Related papers: Field Theory Done Right
We show how to use quantum mechanics on the group manifold U(N) as a tool for problems in U(N) representation theory. The quantum mechanics reduces to free fermions on the circle, which in the large N limit become relativistic. The theory…
This chapter is a non-expert introduction to the effective field theory of large scale structure. First, we give a detailed pedagogical explanation of why previous attempts to build non-linear cosmological perturbation theory failed. After…
I review the formalism, Feynman rules, and combinatorics that constrain a field to propagate ``classically", strictly in tree diagrams, either by itself, or interacting with other, purely quantum fields. The perturbation theory is…
Lattice regularization is a standard technique for the nonperturbative definition of a quantum theory of fields. Several approaches to the construction of a quantum theory of gravity adopt this technique either explicitly or implicitly. A…
This is the 5-th paper in the series devoted to explicit formulating of the rules needed to manage an effective field theory of strong interactions in S-matrix sector. We discuss the principles of constructing the meaningful perturbation…
In these lectures we consider some topics of Quantum Field Theory in Curved Space. In the first one particle creation in curved space is studied from a mathematical point of view, especially, particle production at a given time using the so…
We develop a general framework for quantum field theory on noncommutative spaces, i.e., spaces with quantum group symmetry. We use the path integral approach to obtain expressions for $n$-point functions. Perturbation theory leads us to…
Certain aspects of some unitary quantum systems are well-described by evolution via a non-Hermitian effective Hamiltonian, as in the Wigner-Weisskopf theory for spontaneous decay. Conversely, any non-Hermitian Hamiltonian evolution can be…
While the notion of open quantum systems is itself old, most of the existing studies deal with quantum mechanical systems rather than quantum field theories. After a brief review of field theoretical/path integral tools currently available…
We introduce a novel method for the renormalization of the Hamiltonian operator in Quantum Field Theory in the spirit of the Wilson renormalization group. By a series of unitary transformations that successively decouples the high-frequency…
Neurons in the brain show great diversity in their individual properties and their connections to other neurons. To develop an understanding of how neuronal diversity contributes to brain dynamics and function at large scales we start with…
We present a general formalism that allows for the computation of large-order renormalized expansions in the spacetime representation, effectively doubling the numerically attainable perturbation order of renormalized Feynman diagrams. We…
We show that the tree-level spectrum of heavy particles can be directly extracted from the Wilson coefficients of the corresponding effective field theory at low energies. This procedure is exact when the number of resonances is finite, and…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
A method is developed to construct a non-local massless scalar field theory in a flat quantised space-time generated by an operator algebra. Implicit in the operator algebra is a fundamental length scale of the space-time. The fundamental…
Predicting phenomena that mix few-photon quantum optics with strong field nonlinear optics is hindered by the use of separate theoretical formalisms for each regime. We close this gap with a unified effective field theory valid for…
These lectures deal with selected aspects of quantum field theory in curved spacetime including the following topics: (1) Quantization of fields on a curved background, particle creation by gravitational fields, particle creation in an…
We discuss the quantized theory of a pure-gauge non-abelian vector field (flat connection) as it would appear in a mass term a` la Stueckelberg. However the paper is limited to the case where only the flat connection is present (no field…
The aim of these lectures is to describe a construction, as self-contained as possible, of renormalized gauge theories. Following a suggestion of Polchinski, we base our analysis on the Wilson renormalization group method. After a…
We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories…