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.     

An energy-momentum tensor in gauge theories

We consider the renormalization of the twist two, dimension four gauge invariant operator O_μν⁽¹⁾ = − F_μσF_νσ − g_{μν 0}. By using the general theory of renormalization of gauge invariant operators, we find the gauge noninvariant operator O⁽²⁾ with which it mixes. We construct a finite combination of O⁽¹⁾ and O⁽²⁾ and show that it is an acceptable energy momentum tensor for gauge theories. We compare our energy momentum tensor with that constructed by Freedman, Muzinich, and Weinberg.     

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.     

Generalized geometries and scalar tensor theories

Those generalized geometries satisfying the conditions that (a) parallel transfer with respect to the connection is path independent and (b) the geodesics of the metricg have the same trajectories as the autoparallels of the connection , are determined. Some uniqueness theorems of the metric in terms of the curvature are shown for such generalized geometries. Geometries of this type may be useful for constructing geometrized theories of gravitation more general than Einstein's theory.     

The energy-momentum tensor of a static gravitational field

The method of a tetrad field proposed by Rayski was used to determine the energy-momentum tensor for an approximate solution of the Einstein equations in the static case, from which it follows that the static gravitational field has non-zero mass but zero momentum, as was to be expected.In conclusion the author thanks P. Burcev for fruitful discussions and great interest in this work.     

The energy-momentum tensor in Yang-Mills field theory and its uniqueness

The uniqueness of the energy-momentum tensor in Yang-Mills field theory is established under general conditions.     

The energy-momentum spectrum in local field theories with broken Lorentz-symmetry

Assuming locality of the observables and positivity of the energy it is shown that the joint spectrum of the energy-momentum operators has a Lorentz-invariant lower boundary in all superselection sectors. This result is of interest if the Lorentz-symmetry is (spontaneously) broken, such as in the charged sectors of quantum electrodynamics.     

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.     

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.     

Non-abelian gauge couplings in thermal gauge field theories

Properties of the effective gauge couplings renormalized at finite temperature and density in thermal non-abelian gauge field theories are studied within one-loop approximations. Strong and severe vertex dependence is shown to come out both in the temperature and chemical potential dependences. Difficulties appearing in the perturbative calculation of physical quantities, indicated by the above disaster, are discussed. Also discussed is what insight might be gained from the present analysis into the “magnetic” screening of effective charge.     

The connection between the energy-momentum tensor and the tensor field in presence of a mass gap

The conditions under which a tensor field can be regarded as an energy-momentum tensor are discussed. The problem connected with dilatational and conformal symmetries are exhibited.     

Vacuum instability in scalar field theories

The class of scalar field theories with interaction gφ^2N?1, are studied using the semi-classical approximation. The imaginary part of the vertex functions generated by tunnelling out of the metastable ground state is calculated to first order. Using this result, the leading asymptotic behaviour of the renormalisation group β function for φ³ field theory is obtained in six dimensions. The validity of this result is discussed in view of the extra singularities which appear when the theory is just renormalisable. The structure of the perturbation expansion for n component φ³ theory is also discussed, and cases in which these theories yield perturbation expansions which are Borel summable, are pointed out.     

Supersymmetrization of scalar field theories

We develop a formalism for constructing the vacuum functional and supersymmetrizing a scalar field theory with the help of its ground state representation. The field theory problem is first transformed into a quantum mechanical one for which the ground state representation is well defined. The theory is then supersymmetrized by “taking the square root” of the hamiltonian. Standard approximation techniques are used to construct the vacuum functional with which spontaneous supersymmetry breaking can be analyzed.     

Metric energy-momentum tensor for polarizable particles in an electormagnetic field

Within the covariant Lagrange formalism and the relativistic theory of continuous media, the metric energy-momentum tensor is obtained for spin polarizable particles interacting with an electromagnetic field. An equation of motion of the polarizable particles with a spin of 1/2 in an external electromagnetic field is derived. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 21–29, December, 2006.     

On general-relativistic and gauge field theories

The fundamental open questions of general relativity theory are the unification of the gravitational field with other fields, aiming at a unified geometrization of physics, as well as the renormalization of relativistic gravitational theory in order to obtain their self-consistent solutions. These solutions are to furnish field-theoretic particle models—a problem first discussed by Einstein. In addition, we are confronted with the issue of a coupling between gravitational and matter fields determined (not only) by Einstein's principle of equivalence, and also with the question of the geometric meaning of a gravitational quantum theory. In our view, all these problems are so closely related that they warrant a general solution. We treat mainly the concepts suggested by Einstein and Weyl.     

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.     

Classical energy-momentum tensor renormalization via effective field theory methods

We apply the Effective Field Theory approach to General Relativity, introduced by Goldberger and Rothstein, to study point-like and string-like sources in the context of scalar-tensor theories of gravity. Within this framework we compute the classical energy-momentum tensor renormalization to first Post-Newtonian order or, in the case of extra scalar fields, up to first order in the (non-derivative) trilinear interaction terms: this allows to write down the corrections to the standard (Newtonian) gravitational potential and to the extra-scalar potential. In the case of one-dimensional extended sources we give an alternative derivation of the renormalization of the string tension enabling a re-analysis of the discrepancy between the results obtained by Dabholkar and Harvey in one paper and by Buonanno and Damour in another, already discussed in the latter.