Related papers: Scalar Field Quantization Without Divergences In A…
Guided by idealized but soluble nonrenormalizable models, a nontraditional proposal for the quantization of covariant scalar field theories is advanced, which achieves a term-by-term, divergence-free perturbation analysis of interacting…
Covariant scalar fields exhibit divergences when quantized in two or more spacetime dimensions: n \geg 2. Does perturbation theory, effective theories, the renormalization group, etc., tell us all there is to know about these problems? An…
A natural procedure is introduced to replace the traditional, perturbatively generated counter terms to yield a formulation of covariant, self-interacting, nonrenormalizable scalar quantum field theories that has the added virtue of…
Standard Model with a classical conformal invariance holds the promise to give a better understanding of the hierarchy problem and could pave the way for beyond the standard model physics. So, we give here a mathematical treatment of a…
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
Divergences that arise in the quantization of scalar quantum field models by means of a lattice-space functional integration may be attributed to a single integration variable, and this fact is demonstrated by showing that if the integrand…
D-theory is an alternative non-perturbative approach to quantum field theory formulated in terms of discrete quantized variables instead of classical fields. Classical scalar fields are replaced by generalized quantum spins and classical…
Amplitudes $A_n$ in $d$-dimensional scalar field theory are generated, to all orders in the coupling constant and at $n$-point. The amplitudes are expressed as a series in the mass $m$ and coupling $\lambda$. The inputs are the classical…
A simple theoretical model of scalar fields in one spatial dimension with internal symmetry is considered. Assuming the existence of localized classical field configurations, the Schr\"{o}dinger picture is used to describe their quantum…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple…
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…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…
The field theory quantized on the {\it light-front} is compared with the conventional equal-time quantized theory. The arguments based on the {\it microcausality} principle imply that the light-front field theory may become nonlocal with…
We derive quantum kinetic equations for scalar fields undergoing coherent evolution either in time (coherent particle production) or in space (quantum reflection). Our central finding is that in systems with certain space-time symmetries,…
We propose fundamental scale invariance as a new theoretical principle beyond renormalizability. Quantum field theories with fundamental scale invariance admit a scale-free formulation of the functional integral and effective action in…
We review the status of (scalar) quantum field theory on curved spacetimes using a novel formulation in terms of non linear functionals over the smooth configuration fields. In particular, this entails also a new foundation of locally…
We describe a novel duality symmetry of Phi(4)-theory defined on noncommutative Euclidean space and with noncommuting momentum coordinates. This duality acts on the fields by Fourier transformation and scaling. It is an extension, to…
Nonrenormalizable scalar fields, such as \varphi^4_n, n\ge5, require infinitely many distinct counter terms when perturbed about the free theory, and lead to free theories when defined as the continuum limit of a lattice regularized theory…
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes of gravitational or scalar fields. In this work we…
Conventional quantization of covariant scalar field models $\phi^4_n$, for spacetime dimensions $n\ge5$ are trivial, and this may also be true for $n=4$ as well. However, an alternative ${\cal O}(\hbar)$ counterterm leads to nontrivial…