Related papers: Field redefinitions in effective theories at highe…
The algebra of observables associated with a quantum field theory is invariant under the connected component of the Lorentz group and under parity reversal, but it is not invariant under time reversal. If we take general covariance…
We investigate the high-order behavior of perturbative matching conditions in effective field theories. These series are typically badly divergent, and are not Borel summable due to infrared and ultraviolet renormalons which introduce…
This article lays out a complete framework for an effective theory of cosmological perturbations with corrections from canonical quantum gravity. Since several examples exist for quantum-gravity effects that change the structure of…
Following a Four Dimensional Renormalization approach to ultraviolet divergences (FDR), we extend the concept of predictivity to non-renormalizable quantum field theories at arbitrarily large perturbative orders. The idea of topological…
In the present paper we propose a new approach to quantum fields in terms of category algebras and states on categories. We define quantum fields and their states as category algebras and states on causal categories with partial involution…
Truncations of effective field theory expansions are technically necessary but inherently intertwined with the redundancies of general field redefinitions. This can be viewed as a juxtaposition of power-counting and theoretical…
In this chapter, we will review the field-theoretic treatment of General Relativity based on an effective field theory extension of the Einstein-Hilbert action. This pragmatic route to low-energy quantum effects in gravity critically…
We discuss spacetime instability for effective field theories of quantum gravity. The effective action of gravity introduces infinite higher derivative curvature terms $R^{2}, { R }_{ \mu \nu }{ R }^{ \mu \nu }, R_{\mu\nu\kappa\lambda}…
In the first part of the paper we define a perturbative (pre-formal) geometry and formulate a theorem on the relation between the construction of a perturbative neighborhood of affine varieties and the higher tangent bundles. In the second…
Results of perturbation theory in quantum field theory generally depend on the renormalization scheme that is in use. In particular, they depend on the scale. We try to make perturbation theory scheme invariant by re-expanding with respect…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
We define covariantly a deformation of a given algebra, then we will see how it can be related to a deformation quantization of a class of observables in Quantum Field Theory. Then we will investigate the operator order related to this…
We present a derivation of the effect of the classical field configuration to the diffusion equations. Using the formalism of the thermo field dynamics we propose a systematic and consistent way to treat the classical background and to…
In quantum field theory there is now a well developed technique, effective field theory, which allows one to obtain low energy quantum predictions in ``non-renormalizable'' theories, using only the degrees of freedom and interactions…
It is shown that loop divergences emerging in the Green functions in quantum field theory originate from correspondence of the Green functions to {\em unmeasurable} (and hence unphysical) quantities. This is because no physical quantity can…
I briefly summarized some recent work which uses the techniques of effective field theory to make quantum predictions in general relativity. In contrast to conventional expectations, these are in fact well behaved. The leading quantum…
Since fields in the heavy quark effective theory are described by both a velocity and a residual momentum, there is redundancy in the theory: small shifts in velocity may be absorbed into a redefinition of the residual momentum. We…
The perturbative treatment of quantum field theory is formulated within the framework of algebraic quantum field theory. We show that the algebra of interacting fields is additive, i.e. fully determined by its subalgebras associated to…
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String…
Perturbative aspects of ultraviolet and infrared dynamics of noncommutative quantum field theory is examined in detail. It is observed that high loop momentum contribution to the nonplanar diagram develops a new infrared singularity with…