Book ChapterDOI
Covariant Perturbation Theory
Masud Chaichian,Nikolai F. Nelipa +1 more
- pp 79-106
TLDR
In this paper, an expression for the matrix element of the S-matrix, or for the transition amplitude between two states, in terms of the path integral is given. But, effective general methods of analytic calculations of these integrals are lacking as yet and one has to resort to approximate ones.Abstract:
In the preceding chapter, the expressions for the vacuum-to-vacuum transition amplitude have been obtained Of practical interest, however, are transitions of a system of initially free particles into a final system of free particles As shown in Sect 11, such transitions are described by the matrix elements of the S-matrix Therefore, we shall find in this chapter an expression for the matrix element of the S-matrix, or for the transition amplitude between two states, in terms of the path integral Unfortunately, effective general methods of analytic calculations of these integrals are lacking as yet and one has to resort to approximate ones Most developed are the methods of perturbation theory representing the transition amplitude as a series in the coupling constantread more
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Journal ArticleDOI
Positivity bounds and the massless spin-2 pole
Lasma Alberte,Claudia de Rham,Claudia de Rham,Sumer Jaitly,Andrew J. Tolley,Andrew J. Tolley +5 more
TL;DR: In this article, it was shown that applying these arguments would constrain the low-energy coupling constants in a way which is incompatible with their actual values, and that the standard positivity bounds are inapplicable with gravity, and highlight a number of issues that impinge on the formulation of a three-dimensional amplitude which simultaneously satisfies the required properties of analyticity, positivity, and crossing symmetry.
Journal ArticleDOI
Riding on irrelevant operators
TL;DR: In this article, the authors investigated the stability of a class of derivative theories known as $P(X)$ and Galileons against corrections generated by quantum effects and showed that these theories are stable under quantum corrections at all loops in regions where the kinetic term is large compared to the strong coupling scale.
Journal ArticleDOI
Riding on irrelevant operators
TL;DR: In this paper, the stability of a class of derivative theories known as P (X) and Galileons against corrections generated by quantum eects is investigated, using an exact renormalisation group approach to argue that these theories are stable under quantum corrections.
Journal ArticleDOI
Covariant non-local action for massless QED and the curvature expansion
TL;DR: In this paper, the authors explore the properties of non-local effective actions which include gravitational couplings and present an alternative procedure to construct the non-linear completion which is in one-to-one correspondence with the more familiar diagrammatic expansion of the effective action, and show that the anomaly requires both the anomalous logarithm as well as 1/□ term where the latter is related to the Riegert action.
Journal ArticleDOI
High energy bosons do not propagate
TL;DR: In this paper, it was shown that in the high-momentum limit, the quadratic part of the spectral action does not contain positive powers of the derivatives, which is interpreted as the fact that the two-point Green functions vanish for nearby points.