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J. Frenkel

Publications and source records attributed to J. Frenkel.

At least 91 records · Page 5Linked to original sources
arXiv2001

Induced parity violating thermal effective action for (2+1)-dimensional fermions interacting with a non-Abelian background

We study the parity breaking effective action in 2+1 dimensions, generated, at finite temperature, by massive fermions interacting with a non-Abelian gauge background. We explicitly calculate, in the static limit, parity violating amplitudes up to the seven point function, which allows us to determine the corresponding effective actions. We derive the exact parity violating effective action when $\vec{E}=0$. When $\vec{E}\neq 0$, there are families of terms that can be determined order by order in perturbation theory. We attempt to generalize our results to non-static backgrounds through the use of time ordered exponentials and prove gauge invariance, both {\it small} and {\it large}, of the resulting effective action. We also point out some open questions that need to be further understood.

hep-th↗
arXiv2001

Derivative Expansion and the Effective Action for the Abelian Chern-Simons Theory at Higher Orders

We study systematically the higher order corrections to the parity violating part of the effective action for the Abelian Chern-Simons theory in 2+1 dimensions, using the method of derivative expansion. We explicitly calculate the parity violating parts of the quadratic, cubic and the quartic terms (in fields) of the effective action. We show that each of these actions can be summed, in principle, to all orders in the derivatives. However, such a structure is complicated and not very useful. On the other hand, at every order in the powers of the derivatives, we show that the effective action can also be summed to all orders in the fields. The resulting actions can be expressed in terms of the leading order effective action in the static limit. We prove gauge invariance, both large and small of the resulting effective actions. Various other features of the theory are also brought out.

hep-th↗
arXiv2001

Absence of higher order corrections to the non-Abelian topological mass term

We study the Yang-Mills-Chern-Simons theory systematically in an effort to generalize the Coleman-Hill result to the non-Abelian case. We show that, while the Chern-Simons coefficient is in general gauge dependent in a non-Abelian theory, it takes on a physical meaning in the axial gauge. Using the non-Abelian Ward identities as well as the analyticity of the amplitudes in the momentum variables, we show that, in the axial gauge, the Chern-Simons coefficient does not receive any quantum correction beyond one loop. This allows us to deduce that the ratio ${4πm\over g^{2}}$ is unrenormalized, in a non-Abelian theory, beyond one loop in any infrared safe gauge. This is the appropriate generalization of the Coleman-Hill result to non-Abelian theories. Various other interesting properties of the theory are also discussed.

hep-th↗
arXiv2000

Absence of higher order corrections to the non-Abelian Chern-Simons coefficient

We extend the Coleman-Hill analysis to non-Abelian Chern-Simons theories containing a tree level topological mass term. We show, in the case of a pure Yang-Mills-Chern-Simons theory, that there are no corrections to the coefficient of the Chern-Simons term beyond one loop in the axial gauge. Our arguments use constraints coming only from small gauge Ward identities as well as the analyticity of the amplitudes, much like the proof in the Abelian case. Some implications of this result are also discussed.

hep-th↗
arXiv2000

Two-loop corrections to the topological mass term in thermal QED_3

We study the radiative corrections to the Chern-Simons mass term at two loops in 2+1 dimensional quantum electrodynamics at finite temperature. We show that, in contrast to the behavior at zero temperature, thermal effects lead to a non vanishing contribution at this order. Using this result, as well as the large gauge Ward identity for the leading parity violating terms in the static limit, we determine the leading order parity violating effective action in this limit at two loops, which generalizes the one-loop effective action proposed earlier.

hep-th↗
arXiv2000

Behavior of the thermal gluon self-energy in the Coulomb gauge

We study, to one loop order, the behavior of the gluon self-energy in the non covariant Coulomb gauge at finite temperature. The cancellation of the peculiar energy divergences, which arise in such a gauge, is explicitly verified in the complete two point function of the Yang-Mills theory. At high temperatures, the leading T^2 term is determined to be transverse and nonlocal, in agreement with the results obtained in covariant gauges. The coefficient of the sub-leading ln(T) contribution, is non transverse but local and coincides (up to a multiplicative constant) with that of the ultraviolet pole term of the zero temperature amplitude.

hep-th↗
arXiv2000

Thermal forward scattering amplitudes in temporal gauges

We employ the thermal forward scattering amplitudes technique in order to compute the gluon self-energy in a class of temporal gauges. The leading T^2 and the sub-leading ln(T) contributions are obtained for temperatures high compared with the external momentum. The logarithmic contributions have the same structure as the ultraviolet pole terms which occur at zero temperature (we have recently extended this result to the Coulomb gauge). We also show that the prescription poles, characteristic of temporal gauges, do not modify the leading and sub-leading high-temperature behavior. The one-loop calculation shows that the thermal self-energy is transverse. This result has also been extended to higher orders, using the BRS identities.

hep-th↗
arXiv2000

Parity-violating electromagnetic interactions in QED_3 at finite temperature

We study the parity-breaking terms generated by the box diagram in 2+1 dimensional thermal QED. These lead, in the long wave limit, to a gauge invariant extensive action which behaves as 1/T at high temperature. In contrast, the effective action in the static limit involves leading non-extensive terms proportional to 1/T^3 at high temperature, which violate large gauge invariance. We derive a non-linear large gauge Ward identity, which relates the leading static terms of different order in perturbation theory and whose solution coincides with the all order effective action proposed earlier.

hep-ph↗
arXiv2000

Finite temperature gluon self-energy in a class of temporal gauges

The approach which relates thermal Green functions to forward scattering amplitudes of on-shell thermal particles is applied to the calculation of the gluon self-energy, in a class of temporal gauges. We show to all orders that, unlike the case of covariant gauges, the exact self-energy of the gluon is transverse at finite temperature. The leading T^2 and the sub-leading ln(T) contributions are obtained for temperatures T high compared with the external momentum. The logarithmic contributions have the same structure as the ultraviolet pole terms which occur at zero temperature.

hep-th↗
arXiv2000

Parity-breaking electromagnetic interactions in thermal QED_3

We examine the parity violating terms generated by the box diagram in QED_3 at finite temperature. These lead to both extensive as well as non-extensive effective actions, which have very distinct behavior in the long wavelength and static limits. We discuss a large gauge Ward identity for the leading terms in the static limit, whose solution coincides with the effective action proposed earlier.

hep-ph↗
arXiv1999

Large Gauge Ward Identity

We study the question of the Ward identity for "large" gauge invariance in 0+1 dimensional theories. We derive the relevant Ward identities for a single flavor fermion and a single flavor complex scalar field interacting with an Abelian gauge field. These identities are nonlinear. The Ward identity for any other complicated theory can be derived from these basic sets of identities. However, the structure of the Ward identity changes since these are nonlinear identities. In particular, we work out the "large" gauge Ward identity for a supersymmetric theory involving a single flavor of fermion as well as a complex scalar field. Contrary to the effective action for the individual theories, the solution of the Ward identity in the supersymmetric theory involves an infinity of Fourier component modes. We comment on which features of this analysis are likely/unlikely to generalize to the 2+1 dimensional theory.

hep-th↗
arXiv1999

General structure of the graviton self-energy

The graviton self-energy at finite temperature depends on fourteen structure functions. We show that, in the absence of tadpoles, the gauge invariance of the effective action imposes three non-linear relations among these functions. The consequences of such constraints, which must be satisfied by the thermal graviton self-energy to all orders, are explicitly verified in general linear gauges to one loop order.

hep-th↗
arXiv1999

Retarded thermal Greens functions and forward scattering amplitudes at two loops

In this paper, we extend our earlier one loop analysis to two loops and give a simple diagrammatic description for the retarded Greens functions at finite temperature, in terms of forward scattering amplitudes of on-shell thermal particles. We present a simple discussion, which can be easily generalized to any field theory, of the temperature dependent parts of the retarded two and three point functions in scalar field theory and QED. As an application of our result at two loops, we show how the infrared singularities in the thermal part of the retarded photon self-energy, cancel in QED_2 in the limit of vanishing electron mass.

hep-th↗
arXiv1998

A Soluble Theory of Massless Scalar QED_2

In this brief report, we analyze a generalized theory of massless scalar QED_2 and show that, unlike the conventional scalar QED_2, it is free from infrared divergence problems. The model is exactly soluble and may describe, in an 1+1 dimensional space-time, noninteracting spin-one tachyons.

hep-th↗
arXiv1998

Retarded Greens Functions and Forward Scattering Amplitudes in Thermal Field Theory

In this paper, we give a simple diagrammatic identification of the unique combination of the causal n-point vertex functions in the real time formalism that would coincide with the corresponding functions obtained in the imaginary time formalism. Furthermore, we give a simple calculational method for evaluating the temperature dependent parts of the retarded vertex functions, to one loop, by identifying them with the forward scattering amplitudes of on-shell thermal particles. As an application of the method, we calculate and show that the temperature dependent parts of all the retarded functions vanish at one loop order for 1+1 dimensional massless QED. We further point out that, in this model, in fact, the temperature dependent parts of all the retarded vertex functions vanish to all orders in perturbation theory.

hep-th↗
arXiv1998

The structure of the graviton self-energy at finite temperature

We study the graviton self-energy function in a general gauge, using a hard thermal loop expansion which includes terms proportional to T^4, T^2 and log(T). We verify explicitly the gauge independence of the leading T^4 term and obtain a compact expression for the sub-leading T^2 contribution. It is shown that the logarithmic term has the same structure as the ultraviolet pole part of the T=0 self-energy function. We argue that the gauge-dependent part of the T^2 contribution is effectively canceled in the dispersion relations of the graviton plasma, and present the solutions of these equations.

hep-th↗
arXiv1998

The Boltzmann Equation in Scalar Field Theory

We derive the classical transport equation, in scalar field theory with a V(phi) interaction, from the equation of motion for the quantum field. We obtain a very simple, but iterative, expression for the effective action which generates all the n-point Green functions in the high-temperature limit. An explicit closed form is given in the static case.

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