Related papers: Divergence-free Nonrenormalizable Models
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
This paper addresses three topics concerning the quantization of non-commutative field theories (as defined in terms of the Moyal star product involving a constant tensor describing the non-commutativity of coordinates in Euclidean space).…
We derive the renormalized nonequilibrium equations of motion for a scalar field and its quantum back reaction in a conformally flat Friedmann-Robertson-Walker universe. We use a fully covariant formalism proposed by us recently for…
A suitable counterterm for a Euclidean space lattice version of \phi^4_n theories, n\ge 4, is combined with several additional procedures so that in the continuum limit the resultant quantum field theory is nontrivial. Arguments to support…
Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…
Present day quantum field theory (QFT) is founded on canonical quantization, which has served quite well, but also has led to several issues. The free field describing a free particle (with no interaction term) can suddenly become…
This paper summarizes a research program that has been underway for a decade. The objective is to find a fast and accurate scheme for solving quantum problems which does not involve a Monte Carlo algorithm. We use an alternative strategy…
We study the natural scheme-independent quantity obtained from the three-sphere partition function of a $(2+1)$-dimensional quantum field theory by removing all local counterterm ambiguities. At conformal fixed points this quantity equals…
Instead of assuming that they depend only on the background variables, we investigate the hypothesis that counter-terms appearing in the deformed algebra approach to loop quantum cosmology depend on the full phase-space variables. We derive…
In this work a class of massive scalar field theories with self-interactions described by a general potential is studied. Under the sole condition that the potential admits the Fourier representation, it is shown that such theories may be…
Scheme independence of exact renormalization group equations, including independence of the choice of cutoff function, is shown to follow from general field redefinitions, which remains an inherent redundancy in quantum field theories.…
This is a nontechnical introduction to recent work on quantum gravity using ideas from higher-dimensional algebra. We argue that reconciling general relativity with the Standard Model requires a `background-free quantum theory with local…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
We consider the spectral correlations of clean globally hyperbolic (chaotic) quantum systems. Field theoretical methods are applied to compute quantum corrections to the leading (`diagonal') contribution to the spectral form factor.…
A new approach to nonperturbative calculations in quantum electrodynamics is proposed. The approach is based on a regular iteration scheme for solution of Schwinger-Dyson equations for generating functional of Green functions. The approach…
We add non-linear and state-dependent terms to quantum field theory. We show that the resulting low-energy theory, non-linear quantum mechanics, is causal, preserves probability and permits a consistent description of the process of…
Symanzik showed that quantum field theory can be formulated on a space with boundaries by including suitable surface interactions in the action to implement boundary conditions. We show that to all orders in perturbation theory all the…
Through defining irreducible loop integrals (ILIs), a set of consistency conditions for the regularized (quadratically and logarithmically) divergent ILIs are obtained to maintain the generalized Ward identities of gauge invariance in…
In this article I show why the fundamental constants obtain perturbative corrections in higher orders, why the renormalizations work and how to reformulate the theory in order to avoid these technical and conceptual complications. I…
This paper describes and proves a canonical procedure to decouple perturbations and optimize their gauge around backgrounds with one non-homogeneous dimension, namely of co-homogeneity 1, while preserving locality in this dimension.…