build nilpotent BRST operators, at least of the standard form.

scholarly journals FERMIONS FROM PHOTONS: BOSONIZATION OF QED IN 2+1 DIMENSIONS

1994 ◽  
Vol 09 (27) ◽  
pp. 4669-4700 ◽  
Author(s):  
A. KOVNER ◽  
P.S. KURZEPA
Keyword(s):  
Perturbation Theory ◽  
Vector Potential ◽  
Energy Momentum Tensor ◽  
Lorentz Invariance ◽  
Hamiltonian Formalism ◽  
Momentum Tensor ◽  
Regularization Procedure ◽  
Local Polynomial ◽  
Definition Of ◽  
Chern Simons

We perform the complete bosonization of (2+1)-dimensional QED with one fermionic flavor in the Hamiltonian formalism. The Fermi operators are explicitly constructed in terms of the vector potential and the electric field. We carefully specify the regularization procedure involved in the definition of these operators, and calculate the fermionic bilinears and the energy-momentum tensor. The algebra of bilinears exhibits the Schwinger terms which also appear in perturbation theory. The bosonic Hamiltonian is a local, polynomial functional of Ai and Ei, and we check explicitly the Lorentz invariance of the resulting bosonic theory. Our construction is conceptually very similar to Mandelstam’s construction in 1+1 dimensions, and is dissimilar from the recent bosonization attempts in 2+1 dimensions, which hinge crucially on the presence of a Chern-Simons term.

The Maxwell equations

2018 ◽  
Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan
Keyword(s):  
Electromagnetic Field ◽  
Angular Momentum ◽  
Variational Principle ◽  
Maxwell Equations ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Field Energy ◽  
Total Charge ◽  
Faraday’S Law ◽  
System Energy

This chapter presents Maxwell equations determining the electromagnetic field created by an ensemble of charges. It also derives these equations from the variational principle. The chapter studies the equation’s invariances: gauge invariance and invariance under Poincaré transformations. These allow us to derive the conservation laws for the total charge of the system and also for the system energy, momentum, and angular momentum. To begin, the chapter introduces the first group of Maxwell equations: Gauss’s law of magnetism, and Faraday’s law of induction. It then discusses current and charge conservation, a second set of Maxwell equations, and finally the field–energy momentum tensor.

Dynamics of extended bodies in general relativity - II. Moments of the charge-current vector

1970 ◽  
Vol 319 (1539) ◽  
pp. 509-547 ◽  
Keyword(s):  
Tensor Field ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
The Body ◽  
Total Charge ◽  
Subsequent Paper ◽  
Multipole Moments ◽  
Current Vector ◽  
Charge Current ◽  
Infinite Set

The problem is considered of defining multipole moments for a tensor field given on a curved spacetime, with the aim of applying this to the energy-momentum tensor and charge-current vector of an extended body. Consequently, it is assumed that the support of the tensor field is bounded in spacelike directions. A definition is proposed for ‘a set of multipole moments’ of such a tensor field relative to an arbitrary bitensor propagator. This definition is not fully determinate, but any such set of moments completely determines the original tensor field. By imposing additional conditions on the moments in two different ways, two uniquely determined sets of moments are obtained for a vector field J α . The first set, the complete moments , always exists and agrees with moments defined less explicitly by Mathisson. If V α J α = 0, as is the case for the charge-current vector, these moments are interrelated by an infinite set of corresponding restrictions. The second set, the reduced moments , exists if and only if V α J α = 0. These avoid such an infinite set of interrelations, there being instead only one such restriction, the constancy of the total charge of the body. The energy-momentum tensor will be treated in a subsequent paper.

Dynamics of extended bodies in general relativity III. Equations of motion

1974 ◽  
Vol 277 (1264) ◽  
pp. 59-119 ◽  
Keyword(s):  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
High Order ◽  
Total Momentum ◽  
The Body ◽  
Full Description ◽  
Total Charge ◽  
Current Vector ◽  
Charge Current

A study is made of the motion of an extended body in arbitrary gravitational and electromagnetic fields. In a previous paper it was shown how to construct a set of reduced multipole moments of the charge-current vector for such a body. This is now extended to a corresponding treatment of the energy-momentum tensor. It is shown that, taken together, these two sets of moments have the following three properties. First, they provide a full description of the body, in that they determine completely the energy-momentum tensor and charge-current vector from which they are constructed. Secondly, they include the total charge, total momentum vector and total angular momentum (spin) tensor of the body. Thirdly, the only restrictions on the moments, apart from certain symmetry and orthogonality conditions, are the equations of motion for the total momentum and spin, and the conservation of total charge. The time dependence of the higher moments is arbitrary, since the process of reduction used to construct the moments has eliminated those contributions to these moments whose behaviour is determinate. The uniqueness of the chosen set of moments is investigated, leading to the discovery of a set of properties which is sufficient to characterize them uniquely. The equations of motion are first obtained in an exact form. Under certain conditions, the contributions from the moments of sufficiently high order are seen to be negligible. It is then convenient to make the multipole , in which these high order terms are omitted. When this is done, further simplifications can be made to the equations of motion. It is shown that they take an especially simple form if use is made of the extension operator of Veblen & Thomas. This is closely related to repeated covariant differentiation, but is more useful than that for present purposes. By its use, an explicit form is given for the equations of motion to any desired multipole order. It is shown that they agree with the corresponding Newtonian equations in the appropriate limit.

GENERATING FUNCTION FOR 2d WZW MODEL CORRELATORS AND THE SUGAWARA CONSTRUCTION FROM THE 2+1 CHERN-SIMONS THEORY

1990 ◽  
Vol 05 (17) ◽  
pp. 1365-1371 ◽  
Author(s):  
V.V. FOCK ◽  
YAN. I. KOGAN
Keyword(s):  
Generating Function ◽  
Coherent States ◽  
Energy Momentum Tensor ◽  
Vacuum State ◽  
Momentum Tensor ◽  
Simons Theory ◽  
Generating Functional ◽  
Chern Simons ◽  
Chern Simons Theory

The vacuum state of the Chern-Simons theory in the sl(2, R) coherent states representation is a generating functional for the chiral currents and the energy-momentum tensor.

CASIMIR EFFECT FOR THE ROBIN SURFACES IN STATIC ROBERTSON–WALKER SPACE–TIME

2011 ◽  
Vol 20 (02) ◽  
pp. 161-168 ◽  
Author(s):  
MOHAMMAD R. SETARE ◽  
M. DEHGHANI
Keyword(s):  
Scalar Field ◽  
Energy Momentum Tensor ◽  
Casimir Effect ◽  
Vacuum Expectation ◽  
Robin Boundary Condition ◽  
Momentum Tensor ◽  
Space Time ◽  
Conformally Invariant ◽  
Time Space ◽  
Robin Boundary

We investigate the energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved surfaces in k = -1 static Robertson–Walker space–time. We assume that the scalar field satisfies the Robin boundary condition on the surfaces. Robertson–Walker space–time space is conformally related to Rindler space; as a result we can obtain vacuum expectation values of the energy–momentum tensor for a conformally invariant field in Robertson–Walker space–time space from the corresponding Rindler counterpart by the conformal transformation.

scholarly journals Cutoff AdS3 versus $$ T\overline{T} $$ CFT2 in the large central charge sector: correlators of energy-momentum tensor

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Yi Li ◽  
Yang Zhou
Keyword(s):  
Field Theory ◽  
Euclidean Plane ◽  
Energy Momentum Tensor ◽  
Central Charge ◽  
Momentum Tensor ◽  
Two Dimensional ◽  
Conformal Field ◽  
Operator Identity ◽  
Pure Gravity ◽  
Charge Sector

Abstract In this article we probe the proposed holographic duality between $$ T\overline{T} $$ T T ¯ deformed two dimensional conformal field theory and the gravity theory of AdS3 with a Dirichlet cutoff by computing correlators of energy-momentum tensor. We focus on the large central charge sector of the $$ T\overline{T} $$ T T ¯ CFT in a Euclidean plane and a sphere, and compute the correlators of energy-momentum tensor using an operator identity promoted from the classical trace relation. The result agrees with a computation of classical pure gravity in Euclidean AdS3 with the corresponding cutoff surface, given a holographic dictionary which identifies gravity parameters with $$ T\overline{T} $$ T T ¯ CFT parameters.

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