Operator regularization and one-loop Green’s functions

McKeon, D. G. C.; Sherry, T. N.

doi:10.1103/physrevd.35.3854

Cited by 59 publications

(59 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is immediately apparent that (2.32) is identical to (2.19) upon insertion of a complete set of momentum states into the later, as in [8,5], provided these momentum states have Let us now consider how the four-point function can be computed in quantum electrodynamics [12] and compare the result with that obtained in [7] where the Barton expansion was employed.…”

Section: (220)mentioning

confidence: 99%

“…An expansion due to Schwinger [8] Str e A+B = Str 2) is what has been regulated and hence the designation "operator regularization" is used in [5].…”

Section: The Barton Expansion and The Qmpimentioning

confidence: 99%

“…An alternate approach involves regulating the one-loop generating functional using the zeta function [4,5] and then computing matrix elements of the form < x|e −Ht |y > that arise in this procedure by a quantum mechanical path integral (QMPI). The QMPI is over a space compactfied in the temporal direction; in place of a sum over Matsubara frequencies, a sum over winding numbers is encountered [6].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Barton expansion and the path integral approach in thermal field theory

Brandt

McKeon

1996

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

It has been shown how on-shell forward scattering amplitudes (the "Barton expansion") and quantum mechanical path integral (QMPI) can both be used to compute temperature dependent effects in thermal field theory.We demonstrate the equivalence of these two approaches and then apply the QMPI to compute the high temperature expansion for the four-point function in QED, obtaining results consistent with those previously obtained from the Barton expansion. 11.10.Wx

show abstract

Section: (220)mentioning

confidence: 99%

“…An expansion due to Schwinger [8] Str e A+B = Str 2) is what has been regulated and hence the designation "operator regularization" is used in [5].…”

Section: The Barton Expansion and The Qmpimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Barton expansion and the path integral approach in thermal field theory

Brandt

McKeon

1996

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…Any abstract mathematical proposal to extract these finite parts from complicated multi-loop diverging amplitudes is unlikely to be consistent with this requirement and, in particular, will violate unitarity. Such difficulties are seen, for example, in the operator regularization method [4], which could be viewed as an interesting attempt to generalize the zeta function scheme.…”

Section: On the Zeta Function Regularizationmentioning

confidence: 99%

Multi-loop zeta function regularization and spectral cutoff in curved spacetime

Bilal

Ferrari

2013

Nuclear Physics B

View full text Add to dashboard Cite

We emphasize the close relationship between zeta function methods and arbitrary spectral cutoff regularizations in curved spacetime. This yields, on the one hand, a physically sound and mathematically rigorous justification of the standard zeta function regularization at one loop and, on the other hand, a natural generalization of this method to higher loops. In particular, to any Feynman diagram is associated a generalized meromorphic zeta function. For the one-loop vacuum diagram, it is directly related to the usual spectral zeta function. To any loop order, the renormalized amplitudes can be read off from the pole structure of the generalized zeta functions. We focus on scalar field theories and illustrate the general formalism by explicit calculations at one-loop and two-loop orders, including a two-loop evaluation of the conformal anomaly.

show abstract

“…(For example, addition of a Yang-Mills term to the Chern-Simons Lagrangian [3,5,8], while rendering the theory super-renormalizable, does not respect its topological nature and simple Pauli-Villars regularization [2] breaks the BRS invariance of the tree-level effective action. [6]) A way of circumventing this difficulty is to use a variant of operator regularization [10]; in this approach the initial Lagrangian is not modified -rather, the operators occurring in the closed form expression for the generating functional are regulated.…”

Section: Introductionmentioning

confidence: 99%

Gauge Dependence in Chern–simons Theory

Dilkes

Martin

McKeon

et al. 1999

Int. J. Mod. Phys. A

Self Cite

View full text Add to dashboard Cite

We compute the contribution to the modulus of the one-loop effective action in pure non-Abelian Chern-Simons theory in an arbitrary covariant gauge. We find that the results are dependent on both the gauge parameter (α) and the metric required in the gauge fixing. A contribution arises that has not been previously encountered; it is of the form (α/ p 2 )ǫ µλν p λ . This is possible as in three dimensions α is dimensionful. A variant of proper time regularization is used to render these integrals well behaved (although no divergences occur when the regularization is turned off at the end of the calculation). Since the original Lagrangian is unaltered in this approach, no symmetries of the classical theory are explicitly broken and ǫ µλν is handled unambiguously since the system is three dimensional at all stages of the calculation. The results are *

show abstract

Operator regularization and one-loop Green’s functions

Cited by 59 publications

References 33 publications

Barton expansion and the path integral approach in thermal field theory

Barton expansion and the path integral approach in thermal field theory

Multi-loop zeta function regularization and spectral cutoff in curved spacetime

Gauge Dependence in Chern–simons Theory

Contact Info

Product

Resources

About