It is shown that the triangle anomaly can be evaluated in the light-cone gauge and that the result obtained is consistent with the usual covariant one. We use two different procedures: (i) Eliminating the nonphysical fields from the covariant anomalous Ward identity. (ii) Carrying out a chiral transformation on the light-cone Lagrangian. The use of both dimensional and Pauli-Villars regularisations are discussed.

We examine the supersymmetry Ward identity for supersymmetric Yang-Mills theories in the axial gauge. In the pure N = 1 (no matter) case the Ward identity leads to supersymmetric counterterms to all orders. This result does not survive the introduction of matter fields, however, and we therefore conclude that the gauge is not useful in the context of supersymmetry.

It is demonstrated that in the light-cone gauge the nonabelian anomaly is seen as a breakdown of Poincaré invariance.

The authors evaluate the axial anomaly using the light-cone gauge and light-cone coordinates. In addition to the generally accepted result they find extra non-Lorentz-covariant contributions.

We demonstrate that the light-cone gauge is a feasible tool for multi-loop computations by using it to evaluate the two-loop scalar anomalous dimension, γ(2), in a general gauge theory. In the special case of supersymmetry we obtain agreement with previous results which were derived using non-light-cone techniques.

We evaluate the one-loop effective potential, V1, in the light-cone gauge for a general gauge theory with arbitrary scalar and fermion representations. In the case of a general N = 1 supersymmetric gauge theory the result for V1 is simpler than in the Landau gauge; the form of STrM4 is particularly elegant, and in one-loop finite theories we find STrM4 = 0. We show how the renormalisation group relates STrM4 to the scalar anomalous dimension, γ, and we give an explicit calculation of γ in the light-cone gauge.

We consider the background field method for quantum gravity beyond one loop. It is pointed out that the ghost-containing and pure-gauge diagrams separately satisfy the relevant Ward identities. We illustrate this by considering the two-loop graviton self-energy calculation. An analogous situation exists for the Yang-Mills theory, the results for which are given in an appendix. In the light of our results we discuss the feasibility of carrying out a calculation to determine whether quantum gravity is two-loop finite.

We consider the evaluation of Feynman integrals in the light-cone gauge. The various prescriptions that can be used to remove the ambiguities arising in this gauge are discussed. As an example we evaluate the one-loop contribution to the gluon self-energy in N = 4 supersymmetry. Only the gluon loop contribution differs from the usual covariant result and this can be shown to involve only one integral peculiar to the light-cone gauge. Dimensional regularization is employed to evaluate this integral using both the principal value prescription and the prescription suggested by Mandelstam.

The BRS identities for supergravity in the axial gauge are derived and an identity involving the graviton self energy is verified to one-loop. It is demonstrated that even in a gauge where the anti-symmetric part of the vierbein field does not propagate, it does not decouple from the BRS identities.

We consider the BRS identities for N = 1 supergravity in a covariant gauge. It is shown that, as in the axial gauge, the anti-symmetric part of the vierbein does contribute to the BRS identities, even though one can choose a gauge in which it does not propagate.

We have calculated the pole part of the one-loop graviton self-energy in the noncovariant axial gauge ${n}_{\ensuremath{\mu}}{\ensuremath{\varphi}}_{\ensuremath{\mu}\ensuremath{\nu}}=0$, ${n}^{2}\ensuremath{\ne}0$, where ${\ensuremath{\varphi}}_{\ensuremath{\mu}\ensuremath{\nu}}$ is the physical gravition field and ${n}_{\ensuremath{\mu}}$ is an arbitrary but constant vector. It is shown that the self-energy is, unexpectedly, both nontransverse and ${n}_{\ensuremath{\mu}}$ dependent, even though it satisfies the correct gravitational Ward identity. This Ward identity is found to contain a term corresponding to a "pincer" Feynman diagram which is directly responsible for the nontransversality of the graviton self-energy. Ghost particles do not contribute to the graviton amplitude. All aixal-gauge integrals are consistently evaluated in the context of dimensional regularization and by applying the principal-value prescription.

Ward identities are derived in a general axial gauge by considering three distinct expressions for the gauge-breaking part of the Yang-Mills Lagrangian. The Ward identities are verified by calculating the one-loop self-energies in the appropriate axial gauge. It is shown, in particular, that one of the three gauge-breaking terms, namely (2..cap alpha..n/sup 2/)/sup -1/(nxA/sup a/)partial/sup 2/(nxA/sup a/), gives rise to a self-energy which is nontransverse. The latter gauge includes the planar gauge (..cap alpha.. = -1). The effect of the general axial gauge on the Yang-Mills counterterms is analyzed and the implications for quantum gravity are briefly discussed.

Commenting on a previous paper, we present two further results on the general axial gauge in quantum gravity: (i) We are now able to give the infinite part of the complete graviton self-energy ${\ensuremath{\pi}}_{\ensuremath{\mu}\ensuremath{\nu},\ensuremath{\rho}\ensuremath{\sigma}}$ in the axial gauge, rather than its corresponding scalar amplitudes. (ii) We present results for more general axial gauges and show that for any value of the gauge parameter the infinite part of the graviton self-energy remains nontransverse and ${n}_{\ensuremath{\mu}}$ dependent.

Derives the BRS identities for quantum gravity in the axial gauge and uses them to explain why the one-loop counterterm is not generally covariant.

We calculate the two-loop contribution to the β function of pure Yang-Mills theory in an arbitrary gauge using the background field method. This serves as a further check on the consistency of the method beyond one loop, explicitly verifying Kallosh's theorem, and also clarifies the role of the gauge parameter in this technique.

It is shown that the Yang-Mills self-energy in the planar gauge is non-transverse, even though this self-energy satisfies the appropriate Ward identity. The non-transversality implies that the one-loop counterterm is no longer proportional to (Fμνa)2.

We apply the technique of dimensional reduction to both supersymmetric and non-supersymmetric theories. Explicit one- and two-loop calculations show that in the latter case the technique is a viable alternative to conventional dimensional regularization, while in the former it preserves the Slavnov-Taylor identities of both supersymmetry and gauge invariance.

It is argued that the application of the dimensional regularisation technique to one-loop quantum gravity calculations is ambiguous. However, for the calculation of on-mass-shell S-matrix elements, this ambiguity can be resolved by requiring consistency with results obtained from other regularisation schemes. Some discussion is also given of the implications of this work for recent attempts to use higher derivative Lagrangians to solve the renormalisability problem in quantum gravity.

The one-loop graviton contribution to the graviton self-energy is calculated in a two-parameter gauge. The Slavnov and BRS identities are shown to be satisfied. A one-parameter family of gauges is also found in which the appropriate counterterm is part of a generally covariant object. Contrary to previous speculation, the spin-two and spin-zero parts of the counterterm can change sign. The significance of this result is discussed in detail.

The one-loop graviton contribution to the graviton self-energy is calculated in a general gauge. The Slavnov identities are shown to be satisfied. It is found to be impossible to choose the gauge parameter such that the counterterms are generally covariant.