Related papers: Field Theory Done Right
A structural explanation of the coupling constants in the standard model, i.e the fine structure constant and the Weinberg angle, and of the gauge fixing contributions is given in terms of symmetries and representation theory. The coupling…
We develop a quantization scheme for the quantum theory of a real scalar field on a class of non-commutative spacetime models collectively known as T-Minkowski. Requiring the theory to be covariant under T-Poincar\'e transformations, we…
We discuss the formulation of a non-relativistic effective field theory for two-body P-wave scattering in the presence of shallow states and critically address various approaches to renormalization proposed in the literature. It is…
In the present article we display a new constructive quantum field theory approach to quantum gauge field theory, utilizing the recent progress in the integration theory on the moduli space of generalized connections modulo gauge…
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…
We announce results about the nonperturbative mathematically rigorous construction of the $:\!\phi^4_4\!:$ quantum field theory in four-dimensional space-time. The complex structure of solutions of the classical nonlinear (real-valued) wave…
We develop a field-theoretic description of large-scale structure formation by taking the non-relativistic limit of a canonically transformed, real scalar field which is minimally coupled to scalar gravitational perturbations in…
This is an elementary introduction to Wilson renormalization group and continuum effective field theories. We first review the idea of Wilsonian effective theory and derive the flow equation in a form that allows multiple insertion of…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
This paper is the first in a series devoted to the development of a rigorous renormalisation group method for lattice field theories involving boson fields, fermion fields, or both. Our immediate motivation is a specific model, involving…
In this paper, we establish an analog of Wightman's reconstruction theorem for nonlocal quantum field theory with a fundamental length. In our setting, the Wightman generalized functions are defined on test functions analytic in a complex…
The state space and observables for the leading order of the large-N theory are constructed. The obtained model ("theory of infinite number of fields") is shown to obey Wightman-type axioms (including invariance under boost transformations)…
The transition from a classical to quantum theory is investigated within the context of orthogonal and symplectic Clifford algebras, first for particles, and then for fields. It is shown that the generators of Clifford algebras have the…
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…
It is shown how the theory of the fields can be constructed in a consistent way in quantized spaces. All constructions are connected with unitary irreducible representations of real forms of six dimensional rotation algebras O(1,5), O(2,4),…
A redesigned starting point for covariant \phi^4_n, n\ge 4, models is suggested that takes the form of an alternative lattice action and which may have the virtue of leading to a nontrivial quantum field theory in the continuum limit. The…
We present a consistent quantum theory of the electromagnetic field in nonlinearly responding causal media, with special emphasis on $\chi^{(2)}$ media. Starting from QED in linearly responding causal media, we develop a method to construct…
We present an effective theory to describe the quantization of spherically symmetric vacuum in loop quantum gravity. We include anomaly-free holonomy corrections through a canonical transformation of the Hamiltonian of general relativity,…
Starting from a given factorizing S-matrix $S$ in two space-time dimensions, we review a novel strategy to rigorously construct quantum field theories describing particles whose interaction is governed by $S$. The construction procedure is…
A new application of quantum field theory is developed that gives a description of the internal dynamics of dressed elementary particles and predicts their masses. The fermionic and bosonic quantum fields are treated as interdependent…