The axial gauge BRS identities in supergravity

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.     

The Nappi-Witten string in the light-cone gauge

Some of the motivations for as well as the main points of the quantization of the Nappi-Witten string in the light-cone gauge are reviewed.     

The triangle anomaly in the light-cone gauge

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.     

Lorentz-invariant renormalizability of an Abelian gauge theory

Lorentz-invariant renormalizability is proved for an Abelian gauge theory in a certain class of Lorentz-invariant gauges.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 70–74, April, 1981.     

QCD calculations in the light-cone gauge

The non-singlet quark structure function is calculated in the leading logarithm approximation in an axial gauge with n² = 0, the light-cone gauge. The choice n² = 0 leads to a simple identity for loop integrals involving the extra n · k denominators. We compare the results graph by graph with both Feynman gauge QCD and a scalar gluon theory. The leading diagrams are the same “rainbow” diagrams as for the case of the scalar theory.The techniques are also applied to quark-quark scattering at large transverse momentum. The leading diagrams have the same dressed ladder-form factor structure.     

One-loopN-point functions in the light-cone gauge

We consider, in the light-cone gauge, the possible structure of the counterterms arising in the solution to the renormalization equation. Using the structure of these counterterms and the noncovariant formalism of the integrals as guidelines, we also examine to one-loop order the divergence and nonlocality of theN-point gluon vertex functions forN≧5.     

On the renormalizability of a gauge theory of gravitation

One-loop divergences in gauge theory of gravitation with a quadratic Lagrangian are computed. The renormalizability of the theory in the case of Riemannian background is shown.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 43–49, December, 1984.     

Multiplicative renormalizability of Abelian supergauge theory in the Wess-Zumino gauge

It is shown that in the general case the renormalization of the Abelian supergauge supersymmetrical theory is not multiplicative. However, the renormalization is multiplicative in the supersymmetrical gauge and the Wess-Zumino gauge.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 25–29, September, 1981.I am indebted to B. Voronov for a discussion of the above topics.     

Interacting membrane picture in the light-cone gauge

An attempt is made to formulate the interacting membrane picture in the light-cone gauge, which is analogous to the interacting string picture of Mandelstam. The possible emission of strings from the membrane is also discussed.     

Renormalization of Wilson operators in the light-cone gauge

We test the renormalization of Wilson operators and the Mandelstam–Leibbrandt gauge in the case when the sides of the loop are parallel to the vectors used in the M–L gauge. Graphs which in the Feynman gauge are free of ultra-violet divergences, in the M–L gauge show double divergences and single divergences with non-local Si and Ci functions. These non-local functions cancel out when we add all graphs together and the constraints of gauge invariance are satisfied. In Appendix C we briefly discuss the problems of the M–L gauge for loops containing spacelike lines. Received: 31 May 2000 / Published online: 23 January 2001     

On the light-cone quantization of non-abelian gauge theory

The implications of periodic boundary conditions in the light-cone quantization of non-abelian fields are studied. Formulation of the theory in the singularity-free case is presented. Some consequences of field singularities are discussed.     

On zero modes and gauge fixing in light-cone quantized gauge theories

It is shown that regularistation by dimensional reduction is a viable alternative to dimensional regularisation in non-supersymmetric theories.

     

Cut-off versus dimensional regularization in the light-cone gauge

The conventional cut-off method is applied to massless light-cone gauge Feynman integrals. Despite the presence of non-local terms in the unintegrated expression for the Yang-Mills self-energy, the cut-off procedure yields the same ultra-violet behaviour as the lengthier technique of dimensional regularization.     

Gauge fixing,BRS invariance and Ward identities for randomly stirred flows

The Galilean invariance of the Navier–Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi–Rouet–Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier–Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.