On the energy-momentum tensor in gauge field theories

The energy-momentum tensor in spontaneously broken non-Abelian gauge field theories is studied. The motivation is to show that recent results on the finiteness and gauge independence of S-matrix elements in gauge theories extends to observable amplitudes for transitions in a gravitational field. Path integral methods and dimensional regularization are used throughout. Green's functions Γ_μν^(j)(q; p₁,…,p_j) involving the energy-momentum tensor and j particle fields are proved finite to all orders in perturbation theory to zero and first order in q, and finite to one loop order for general q. Amputated Green's functions of the energy momentum tensor are proved to be gauge independent on mass shell.     

The energy-momentum tensor in scalar and gauge field theories

A previous study of the energy-momentum tensor in ?⁴ theory and spontaneously broken non-Abelian gauge field theories is extended here to show finiteness to all orders in perturbation theory. Divergences of Green's functions Γ_μν^(j) (q; p₁, …, p_j) involving the energy-momentum tensor θ_μν and j particle fields are removed by counterterms of the ordinary Lagrangian plus a renormalization of the coefficient of the Callan-Coleman-Jackiw improvement term in θ_μν. Physically the extra renormalization means that the mean square “mass radius” of elementary spin zero particles must be specified from experiment.     

Quantization and unitary in antisymmetric tensor gauge theories

Following the procedure of Batalin and Vilkovisky we discuss the quantization of a non-abelian antisymmetric tensor gauge theory and describe the verification of one-loop unitarity for the quantized model, using the Ward identities and the procedure of 't Hooft and Veltman. The quantization of this system is similar to that of the Witten string field theory, requiring among other things the presence of three-ghost couplings.     

The fermionic energy-momentum tensor in terms of currents in an external gauge field

It is shown that for two-dimensional massless Dirac fields interacting with external gauge fields, the energy-momentum tensor can be expressed in terms of the current via the Sugawara-Sommerfield formula.     

Antisymmetric tensor gauge theories and non-linear σ-models

Antisymmetric tensor fields B_μν subject to the gauge transformation δB_μν = ?_μξ_ν ? ?_νξ_μ can describe spinless particles. We investigate the properties of field theories with a “non-abelian generalization” of this invariance. One class of such theories is equivalent to non-linear principal chiral σ-models, another to massive Yang-Mills theories. A supersymmetric analogue in 2 + 2 superspace is constructed and leads to the supersymmetric σ-model defined on a general riemannian manifold.     

Covariant quantization of non-Abelian antisymmetric tensor gauge theories

The non-Abelian Freedman-Townsend gauge tensor model is quantized in large class of covariant gauges using the geometrical reinterpretation of the BRS equations. In addition to the now usual pyramid of gauge and ghost states, a pyramid of auxiliary fields is found in our construction. These fields enforce the consistency of equations of motion and the integrability of the BRS equations.     

Space-times with covariant-constant energy-momentum tensor

It is shown that a general relativistic space-time with covariant-constant energy-momentum tensor is Ricci symmetric. Two particular types of such general relativistic space-times are considered and the nature of each is determined.     

New energy-momentum tensor in relativistic gravitation theory

Expressions for a new canonical energy-momentum tensor and an internal angular momentum of the gravitational field are derived in the context of bimetric relativistic gravitation theory based on the variational principle. A system of relations for the determining parameters of the gravitational field and matter involving, in particular, the continuity condition for the energy-momentum flux density is formulated on the discontinuity surface. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–58, April, 2006.     

On the new improved energy-momentum tensor

The requirement of the conformal covariance of the theory in the limit of vanishing masses leads to improving terms in energy-momentum tensor. Some consequences of the fact are briefly summarized.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975.     

Classical solutions and the energy-momentum tensor

A hyperelliptic two-meron solution of the massless scalar φ^N theory in $\text{n =}\text{2N}\text{(N ? 2)}$ Euclidean dimensions is given. This solution (which interpolates between the two-meron solution and the instanton solution of this theory) is used to illustrate several theory-independent statements which can be made about the energy-momentum tensor for instanton, meron and elliptic meron solutions of all scale invariant classical field theories.     

Dispersion invariant and energy-momentum tensor in macroscopic electrodynamics

Moscow Radio Engineering Institute, Academy of Sciences of the USSR, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 33, No. 11, pp. 1221–1227, November, 1990.     

The energy-momentum tensor near a black hole

The energy-momentum tensor for a conformally invariant scalar field near a Schwarzschild black hole in thermal equilibrium with radiation is found by a combination of analytical and numerical techniques. Calculations are performed in the Euclidean section of the spacetime, and divergences isolated using the heat kernel expansion. It is found that the results agree well with those of Candelas [1], but that there are significant differences from the Gaussian approximation of Page [2].     

Charges in gauge theories

In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green’s functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions. An erratum to this article is available at .     

An effective Lagrangian for dynamically broken gauge theories

Dynamical symmetry breaking in non-abelian gauge theories is studied by computing an effective potential for composite operators. We obtain consistent solutions of chiral and gauge symmetry breaking which are, in some cases, compatible with a short distance behavior. The effective theory determined is in agreement with the tumbling hypothesis.     

Some remarks on the energy-momentum tensor in general relativity

In general relativity, the energy-momentum tensor of a classical tensor field can be constructed by varying the action of the field with respect to the background metric. This paper suggests an alternative interpretation of the construction which also makes sense for spinor fields, and which gives some insight into the locality of energy-momentum operators in generally covariant quantum field theory.     

The energy-momentum tensor in a non-Abelian quark gluon theory

A finite energy-momentum tensor is constructed in an asymptotically free non-Abelian gauge theory with massive fermions (quarks). An explicit formula is found for the trace when inserted into a gauge-invariant Green function, and its properties at short distances are discussed.