Related papers: Quantization of Non-Polynomial Field Theories
We are concerned with the issue of quantization of a scalar field in a diffeomorphism invariant manner. We apply the method used in Loop Quantum Gravity. It relies on the specific choice of scalar field variables referred to as the polymer…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
We study classical field theories in a background field configuration where all modes of the theory are excited, matching the zero-point energy spectrum of quantum field theory. Our construction involves elements of a theory of classical…
We consider a scalar $\phi^4$ theory on canonically deformed Euclidean space in 4 dimensions with an additional oscillator potential. This model is known to be renormalisable. An exterior gauge field is coupled in a gauge invariant manner…
Polar coordinates are used for the complex scalar free field in D=4 dimensions. The resulting non renormalizable theory is healed by using a recently proposed symmetric subtraction procedure. The existence of the coordinates transformation…
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…
We study the renormalisation of the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric scalar field theory with the interaction $\phi^2(i\phi)^\varepsilon$ using the Wilsonian approach and without any expansion in $\varepsilon$. Specifically,…
We first carry out the soliton sector quantization of the spatially cut-off $\phi^4_{1+1}$ theory with double well potential in the semiclassical limit, deriving the nonrelativistic Schr\"odinger equation as an equation describing the…
The purpose of this short letter is to clarify which set of pieces of Feynman graphs are resummed in a Loop Vertex Expansion, and to formulate a conjecture on the $\phi^4$ theory in non-integer dimension.
We compute template formulae of all four-loop $\beta$-functions and anomalous dimensions of arbitrary renormalisable quantum field theories with fermions and scalar fields in the $\overline{\text{MS}}$ scheme. Using these results, novel…
We develop a non-perturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularisation.…
Looking for an observable manifestation of the so-called unnaturalness of scalar fields we introduce a seemingly new set of differential equations for connected Green functions. These equations describe the momentum dependence of the Green…
Traditional quantum field theory can lead to enormous zero-point energy, which markedly disagrees with experiment. Unfortunately, this situation is built into conventional canonical quantization procedures. For identical classical theories,…
We study renormalization in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model, where the matrix size plays the role of a UV cutoff. We define correlation functions by using the Berezin symbol identified…
Polymer quantization is a non-standard approach to quantizing a classical system inspired by background independent approaches to quantum gravity such as loop quantum gravity. When applied to field theory it introduces a characteristic…
Abandoning dimensional regularization allows important simplifications in loop calculations and gives a handle to interpret non-renormalizable Quantum Field Theories. I review the current status of FDR, a fully four-dimensional approach to…
A diagram approach to classical nonlinear stochastic field theory is introduced. This approach is intended to serve as a link between quantum and classical field theories, resulting in an independent constructive characterisation of the…
Explicit two-loop calculations in noncommutative $\phi^4_4$ theory are presented. It is shown that the model is two-loop renormalizable.
The critical behaviour of a non-local scalar field theory is studied. This theory has a non-local kinetic term which involves a real power 1-2\alpha of the Laplacian. The interaction term is the usual local \phi^{4} interaction. The lowest…
By averaging over an ensemble of field configurations, a classical field theory can display many of the characteristics of quantum field theory, including Lorentz invariance, a loop expansion, and renormalization effects. There is…